diff --git a/404.html b/404.html
index 0441f1d..09b719d 100644
--- a/404.html
+++ b/404.html
@@ -377,8 +377,8 @@ <h1>Page not found</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/404.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/404.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/CODE_OF_CONDUCT.html b/CODE_OF_CONDUCT.html
index edac5fb..5faa0ca 100644
--- a/CODE_OF_CONDUCT.html
+++ b/CODE_OF_CONDUCT.html
@@ -399,7 +399,7 @@ <h1>Contributor Code of Conduct</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/CODE_OF_CONDUCT.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/LICENSE.html b/LICENSE.html
index a3c5bfb..b2b2174 100644
--- a/LICENSE.html
+++ b/LICENSE.html
@@ -450,7 +450,7 @@ <h1>Licenses</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/LICENSE.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/aio.html b/aio.html
index 91de554..fb6442b 100644
--- a/aio.html
+++ b/aio.html
@@ -588,7 +588,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
 <div class="accordion-body">
 <ol style="list-style-type: decimal">
 <li><p>You have to do tons of book-keeping! If you perform a QC step
@@ -733,7 +733,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
 <div class="accordion-body">
 <p>Here we add a column called “conservation” that is just an integer
 sequence from 1 to the number of genes.</p>
@@ -810,7 +810,7 @@ <h3 class="callout-title">Exercise 1<a class="anchor" aria-label="anchor" href="
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
 <p>The <code>SingleCellExperiment</code> constructor function can be
 used to create a new <code>SingleCellExperiment</code> object.</p>
@@ -1020,7 +1020,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb4">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1100,7 +1100,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <button class="accordion-button spoiler-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSpoiler1" aria-expanded="false" aria-controls="collapseSpoiler1">
   <h3 class="accordion-header" id="headingSpoiler1">  <div class="note-square"><i aria-hidden="true" class="callout-icon" data-feather="eye"></i></div> Setting the Random Seed </h3>
 </button>
-<div id="collapseSpoiler1" class="accordion-collapse collapse" aria-labelledby="headingSpoiler1" data-bs-parent="#accordionSpoiler1">
+<div id="collapseSpoiler1" class="accordion-collapse collapse" data-bs-parent="#accordionSpoiler1" aria-labelledby="headingSpoiler1">
 <div class="accordion-body">
 <p>Whenever your code involves the generation of random numbers, it’s a
 good practice to set the random seed in R with
@@ -1333,7 +1333,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb25">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1600,7 +1600,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
   <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
 </button>
-<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div id="collapseSolution3" class="accordion-collapse collapse" data-bs-parent="#accordionSolution3" aria-labelledby="headingSolution3">
 <div class="accordion-body">
 <p>Spike-ins are deliberately introduced exogeneous RNA from an exotic
 or synthetic source at a known concentration. This provides a known
@@ -1888,7 +1888,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
   <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
+<div id="collapseSolution4" class="accordion-collapse collapse" data-bs-parent="#accordionSolution4" aria-labelledby="headingSolution4">
 <div class="accordion-body">
 <p>Mathematically, this would require the data to fall on a
 two-dimensional plane (for linear methods like PCA) or a smooth 2D
@@ -2059,7 +2059,7 @@ <h3 class="callout-title">Exercise 2: Dimensionality Reduction<a class="anchor"
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
 <p>First subset the object to include only highly variable genes
 (<code>sce2 &lt;- sce[hvg.sce.var,]</code>) and then apply the
@@ -3571,7 +3571,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
  -->
 </section></section><section id="aio-multi-sample"><p>Content from <a href="multi-sample.html">Multi-sample analyses</a></p>
 <hr>
-<p>Last updated on 2024-07-02 |
+<p>Last updated on 2024-08-19 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 <div class="text-end">
@@ -3585,12 +3585,12 @@ <h2 class="card-header">Overview</h2>
 <div class="inner">
 <h3 class="card-title">Questions</h3>
 <ul>
-<li>How to integrate data from multiple batches, samples, and
+<li>How can we integrate data from multiple batches, samples, and
 studies?</li>
-<li>How to identify differentially expressed genes between experimental
-conditions for each cell type?</li>
-<li>How to identify changes in cell type abundance between experimental
-conditions?</li>
+<li>How can we identify differentially expressed genes between
+experimental conditions for each cell type?</li>
+<li>How can we identify changes in cell type abundance between
+experimental conditions?</li>
 </ul>
 </div>
 </div>
@@ -3615,7 +3615,7 @@ <h3 class="card-title">Objectives</h3>
 <a class="anchor" aria-label="anchor" href="#setup-and-data-exploration"></a>
 </h2>
 <hr class="half-width">
-<p>As said, we will use the the wild-type data from the Tal1 chimera
+<p>As before, we will use the the wild-type data from the Tal1 chimera
 experiment:</p>
 <ul>
 <li>Sample 5: E8.5 injected cells (tomato positive), pool 3</li>
@@ -3759,6 +3759,44 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 method, one may want to remove the sample effects with “batch effect”
 correction methods.</p>
 <p>For now, let’s assume that we want to remove this effect.</p>
+<div id="challenge1" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge1"></a>
+</h3>
+<div class="callout-content">
+<p>It seems like samples 5 and 6 are separated off from the others in
+gene expression space. Given the group of cells in each sample, why
+might this make sense versus some other pair of samples? What is the
+factor presumably leading to this difference?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
+  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+</button>
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div class="accordion-body">
+<p>Samples 5 and 6 were from the same “pool” of cells. Looking at the
+documentation for the dataset under <code>?WTChimeraData</code> we see
+that the pool variable is defined as: “Integer, embryo pool from which
+cell derived; samples with same value are matched.” So samples 5 and 6
+have an experimental factor in common which causes a shared, systematic
+difference in gene expression profiles compared to the other samples.
+That’s why you can see many of isolated blue/orange clusters on the
+first TSNE plot. If you were developing single-cell library preparation
+protocols you might want to preserve this effect to understand how
+variation in pools leads to variation in expression, but for now, given
+that we’re investigate other effects, we’ll want to remove this as
+undesired technical variation.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="correcting-batch-effects">Correcting batch effects<a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a>
 <a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a>
 </h2>
@@ -3789,6 +3827,45 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="fig/multi-sample-rendered-unnamed-chunk-3-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Once we removed the sample batch effect, we can proceed with the
 Differential Expression Analysis.</p>
+<div id="challenge2" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge2"></a>
+</h3>
+<div class="callout-content">
+<p>Having multiple independent samples in each experimental group is
+always helpful, but it particularly important when it comes to batch
+effect correction. Why?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
+  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+</button>
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div class="accordion-body">
+<p>It’s important to have multiple samples within each experimental
+group because it helps the batch effect correction algorithm distinguish
+differences due to batch effects (uninteresting) from differences due to
+biology (interesting).</p>
+<p>Imagine you had one sample that received a drug treatment and one
+that did not, each with 10,000 cells. They differ substantially in
+expression of gene X. Is that an important scientific finding? You can’t
+tell for sure, because the effect of drug is indistinguishable from a
+sample-wise batch effect. But if the difference in gene X holds up when
+you have five treated samples and five untreated samples, now you can be
+a bit more confident. Many batch effect correction methods will take
+information on experimental factors as additional arguments, which they
+can use to help remove batch effects while retaining experimental
+differences.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="differential-expression">Differential Expression<a class="anchor" aria-label="anchor" href="#differential-expression"></a>
 <a class="anchor" aria-label="anchor" href="#differential-expression"></a>
 </h2>
@@ -3987,16 +4064,23 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow<span class="op">=</span><span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fu">seq_len</span><span class="op">(</span><span class="fu">ncol</span><span class="op">(</span><span class="va">y</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span>
 <span>    <span class="fu">plotMD</span><span class="op">(</span><span class="va">y</span>, column<span class="op">=</span><span class="va">i</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre>
 </div>
-<figure><img src="fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Furthermore, we want to check if the samples cluster together based
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb20">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">1</span>,<span class="fl">1</span><span class="op">)</span><span class="op">)</span></span></code></pre>
+</div>
+<p>Furthermore, we want to check if the samples cluster together based
 on their known factors (like the tomato injection in this case).</p>
 <p>To do so, we use the MDS plot, which is very close to a PCA
 representation.</p>
-<div class="codewrapper sourceCode" id="cb20">
+<div class="codewrapper sourceCode" id="cb21">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4007,11 +4091,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 tomato as factors. This design indicates which samples belong to which
 pool and condition, so we can use it in the next step of the
 analysis.</p>
-<div class="codewrapper sourceCode" id="cb21">
+<div class="codewrapper sourceCode" id="cb22">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>, <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>,</span>
+<span>                       data <span class="op">=</span> <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
 <span><span class="va">design</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -4035,7 +4120,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </div>
 <p>Now we can estimate the Negative Binomial (NB) overdispersion
 parameter, to model the mean-variance trend.</p>
-<div class="codewrapper sourceCode" id="cb23">
+<div class="codewrapper sourceCode" id="cb24">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4052,7 +4137,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 Biological Coefficient of Variation and the Average log CPM for each
 gene. Additionally, the Common and Trend BCV are shown in
 <code>red</code> and <code>blue</code>.</p>
-<div class="codewrapper sourceCode" id="cb25">
+<div class="codewrapper sourceCode" id="cb26">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4060,12 +4145,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="fig/multi-sample-rendered-unnamed-chunk-13-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We then fit a Quasi-Likelihood (QL) negative binomial generalized
 linear model for each gene. The <code>robust=TRUE</code> parameter
-avoids distorsions from highly variable clusters. The QL method includes
+avoids distortions from highly variable clusters. The QL method includes
 an additional dispersion parameter, useful to handle the uncertainty and
 variability of the per-gene variance, which is not well estimated by the
 NB dispersions, so the two dispersion types complement each other in the
 final analysis.</p>
-<div class="codewrapper sourceCode" id="cb26">
+<div class="codewrapper sourceCode" id="cb27">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4078,7 +4163,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <pre class="output" tabindex="0"><code>   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  0.3189  0.9705  1.0901  1.0251  1.1486  1.2151 </code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb28">
+<div class="codewrapper sourceCode" id="cb29">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4093,7 +4178,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>QL dispersion estimates for each gene as a function of abundance. Raw
 estimates (black) are shrunk towards the trend (blue) to yield squeezed
 estimates (red).</p>
-<div class="codewrapper sourceCode" id="cb30">
+<div class="codewrapper sourceCode" id="cb31">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4104,7 +4189,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 False Discovery Rate (FDR) of 5%. The low amount of DGEs highlights that
 the tomato injection effect has a low influence on the mesenchyme
 cells.</p>
-<div class="codewrapper sourceCode" id="cb31">
+<div class="codewrapper sourceCode" id="cb32">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4119,7 +4204,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig               4510
 Up                      5</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb33">
+<div class="codewrapper sourceCode" id="cb34">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4144,7 +4229,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>All the previous steps can be easily performed with the following
 function for each cell type, thanks to the <code>pseudoBulkDGE</code>
 function in the <code>scran</code> package.</p>
-<div class="codewrapper sourceCode" id="cb35">
+<div class="codewrapper sourceCode" id="cb36">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4162,7 +4247,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 the results for a cell type. Each of these contains also the
 intermediate results in <code>edgeR</code> format to perform any
 intermediate plot or diagnostic.</p>
-<div class="codewrapper sourceCode" id="cb36">
+<div class="codewrapper sourceCode" id="cb37">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4187,21 +4272,51 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 ENSMUSG00000096730        NA        NA        NA          NA          NA
 ENSMUSG00000095742        NA        NA        NA          NA          NA</code></pre>
 </div>
+<div id="challenge3" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge3"></a>
+</h3>
+<div class="callout-content">
+<p>Clearly some of the results have low p-values. What about the effect
+sizes? What does <code>logFC</code> stand for?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution3" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
+  <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
+</button>
+<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div class="accordion-body">
+<p>“logFC” stands for log fold-change. Rather than reporting e.g. a
+5-fold increase, it’s better to report a logFC of log(5) = 1.61.
+Additive log scales are easier to work with than multiplicative identity
+scales, once you get used to it.</p>
+<p><code>ENSMUSG00000037664</code> seems to have an estimated logFC of
+about -8. That’s a big difference if it’s real.</p>
+</div>
+</div>
+</div>
+</div>
 </div>
 </section><section><h2 class="section-heading" id="differential-abundance">Differential Abundance<a class="anchor" aria-label="anchor" href="#differential-abundance"></a>
 <a class="anchor" aria-label="anchor" href="#differential-abundance"></a>
 </h2>
 <hr class="half-width">
-<p>With DA we test for differences between clusters across conditions,
-to investigate which clusters change accordingly to the treatment (the
-tomato injection in our case).</p>
+<p>With DA we look for differences in cluster <em>abundance</em> across
+conditions (the tomato injection in our case), rather than differences
+in gene expression.</p>
 <p>We first setup some code and variables for further analysis, like
 quantifying the number of cells per each cell type and fit a model to
 catch differences between the injected cells and the background.</p>
-<p>The performed steps are very similar to the ones for DEGs analysis,
-but this time we start our analysis on the computed abundances and
-without normalizing the data with TMM.</p>
-<div class="codewrapper sourceCode" id="cb38">
+<p>The steps are very similar to the ones for DEGs analysis, but this
+time we start our analysis on the computed abundances and without
+normalizing the data with TMM.</p>
+<div class="codewrapper sourceCode" id="cb39">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4222,14 +4337,22 @@ <h3 id="background-on-compositional-effect">Background on compositional effect<a
 <p>As mentioned before, in DA we don’t normalize our data with
 <code>calcNormFactors</code> function, because this approach considers
 that most of the input features do not vary between conditions. This
-cannot be applied to this analysis because we have a small number of
-cell populations that all can change due to the treatment. Leaving us to
-normalize only for library depth, which in pseudo-bulk data means by the
-total number of cells in each sample (cell type).</p>
+cannot be applied to DA analysis because we have a small number of cell
+populations that all can change due to the treatment. This means that
+here we will normalize only for library depth, which in pseudo-bulk data
+means by the total number of cells in each sample (cell type).</p>
 <p>On the other hand, this can lead our data to be susceptible to
-compositional effect, that means that our conclusions can be biased by
-the amount of cells present in each cell type. And this amount of cells
-can be totally unbalanced between cell types.</p>
+compositional effect. “Compositional” refers to the fact that the
+cluster abundances in a sample are not independent of one another
+because each cell type is effectively competing for space in the sample.
+They behave like proportions. If cell type A abundance increases in a
+new condition, that means we’ll observe less of everything else, even if
+everything else is unaffected by the new condition.</p>
+<p>Compositionality means that our conclusions can be biased by the
+amount of cells present in each cell type. And this amount of cells can
+be totally unbalanced between cell types. This is particularly
+problematic for cell types that start at or end up near 0 or 100
+percent.</p>
 <p>For example, a specific cell type can be 40% of the total amount of
 cells present in the experiment, while another just the 3%. The
 differences in terms of abundance of these cell types are detected
@@ -4247,7 +4370,7 @@ <h3 id="assuming-most-labels-do-not-change">Assuming most labels do not change<a
 <p>To do so, we first normalize the data with
 <code>calcNormFactors</code> and then we fit and estimate a QL-model for
 our abundance data.</p>
-<div class="codewrapper sourceCode" id="cb39">
+<div class="codewrapper sourceCode" id="cb40">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4259,14 +4382,17 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </h3>
 <pre class="output" tabindex="0"><code>[1] 1.1029040 1.0228173 1.0695358 0.7686501 1.0402941 1.0365354</code></pre>
 </div>
-<p>We then follow the already seen edgeR analysis steps.</p>
-<div class="codewrapper sourceCode" id="cb41">
+<p>We then use edgeR in a manner similar to what we ran before:</p>
+<div class="codewrapper sourceCode" id="cb42">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">y.ab2</span> <span class="op">&lt;-</span> <span class="fu">estimateDisp</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, trend<span class="op">=</span><span class="st">"none"</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">fit.ab2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFit</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, robust<span class="op">=</span><span class="cn">TRUE</span>, abundance.trend<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">res2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFTest</span><span class="op">(</span><span class="va">fit.ab2</span>, coef<span class="op">=</span><span class="fu">ncol</span><span class="op">(</span><span class="va">design</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="fu">summary</span><span class="op">(</span><span class="fu">decideTests</span><span class="op">(</span><span class="va">res2</span><span class="op">)</span><span class="op">)</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -4277,7 +4403,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 29
 Up                      1</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb43">
+<div class="codewrapper sourceCode" id="cb44">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4304,15 +4430,16 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <h3 id="testing-against-a-log-fold-change-threshold">Testing against a log-fold change threshold<a class="anchor" aria-label="anchor" href="#testing-against-a-log-fold-change-threshold"></a>
 </h3>
 <p>This other approach assumes that the composition bias introduces a
-spurious log2-fold change of no more than a quantity for a non-DA label.
-In other words, we interpret this as the maximum log-fold change in the
-total number of cells given by DA in other labels. On the other hand,
-when choosing , we should not consider fold-differences in the totals
-due to differences in capture efficiency or the size of the original
-cell population are not attributable to composition bias. We then
-mitigate the effect of composition biases by testing each label for
+spurious log2-fold change of no more than a quantity for a non-DA
+label.</p>
+<p>In other words, we interpret this as the maximum log-fold change in
+the total number of cells given by DA in other labels. On the other
+hand, when choosing , we should not consider fold-differences in the
+totals due to differences in capture efficiency or the size of the
+original cell population are not attributable to composition bias. We
+then mitigate the effect of composition biases by testing each label for
 changes in abundance beyond .</p>
-<div class="codewrapper sourceCode" id="cb45">
+<div class="codewrapper sourceCode" id="cb46">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4327,7 +4454,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 32
 Up                      0</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb47">
+<div class="codewrapper sourceCode" id="cb48">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4367,7 +4494,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <a class="anchor" aria-label="anchor" href="#session-info"></a>
 </h2>
 <hr class="half-width">
-<div class="codewrapper sourceCode" id="cb49">
+<div class="codewrapper sourceCode" id="cb50">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4488,33 +4615,47 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
-
+<p>Remember, you can subset SingleCellExperiments with logical indices,
+just like a matrix. You can also access their column data with the
+<code>$</code> accessor, like a data frame.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution4" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
-  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
+  <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb52">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
+<span></span>
+<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span><span class="va">summed.filt.subset</span>, </span>
+<span>    label<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design<span class="op">=</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
+<span>    coef<span class="op">=</span><span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span></code></pre>
+</div>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-muscat" class="callout challenge">
+<div id="exercise-2" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-muscat" class="callout-inner">
-<h3 class="callout-title">Exercise 2: <code>muscat</code><a class="anchor" aria-label="anchor" href="#exercise-2-muscat"></a>
+<div id="exercise-2" class="callout-inner">
+<h3 class="callout-title">Exercise 2:<a class="anchor" aria-label="anchor" href="#exercise-2"></a>
 </h3>
 <div class="callout-content">
-<p>Test differential expressed genes computed with <code>muscat</code>
-package and check for differences in the results.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -4525,19 +4666,33 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" aria-labelledby="headingHint2" data-bs-parent="#accordionHint2">
 <div class="accordion-body">
-
+<p>You can just hand <code>pheatmap()</code> a matrix as its only
+argument. It has a million options, but the defaults are usually pretty
+good.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution5" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
-  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution5" aria-expanded="false" aria-controls="collapseSolution5">
+  <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution5" class="accordion-collapse collapse" aria-labelledby="headingSolution5" data-bs-parent="#accordionSolution5">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb53">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">library</span><span class="op">(</span><span class="va">pheatmap</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
@@ -6364,8 +6519,8 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "url": "https://ccb-hms.github.io/osca-carpentries/aio.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/aio.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/cell_type_annotation.html b/cell_type_annotation.html
index 41912d1..9fd35b6 100644
--- a/cell_type_annotation.html
+++ b/cell_type_annotation.html
@@ -1782,7 +1782,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/cell_type_annotation.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-08-12",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/eda_qc.html b/eda_qc.html
index 105f94f..f1aa56b 100644
--- a/eda_qc.html
+++ b/eda_qc.html
@@ -472,7 +472,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb4">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -551,7 +551,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <button class="accordion-button spoiler-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSpoiler1" aria-expanded="false" aria-controls="collapseSpoiler1">
   <h3 class="accordion-header" id="headingSpoiler1">  <div class="note-square"><i aria-hidden="true" class="callout-icon" data-feather="eye"></i></div> Setting the Random Seed </h3>
 </button>
-<div id="collapseSpoiler1" class="accordion-collapse collapse" aria-labelledby="headingSpoiler1" data-bs-parent="#accordionSpoiler1">
+<div id="collapseSpoiler1" class="accordion-collapse collapse" data-bs-parent="#accordionSpoiler1" aria-labelledby="headingSpoiler1">
 <div class="accordion-body">
 <p>Whenever your code involves the generation of random numbers, it’s a
 good practice to set the random seed in R with
@@ -777,7 +777,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb25">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1040,7 +1040,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
   <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
 </button>
-<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div id="collapseSolution3" class="accordion-collapse collapse" data-bs-parent="#accordionSolution3" aria-labelledby="headingSolution3">
 <div class="accordion-body">
 <p>Spike-ins are deliberately introduced exogeneous RNA from an exotic
 or synthetic source at a known concentration. This provides a known
@@ -1319,7 +1319,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
   <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
+<div id="collapseSolution4" class="accordion-collapse collapse" data-bs-parent="#accordionSolution4" aria-labelledby="headingSolution4">
 <div class="accordion-body">
 <p>Mathematically, this would require the data to fall on a
 two-dimensional plane (for linear methods like PCA) or a smooth 2D
@@ -1483,7 +1483,7 @@ <h3 class="callout-title">Exercise 2: Dimensionality Reduction<a class="anchor"
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
 <p>First subset the object to include only highly variable genes
 (<code>sce2 &lt;- sce[hvg.sce.var,]</code>) and then apply the
@@ -1637,7 +1637,7 @@ <h3 class="callout-title">Further Reading<a class="anchor" aria-label="anchor" h
   "identifier": "https://ccb-hms.github.io/osca-carpentries/eda_qc.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-08-12",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/fig/multi-sample-rendered-unnamed-chunk-25-1.png b/fig/multi-sample-rendered-unnamed-chunk-25-1.png
new file mode 100644
index 0000000..e0aea89
Binary files /dev/null and b/fig/multi-sample-rendered-unnamed-chunk-25-1.png differ
diff --git a/hca.html b/hca.html
index e8b9a38..a363864 100644
--- a/hca.html
+++ b/hca.html
@@ -1029,7 +1029,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/hca.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/images.html b/images.html
index cd3266d..a869d01 100644
--- a/images.html
+++ b/images.html
@@ -436,7 +436,9 @@ <h3 id="multi-sample-figure-5">Figure 5</h3>
 <h3 id="multi-sample-figure-6">Figure 6</h3>
 <figure><img src="fig/multi-sample-rendered-unnamed-chunk-13-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr>
 <h3 id="multi-sample-figure-7">Figure 7</h3>
-<figure><img src="fig/multi-sample-rendered-unnamed-chunk-15-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr></section><section id="large_data"><h2 class="section-heading"><a href="large_data.html">Working with large data</a></h2>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-15-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr>
+<h3 id="multi-sample-figure-8">Figure 8</h3>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr></section><section id="large_data"><h2 class="section-heading"><a href="large_data.html">Working with large data</a></h2>
 <hr class="half-width"></section><section id="hca"><h2 class="section-heading"><a href="hca.html">Accessing data from the Human Cell Atlas (HCA)</a></h2>
 <hr class="half-width">
 <h3 id="hca-figure-1">Figure 1</h3>
@@ -488,8 +490,8 @@ <h3 id="hca-figure-1">Figure 1</h3>
   "url": "https://ccb-hms.github.io/osca-carpentries/images.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/images.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/index.html b/index.html
index a671531..72f916c 100644
--- a/index.html
+++ b/index.html
@@ -585,8 +585,8 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
   "url": "https://ccb-hms.github.io/osca-carpentries/index.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/index.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor-notes.html b/instructor-notes.html
index ed8b773..a990616 100644
--- a/instructor-notes.html
+++ b/instructor-notes.html
@@ -422,8 +422,8 @@ <h1>Instructor Notes</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor-notes.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor-notes.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/404.html b/instructor/404.html
index d653a73..16bce34 100644
--- a/instructor/404.html
+++ b/instructor/404.html
@@ -377,8 +377,8 @@ <h1>Page not found</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/404.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/404.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/CODE_OF_CONDUCT.html b/instructor/CODE_OF_CONDUCT.html
index 6650cfb..22ad17d 100644
--- a/instructor/CODE_OF_CONDUCT.html
+++ b/instructor/CODE_OF_CONDUCT.html
@@ -401,7 +401,7 @@ <h1>Contributor Code of Conduct</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/CODE_OF_CONDUCT.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/LICENSE.html b/instructor/LICENSE.html
index 2e90816..e9bcfe5 100644
--- a/instructor/LICENSE.html
+++ b/instructor/LICENSE.html
@@ -452,7 +452,7 @@ <h1>Licenses</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/LICENSE.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/aio.html b/instructor/aio.html
index 18477fb..b821312 100644
--- a/instructor/aio.html
+++ b/instructor/aio.html
@@ -591,7 +591,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
 <div class="accordion-body">
 <ol style="list-style-type: decimal">
 <li><p>You have to do tons of book-keeping! If you perform a QC step
@@ -736,7 +736,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
 <div class="accordion-body">
 <p>Here we add a column called “conservation” that is just an integer
 sequence from 1 to the number of genes.</p>
@@ -813,7 +813,7 @@ <h3 class="callout-title">Exercise 1<a class="anchor" aria-label="anchor" href="
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
 <p>The <code>SingleCellExperiment</code> constructor function can be
 used to create a new <code>SingleCellExperiment</code> object.</p>
@@ -1024,7 +1024,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb4">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1104,7 +1104,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <button class="accordion-button spoiler-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSpoiler1" aria-expanded="false" aria-controls="collapseSpoiler1">
   <h3 class="accordion-header" id="headingSpoiler1">  <div class="note-square"><i aria-hidden="true" class="callout-icon" data-feather="eye"></i></div> Setting the Random Seed </h3>
 </button>
-<div id="collapseSpoiler1" class="accordion-collapse collapse" aria-labelledby="headingSpoiler1" data-bs-parent="#accordionSpoiler1">
+<div id="collapseSpoiler1" class="accordion-collapse collapse" data-bs-parent="#accordionSpoiler1" aria-labelledby="headingSpoiler1">
 <div class="accordion-body">
 <p>Whenever your code involves the generation of random numbers, it’s a
 good practice to set the random seed in R with
@@ -1337,7 +1337,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb25">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1604,7 +1604,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
   <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
 </button>
-<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div id="collapseSolution3" class="accordion-collapse collapse" data-bs-parent="#accordionSolution3" aria-labelledby="headingSolution3">
 <div class="accordion-body">
 <p>Spike-ins are deliberately introduced exogeneous RNA from an exotic
 or synthetic source at a known concentration. This provides a known
@@ -1892,7 +1892,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
   <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
+<div id="collapseSolution4" class="accordion-collapse collapse" data-bs-parent="#accordionSolution4" aria-labelledby="headingSolution4">
 <div class="accordion-body">
 <p>Mathematically, this would require the data to fall on a
 two-dimensional plane (for linear methods like PCA) or a smooth 2D
@@ -2063,7 +2063,7 @@ <h3 class="callout-title">Exercise 2: Dimensionality Reduction<a class="anchor"
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
 <p>First subset the object to include only highly variable genes
 (<code>sce2 &lt;- sce[hvg.sce.var,]</code>) and then apply the
@@ -3576,7 +3576,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
  -->
 </section></section><section id="aio-multi-sample"><p>Content from <a href="multi-sample.html">Multi-sample analyses</a></p>
 <hr>
-<p>Last updated on 2024-07-02 |
+<p>Last updated on 2024-08-19 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 <p>Estimated time: <i aria-hidden="true" data-feather="clock"></i> 45 minutes</p>
@@ -3591,12 +3591,12 @@ <h2 class="card-header">Overview</h2>
 <div class="inner">
 <h3 class="card-title">Questions</h3>
 <ul>
-<li>How to integrate data from multiple batches, samples, and
+<li>How can we integrate data from multiple batches, samples, and
 studies?</li>
-<li>How to identify differentially expressed genes between experimental
-conditions for each cell type?</li>
-<li>How to identify changes in cell type abundance between experimental
-conditions?</li>
+<li>How can we identify differentially expressed genes between
+experimental conditions for each cell type?</li>
+<li>How can we identify changes in cell type abundance between
+experimental conditions?</li>
 </ul>
 </div>
 </div>
@@ -3621,7 +3621,7 @@ <h3 class="card-title">Objectives</h3>
 <a class="anchor" aria-label="anchor" href="#setup-and-data-exploration"></a>
 </h2>
 <hr class="half-width">
-<p>As said, we will use the the wild-type data from the Tal1 chimera
+<p>As before, we will use the the wild-type data from the Tal1 chimera
 experiment:</p>
 <ul>
 <li>Sample 5: E8.5 injected cells (tomato positive), pool 3</li>
@@ -3765,6 +3765,44 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 method, one may want to remove the sample effects with “batch effect”
 correction methods.</p>
 <p>For now, let’s assume that we want to remove this effect.</p>
+<div id="challenge1" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge1"></a>
+</h3>
+<div class="callout-content">
+<p>It seems like samples 5 and 6 are separated off from the others in
+gene expression space. Given the group of cells in each sample, why
+might this make sense versus some other pair of samples? What is the
+factor presumably leading to this difference?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
+  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+</button>
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div class="accordion-body">
+<p>Samples 5 and 6 were from the same “pool” of cells. Looking at the
+documentation for the dataset under <code>?WTChimeraData</code> we see
+that the pool variable is defined as: “Integer, embryo pool from which
+cell derived; samples with same value are matched.” So samples 5 and 6
+have an experimental factor in common which causes a shared, systematic
+difference in gene expression profiles compared to the other samples.
+That’s why you can see many of isolated blue/orange clusters on the
+first TSNE plot. If you were developing single-cell library preparation
+protocols you might want to preserve this effect to understand how
+variation in pools leads to variation in expression, but for now, given
+that we’re investigate other effects, we’ll want to remove this as
+undesired technical variation.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="correcting-batch-effects">Correcting batch effects<a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a>
 <a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a>
 </h2>
@@ -3795,6 +3833,45 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="../fig/multi-sample-rendered-unnamed-chunk-3-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Once we removed the sample batch effect, we can proceed with the
 Differential Expression Analysis.</p>
+<div id="challenge2" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge2"></a>
+</h3>
+<div class="callout-content">
+<p>Having multiple independent samples in each experimental group is
+always helpful, but it particularly important when it comes to batch
+effect correction. Why?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
+  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+</button>
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div class="accordion-body">
+<p>It’s important to have multiple samples within each experimental
+group because it helps the batch effect correction algorithm distinguish
+differences due to batch effects (uninteresting) from differences due to
+biology (interesting).</p>
+<p>Imagine you had one sample that received a drug treatment and one
+that did not, each with 10,000 cells. They differ substantially in
+expression of gene X. Is that an important scientific finding? You can’t
+tell for sure, because the effect of drug is indistinguishable from a
+sample-wise batch effect. But if the difference in gene X holds up when
+you have five treated samples and five untreated samples, now you can be
+a bit more confident. Many batch effect correction methods will take
+information on experimental factors as additional arguments, which they
+can use to help remove batch effects while retaining experimental
+differences.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="differential-expression">Differential Expression<a class="anchor" aria-label="anchor" href="#differential-expression"></a>
 <a class="anchor" aria-label="anchor" href="#differential-expression"></a>
 </h2>
@@ -3993,16 +4070,23 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow<span class="op">=</span><span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fu">seq_len</span><span class="op">(</span><span class="fu">ncol</span><span class="op">(</span><span class="va">y</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span>
 <span>    <span class="fu">plotMD</span><span class="op">(</span><span class="va">y</span>, column<span class="op">=</span><span class="va">i</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre>
 </div>
-<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Furthermore, we want to check if the samples cluster together based
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb20">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">1</span>,<span class="fl">1</span><span class="op">)</span><span class="op">)</span></span></code></pre>
+</div>
+<p>Furthermore, we want to check if the samples cluster together based
 on their known factors (like the tomato injection in this case).</p>
 <p>To do so, we use the MDS plot, which is very close to a PCA
 representation.</p>
-<div class="codewrapper sourceCode" id="cb20">
+<div class="codewrapper sourceCode" id="cb21">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4013,11 +4097,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 tomato as factors. This design indicates which samples belong to which
 pool and condition, so we can use it in the next step of the
 analysis.</p>
-<div class="codewrapper sourceCode" id="cb21">
+<div class="codewrapper sourceCode" id="cb22">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>, <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>,</span>
+<span>                       data <span class="op">=</span> <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
 <span><span class="va">design</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -4041,7 +4126,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </div>
 <p>Now we can estimate the Negative Binomial (NB) overdispersion
 parameter, to model the mean-variance trend.</p>
-<div class="codewrapper sourceCode" id="cb23">
+<div class="codewrapper sourceCode" id="cb24">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4058,7 +4143,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 Biological Coefficient of Variation and the Average log CPM for each
 gene. Additionally, the Common and Trend BCV are shown in
 <code>red</code> and <code>blue</code>.</p>
-<div class="codewrapper sourceCode" id="cb25">
+<div class="codewrapper sourceCode" id="cb26">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4066,12 +4151,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="../fig/multi-sample-rendered-unnamed-chunk-13-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We then fit a Quasi-Likelihood (QL) negative binomial generalized
 linear model for each gene. The <code>robust=TRUE</code> parameter
-avoids distorsions from highly variable clusters. The QL method includes
+avoids distortions from highly variable clusters. The QL method includes
 an additional dispersion parameter, useful to handle the uncertainty and
 variability of the per-gene variance, which is not well estimated by the
 NB dispersions, so the two dispersion types complement each other in the
 final analysis.</p>
-<div class="codewrapper sourceCode" id="cb26">
+<div class="codewrapper sourceCode" id="cb27">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4084,7 +4169,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <pre class="output" tabindex="0"><code>   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  0.3189  0.9705  1.0901  1.0251  1.1486  1.2151 </code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb28">
+<div class="codewrapper sourceCode" id="cb29">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4099,7 +4184,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>QL dispersion estimates for each gene as a function of abundance. Raw
 estimates (black) are shrunk towards the trend (blue) to yield squeezed
 estimates (red).</p>
-<div class="codewrapper sourceCode" id="cb30">
+<div class="codewrapper sourceCode" id="cb31">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4110,7 +4195,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 False Discovery Rate (FDR) of 5%. The low amount of DGEs highlights that
 the tomato injection effect has a low influence on the mesenchyme
 cells.</p>
-<div class="codewrapper sourceCode" id="cb31">
+<div class="codewrapper sourceCode" id="cb32">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4125,7 +4210,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig               4510
 Up                      5</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb33">
+<div class="codewrapper sourceCode" id="cb34">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4150,7 +4235,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>All the previous steps can be easily performed with the following
 function for each cell type, thanks to the <code>pseudoBulkDGE</code>
 function in the <code>scran</code> package.</p>
-<div class="codewrapper sourceCode" id="cb35">
+<div class="codewrapper sourceCode" id="cb36">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4168,7 +4253,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 the results for a cell type. Each of these contains also the
 intermediate results in <code>edgeR</code> format to perform any
 intermediate plot or diagnostic.</p>
-<div class="codewrapper sourceCode" id="cb36">
+<div class="codewrapper sourceCode" id="cb37">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4193,21 +4278,51 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 ENSMUSG00000096730        NA        NA        NA          NA          NA
 ENSMUSG00000095742        NA        NA        NA          NA          NA</code></pre>
 </div>
+<div id="challenge3" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge3"></a>
+</h3>
+<div class="callout-content">
+<p>Clearly some of the results have low p-values. What about the effect
+sizes? What does <code>logFC</code> stand for?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution3" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
+  <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
+</button>
+<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div class="accordion-body">
+<p>“logFC” stands for log fold-change. Rather than reporting e.g. a
+5-fold increase, it’s better to report a logFC of log(5) = 1.61.
+Additive log scales are easier to work with than multiplicative identity
+scales, once you get used to it.</p>
+<p><code>ENSMUSG00000037664</code> seems to have an estimated logFC of
+about -8. That’s a big difference if it’s real.</p>
+</div>
+</div>
+</div>
+</div>
 </div>
 </section><section><h2 class="section-heading" id="differential-abundance">Differential Abundance<a class="anchor" aria-label="anchor" href="#differential-abundance"></a>
 <a class="anchor" aria-label="anchor" href="#differential-abundance"></a>
 </h2>
 <hr class="half-width">
-<p>With DA we test for differences between clusters across conditions,
-to investigate which clusters change accordingly to the treatment (the
-tomato injection in our case).</p>
+<p>With DA we look for differences in cluster <em>abundance</em> across
+conditions (the tomato injection in our case), rather than differences
+in gene expression.</p>
 <p>We first setup some code and variables for further analysis, like
 quantifying the number of cells per each cell type and fit a model to
 catch differences between the injected cells and the background.</p>
-<p>The performed steps are very similar to the ones for DEGs analysis,
-but this time we start our analysis on the computed abundances and
-without normalizing the data with TMM.</p>
-<div class="codewrapper sourceCode" id="cb38">
+<p>The steps are very similar to the ones for DEGs analysis, but this
+time we start our analysis on the computed abundances and without
+normalizing the data with TMM.</p>
+<div class="codewrapper sourceCode" id="cb39">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4228,14 +4343,22 @@ <h3 id="background-on-compositional-effect">Background on compositional effect<a
 <p>As mentioned before, in DA we don’t normalize our data with
 <code>calcNormFactors</code> function, because this approach considers
 that most of the input features do not vary between conditions. This
-cannot be applied to this analysis because we have a small number of
-cell populations that all can change due to the treatment. Leaving us to
-normalize only for library depth, which in pseudo-bulk data means by the
-total number of cells in each sample (cell type).</p>
+cannot be applied to DA analysis because we have a small number of cell
+populations that all can change due to the treatment. This means that
+here we will normalize only for library depth, which in pseudo-bulk data
+means by the total number of cells in each sample (cell type).</p>
 <p>On the other hand, this can lead our data to be susceptible to
-compositional effect, that means that our conclusions can be biased by
-the amount of cells present in each cell type. And this amount of cells
-can be totally unbalanced between cell types.</p>
+compositional effect. “Compositional” refers to the fact that the
+cluster abundances in a sample are not independent of one another
+because each cell type is effectively competing for space in the sample.
+They behave like proportions. If cell type A abundance increases in a
+new condition, that means we’ll observe less of everything else, even if
+everything else is unaffected by the new condition.</p>
+<p>Compositionality means that our conclusions can be biased by the
+amount of cells present in each cell type. And this amount of cells can
+be totally unbalanced between cell types. This is particularly
+problematic for cell types that start at or end up near 0 or 100
+percent.</p>
 <p>For example, a specific cell type can be 40% of the total amount of
 cells present in the experiment, while another just the 3%. The
 differences in terms of abundance of these cell types are detected
@@ -4253,7 +4376,7 @@ <h3 id="assuming-most-labels-do-not-change">Assuming most labels do not change<a
 <p>To do so, we first normalize the data with
 <code>calcNormFactors</code> and then we fit and estimate a QL-model for
 our abundance data.</p>
-<div class="codewrapper sourceCode" id="cb39">
+<div class="codewrapper sourceCode" id="cb40">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4265,14 +4388,17 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </h3>
 <pre class="output" tabindex="0"><code>[1] 1.1029040 1.0228173 1.0695358 0.7686501 1.0402941 1.0365354</code></pre>
 </div>
-<p>We then follow the already seen edgeR analysis steps.</p>
-<div class="codewrapper sourceCode" id="cb41">
+<p>We then use edgeR in a manner similar to what we ran before:</p>
+<div class="codewrapper sourceCode" id="cb42">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">y.ab2</span> <span class="op">&lt;-</span> <span class="fu">estimateDisp</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, trend<span class="op">=</span><span class="st">"none"</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">fit.ab2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFit</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, robust<span class="op">=</span><span class="cn">TRUE</span>, abundance.trend<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">res2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFTest</span><span class="op">(</span><span class="va">fit.ab2</span>, coef<span class="op">=</span><span class="fu">ncol</span><span class="op">(</span><span class="va">design</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="fu">summary</span><span class="op">(</span><span class="fu">decideTests</span><span class="op">(</span><span class="va">res2</span><span class="op">)</span><span class="op">)</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -4283,7 +4409,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 29
 Up                      1</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb43">
+<div class="codewrapper sourceCode" id="cb44">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4310,15 +4436,16 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <h3 id="testing-against-a-log-fold-change-threshold">Testing against a log-fold change threshold<a class="anchor" aria-label="anchor" href="#testing-against-a-log-fold-change-threshold"></a>
 </h3>
 <p>This other approach assumes that the composition bias introduces a
-spurious log2-fold change of no more than a quantity for a non-DA label.
-In other words, we interpret this as the maximum log-fold change in the
-total number of cells given by DA in other labels. On the other hand,
-when choosing , we should not consider fold-differences in the totals
-due to differences in capture efficiency or the size of the original
-cell population are not attributable to composition bias. We then
-mitigate the effect of composition biases by testing each label for
+spurious log2-fold change of no more than a quantity for a non-DA
+label.</p>
+<p>In other words, we interpret this as the maximum log-fold change in
+the total number of cells given by DA in other labels. On the other
+hand, when choosing , we should not consider fold-differences in the
+totals due to differences in capture efficiency or the size of the
+original cell population are not attributable to composition bias. We
+then mitigate the effect of composition biases by testing each label for
 changes in abundance beyond .</p>
-<div class="codewrapper sourceCode" id="cb45">
+<div class="codewrapper sourceCode" id="cb46">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4333,7 +4460,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 32
 Up                      0</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb47">
+<div class="codewrapper sourceCode" id="cb48">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4373,7 +4500,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <a class="anchor" aria-label="anchor" href="#session-info"></a>
 </h2>
 <hr class="half-width">
-<div class="codewrapper sourceCode" id="cb49">
+<div class="codewrapper sourceCode" id="cb50">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -4494,33 +4621,47 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
-
+<p>Remember, you can subset SingleCellExperiments with logical indices,
+just like a matrix. You can also access their column data with the
+<code>$</code> accessor, like a data frame.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution4" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
-  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
+  <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb52">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
+<span></span>
+<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span><span class="va">summed.filt.subset</span>, </span>
+<span>    label<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design<span class="op">=</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
+<span>    coef<span class="op">=</span><span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span></code></pre>
+</div>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-muscat" class="callout challenge">
+<div id="exercise-2" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-muscat" class="callout-inner">
-<h3 class="callout-title">Exercise 2: <code>muscat</code><a class="anchor" aria-label="anchor" href="#exercise-2-muscat"></a>
+<div id="exercise-2" class="callout-inner">
+<h3 class="callout-title">Exercise 2:<a class="anchor" aria-label="anchor" href="#exercise-2"></a>
 </h3>
 <div class="callout-content">
-<p>Test differential expressed genes computed with <code>muscat</code>
-package and check for differences in the results.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -4531,19 +4672,33 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" aria-labelledby="headingHint2" data-bs-parent="#accordionHint2">
 <div class="accordion-body">
-
+<p>You can just hand <code>pheatmap()</code> a matrix as its only
+argument. It has a million options, but the defaults are usually pretty
+good.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution5" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
-  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution5" aria-expanded="false" aria-controls="collapseSolution5">
+  <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution5" class="accordion-collapse collapse" aria-labelledby="headingSolution5" data-bs-parent="#accordionSolution5">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb53">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">library</span><span class="op">(</span><span class="va">pheatmap</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
@@ -6372,8 +6527,8 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/aio.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/aio.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/cell_type_annotation.html b/instructor/cell_type_annotation.html
index 39fbae9..a36de11 100644
--- a/instructor/cell_type_annotation.html
+++ b/instructor/cell_type_annotation.html
@@ -1784,7 +1784,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/cell_type_annotation.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-08-12",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/eda_qc.html b/instructor/eda_qc.html
index 271194a..96c0455 100644
--- a/instructor/eda_qc.html
+++ b/instructor/eda_qc.html
@@ -474,7 +474,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb4">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -553,7 +553,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <button class="accordion-button spoiler-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSpoiler1" aria-expanded="false" aria-controls="collapseSpoiler1">
   <h3 class="accordion-header" id="headingSpoiler1">  <div class="note-square"><i aria-hidden="true" class="callout-icon" data-feather="eye"></i></div> Setting the Random Seed </h3>
 </button>
-<div id="collapseSpoiler1" class="accordion-collapse collapse" aria-labelledby="headingSpoiler1" data-bs-parent="#accordionSpoiler1">
+<div id="collapseSpoiler1" class="accordion-collapse collapse" data-bs-parent="#accordionSpoiler1" aria-labelledby="headingSpoiler1">
 <div class="accordion-body">
 <p>Whenever your code involves the generation of random numbers, it’s a
 good practice to set the random seed in R with
@@ -779,7 +779,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
 <div class="accordion-body">
 <div class="codewrapper sourceCode" id="cb25">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
@@ -1042,7 +1042,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
   <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
 </button>
-<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div id="collapseSolution3" class="accordion-collapse collapse" data-bs-parent="#accordionSolution3" aria-labelledby="headingSolution3">
 <div class="accordion-body">
 <p>Spike-ins are deliberately introduced exogeneous RNA from an exotic
 or synthetic source at a known concentration. This provides a known
@@ -1321,7 +1321,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
   <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
+<div id="collapseSolution4" class="accordion-collapse collapse" data-bs-parent="#accordionSolution4" aria-labelledby="headingSolution4">
 <div class="accordion-body">
 <p>Mathematically, this would require the data to fall on a
 two-dimensional plane (for linear methods like PCA) or a smooth 2D
@@ -1485,7 +1485,7 @@ <h3 class="callout-title">Exercise 2: Dimensionality Reduction<a class="anchor"
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
 <div class="accordion-body">
 <p>First subset the object to include only highly variable genes
 (<code>sce2 &lt;- sce[hvg.sce.var,]</code>) and then apply the
@@ -1639,7 +1639,7 @@ <h3 class="callout-title">Further Reading<a class="anchor" aria-label="anchor" h
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/eda_qc.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-08-12",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/hca.html b/instructor/hca.html
index 4649d47..a5d3f6f 100644
--- a/instructor/hca.html
+++ b/instructor/hca.html
@@ -1031,7 +1031,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/hca.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/images.html b/instructor/images.html
index 24b139d..0957a16 100644
--- a/instructor/images.html
+++ b/instructor/images.html
@@ -438,7 +438,9 @@ <h3 id="multi-sample-figure-5">Figure 5</h3>
 <h3 id="multi-sample-figure-6">Figure 6</h3>
 <figure><img src="../fig/multi-sample-rendered-unnamed-chunk-13-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr>
 <h3 id="multi-sample-figure-7">Figure 7</h3>
-<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-15-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr></section><section id="large_data"><h2 class="section-heading"><a href="large_data.html">Working with large data</a></h2>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-15-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr>
+<h3 id="multi-sample-figure-8">Figure 8</h3>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><hr></section><section id="large_data"><h2 class="section-heading"><a href="large_data.html">Working with large data</a></h2>
 <hr class="half-width"></section><section id="hca"><h2 class="section-heading"><a href="hca.html">Accessing data from the Human Cell Atlas (HCA)</a></h2>
 <hr class="half-width">
 <h3 id="hca-figure-1">Figure 1</h3>
@@ -490,8 +492,8 @@ <h3 id="hca-figure-1">Figure 1</h3>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/images.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/images.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/index.html b/instructor/index.html
index d8c3e17..c3be229 100644
--- a/instructor/index.html
+++ b/instructor/index.html
@@ -395,10 +395,10 @@ <h3 class="callout-title">Prerequisites<a class="anchor" aria-label="anchor" hre
  4. <a href="multi-sample.html">Multi-sample analyses</a>
 </td>
 <td>
-How to integrate data from multiple batches, samples, and
-studies?<br>How to identify differentially expressed genes between
-experimental conditions for each cell type?<br>How to identify changes
-in cell type abundance between experimental conditions?
+How can we integrate data from multiple batches, samples, and
+studies?<br>How can we identify differentially expressed genes between
+experimental conditions for each cell type?<br>How can we identify
+changes in cell type abundance between experimental conditions?
 </td>
 </tr><tr><td>
 <span class="visually-hidden">Duration: </span>02h 45m
@@ -669,8 +669,8 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/index.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/index.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/instructor-notes.html b/instructor/instructor-notes.html
index 4bef9d2..a30c053 100644
--- a/instructor/instructor-notes.html
+++ b/instructor/instructor-notes.html
@@ -430,8 +430,8 @@ <h1>Instructor Notes</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/instructor-notes.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/instructor-notes.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/intro-sce.html b/instructor/intro-sce.html
index b35f77e..d847861 100644
--- a/instructor/intro-sce.html
+++ b/instructor/intro-sce.html
@@ -542,7 +542,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
 <div class="accordion-body">
 <ol style="list-style-type: decimal"><li><p>You have to do tons of book-keeping! If you perform a QC step
 that removes dead cells, now you also have to remember to remove that
@@ -682,7 +682,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
 <div class="accordion-body">
 <p>Here we add a column called “conservation” that is just an integer
 sequence from 1 to the number of genes.</p>
@@ -758,7 +758,7 @@ <h3 class="callout-title">Exercise 1<a class="anchor" aria-label="anchor" href="
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
 <p>The <code>SingleCellExperiment</code> constructor function can be
 used to create a new <code>SingleCellExperiment</code> object.</p>
@@ -878,7 +878,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/intro-sce.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-08-12",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/key-points.html b/instructor/key-points.html
index 4abe08c..386bd47 100644
--- a/instructor/key-points.html
+++ b/instructor/key-points.html
@@ -540,8 +540,8 @@ <h2 class="accordion-header" id="flush-headingTwelve">
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/key-points.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/key-points.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/large_data.html b/instructor/large_data.html
index e6c0257..4d30bcf 100644
--- a/instructor/large_data.html
+++ b/instructor/large_data.html
@@ -1403,7 +1403,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/large_data.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/multi-sample.html b/instructor/multi-sample.html
index 504b4e2..58013f2 100644
--- a/instructor/multi-sample.html
+++ b/instructor/multi-sample.html
@@ -331,7 +331,7 @@ <h2 class="accordion-header" id="flush-headingTwelve">
       </div>
       <hr></nav><main id="main-content" class="main-content"><div class="container lesson-content">
         <h1>Multi-sample analyses</h1>
-        <p>Last updated on 2024-07-02 |
+        <p>Last updated on 2024-08-19 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 
@@ -352,12 +352,12 @@ <h2 class="card-header">Overview</h2>
 <div class="card-body">
 <div class="inner">
 <h3 class="card-title">Questions</h3>
-<ul><li>How to integrate data from multiple batches, samples, and
+<ul><li>How can we integrate data from multiple batches, samples, and
 studies?</li>
-<li>How to identify differentially expressed genes between experimental
-conditions for each cell type?</li>
-<li>How to identify changes in cell type abundance between experimental
-conditions?</li>
+<li>How can we identify differentially expressed genes between
+experimental conditions for each cell type?</li>
+<li>How can we identify changes in cell type abundance between
+experimental conditions?</li>
 </ul></div>
 </div>
 </div>
@@ -377,7 +377,7 @@ <h3 class="card-title">Objectives</h3>
 </div>
 <section><h2 class="section-heading" id="setup-and-data-exploration">Setup and data exploration<a class="anchor" aria-label="anchor" href="#setup-and-data-exploration"></a>
 <a class="anchor" aria-label="anchor" href="#setup-and-data-exploration"></a></h2>
-<hr class="half-width"><p>As said, we will use the the wild-type data from the Tal1 chimera
+<hr class="half-width"><p>As before, we will use the the wild-type data from the Tal1 chimera
 experiment:</p>
 <ul><li>Sample 5: E8.5 injected cells (tomato positive), pool 3</li>
 <li>Sample 6: E8.5 host cells (tomato negative), pool 3</li>
@@ -519,6 +519,44 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 method, one may want to remove the sample effects with “batch effect”
 correction methods.</p>
 <p>For now, let’s assume that we want to remove this effect.</p>
+<div id="challenge1" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge1"></a>
+</h3>
+<div class="callout-content">
+<p>It seems like samples 5 and 6 are separated off from the others in
+gene expression space. Given the group of cells in each sample, why
+might this make sense versus some other pair of samples? What is the
+factor presumably leading to this difference?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
+  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+</button>
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div class="accordion-body">
+<p>Samples 5 and 6 were from the same “pool” of cells. Looking at the
+documentation for the dataset under <code>?WTChimeraData</code> we see
+that the pool variable is defined as: “Integer, embryo pool from which
+cell derived; samples with same value are matched.” So samples 5 and 6
+have an experimental factor in common which causes a shared, systematic
+difference in gene expression profiles compared to the other samples.
+That’s why you can see many of isolated blue/orange clusters on the
+first TSNE plot. If you were developing single-cell library preparation
+protocols you might want to preserve this effect to understand how
+variation in pools leads to variation in expression, but for now, given
+that we’re investigate other effects, we’ll want to remove this as
+undesired technical variation.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="correcting-batch-effects">Correcting batch effects<a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a>
 <a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a></h2>
 <hr class="half-width"><p>We correct the effect of samples by aid of the
@@ -547,6 +585,45 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="../fig/multi-sample-rendered-unnamed-chunk-3-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Once we removed the sample batch effect, we can proceed with the
 Differential Expression Analysis.</p>
+<div id="challenge2" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge2"></a>
+</h3>
+<div class="callout-content">
+<p>Having multiple independent samples in each experimental group is
+always helpful, but it particularly important when it comes to batch
+effect correction. Why?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
+  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+</button>
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div class="accordion-body">
+<p>It’s important to have multiple samples within each experimental
+group because it helps the batch effect correction algorithm distinguish
+differences due to batch effects (uninteresting) from differences due to
+biology (interesting).</p>
+<p>Imagine you had one sample that received a drug treatment and one
+that did not, each with 10,000 cells. They differ substantially in
+expression of gene X. Is that an important scientific finding? You can’t
+tell for sure, because the effect of drug is indistinguishable from a
+sample-wise batch effect. But if the difference in gene X holds up when
+you have five treated samples and five untreated samples, now you can be
+a bit more confident. Many batch effect correction methods will take
+information on experimental factors as additional arguments, which they
+can use to help remove batch effects while retaining experimental
+differences.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="differential-expression">Differential Expression<a class="anchor" aria-label="anchor" href="#differential-expression"></a>
 <a class="anchor" aria-label="anchor" href="#differential-expression"></a></h2>
 <hr class="half-width"><p>In order to perform a Differential Expression Analysis, we need to
@@ -741,16 +818,23 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow<span class="op">=</span><span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fu">seq_len</span><span class="op">(</span><span class="fu">ncol</span><span class="op">(</span><span class="va">y</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span>
 <span>    <span class="fu">plotMD</span><span class="op">(</span><span class="va">y</span>, column<span class="op">=</span><span class="va">i</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre>
 </div>
-<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Furthermore, we want to check if the samples cluster together based
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb20">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">1</span>,<span class="fl">1</span><span class="op">)</span><span class="op">)</span></span></code></pre>
+</div>
+<p>Furthermore, we want to check if the samples cluster together based
 on their known factors (like the tomato injection in this case).</p>
 <p>To do so, we use the MDS plot, which is very close to a PCA
 representation.</p>
-<div class="codewrapper sourceCode" id="cb20">
+<div class="codewrapper sourceCode" id="cb21">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -761,11 +845,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 tomato as factors. This design indicates which samples belong to which
 pool and condition, so we can use it in the next step of the
 analysis.</p>
-<div class="codewrapper sourceCode" id="cb21">
+<div class="codewrapper sourceCode" id="cb22">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>, <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>,</span>
+<span>                       data <span class="op">=</span> <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
 <span><span class="va">design</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -789,7 +874,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </div>
 <p>Now we can estimate the Negative Binomial (NB) overdispersion
 parameter, to model the mean-variance trend.</p>
-<div class="codewrapper sourceCode" id="cb23">
+<div class="codewrapper sourceCode" id="cb24">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -806,7 +891,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 Biological Coefficient of Variation and the Average log CPM for each
 gene. Additionally, the Common and Trend BCV are shown in
 <code>red</code> and <code>blue</code>.</p>
-<div class="codewrapper sourceCode" id="cb25">
+<div class="codewrapper sourceCode" id="cb26">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -814,12 +899,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="../fig/multi-sample-rendered-unnamed-chunk-13-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We then fit a Quasi-Likelihood (QL) negative binomial generalized
 linear model for each gene. The <code>robust=TRUE</code> parameter
-avoids distorsions from highly variable clusters. The QL method includes
+avoids distortions from highly variable clusters. The QL method includes
 an additional dispersion parameter, useful to handle the uncertainty and
 variability of the per-gene variance, which is not well estimated by the
 NB dispersions, so the two dispersion types complement each other in the
 final analysis.</p>
-<div class="codewrapper sourceCode" id="cb26">
+<div class="codewrapper sourceCode" id="cb27">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -832,7 +917,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <pre class="output" tabindex="0"><code>   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  0.3189  0.9705  1.0901  1.0251  1.1486  1.2151 </code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb28">
+<div class="codewrapper sourceCode" id="cb29">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -847,7 +932,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>QL dispersion estimates for each gene as a function of abundance. Raw
 estimates (black) are shrunk towards the trend (blue) to yield squeezed
 estimates (red).</p>
-<div class="codewrapper sourceCode" id="cb30">
+<div class="codewrapper sourceCode" id="cb31">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -858,7 +943,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 False Discovery Rate (FDR) of 5%. The low amount of DGEs highlights that
 the tomato injection effect has a low influence on the mesenchyme
 cells.</p>
-<div class="codewrapper sourceCode" id="cb31">
+<div class="codewrapper sourceCode" id="cb32">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -873,7 +958,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig               4510
 Up                      5</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb33">
+<div class="codewrapper sourceCode" id="cb34">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -898,7 +983,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>All the previous steps can be easily performed with the following
 function for each cell type, thanks to the <code>pseudoBulkDGE</code>
 function in the <code>scran</code> package.</p>
-<div class="codewrapper sourceCode" id="cb35">
+<div class="codewrapper sourceCode" id="cb36">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -916,7 +1001,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 the results for a cell type. Each of these contains also the
 intermediate results in <code>edgeR</code> format to perform any
 intermediate plot or diagnostic.</p>
-<div class="codewrapper sourceCode" id="cb36">
+<div class="codewrapper sourceCode" id="cb37">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -941,19 +1026,49 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 ENSMUSG00000096730        NA        NA        NA          NA          NA
 ENSMUSG00000095742        NA        NA        NA          NA          NA</code></pre>
 </div>
+<div id="challenge3" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge3"></a>
+</h3>
+<div class="callout-content">
+<p>Clearly some of the results have low p-values. What about the effect
+sizes? What does <code>logFC</code> stand for?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution3" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
+  <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
+</button>
+<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div class="accordion-body">
+<p>“logFC” stands for log fold-change. Rather than reporting e.g. a
+5-fold increase, it’s better to report a logFC of log(5) = 1.61.
+Additive log scales are easier to work with than multiplicative identity
+scales, once you get used to it.</p>
+<p><code>ENSMUSG00000037664</code> seems to have an estimated logFC of
+about -8. That’s a big difference if it’s real.</p>
+</div>
+</div>
+</div>
+</div>
 </div>
 </section><section><h2 class="section-heading" id="differential-abundance">Differential Abundance<a class="anchor" aria-label="anchor" href="#differential-abundance"></a>
 <a class="anchor" aria-label="anchor" href="#differential-abundance"></a></h2>
-<hr class="half-width"><p>With DA we test for differences between clusters across conditions,
-to investigate which clusters change accordingly to the treatment (the
-tomato injection in our case).</p>
+<hr class="half-width"><p>With DA we look for differences in cluster <em>abundance</em> across
+conditions (the tomato injection in our case), rather than differences
+in gene expression.</p>
 <p>We first setup some code and variables for further analysis, like
 quantifying the number of cells per each cell type and fit a model to
 catch differences between the injected cells and the background.</p>
-<p>The performed steps are very similar to the ones for DEGs analysis,
-but this time we start our analysis on the computed abundances and
-without normalizing the data with TMM.</p>
-<div class="codewrapper sourceCode" id="cb38">
+<p>The steps are very similar to the ones for DEGs analysis, but this
+time we start our analysis on the computed abundances and without
+normalizing the data with TMM.</p>
+<div class="codewrapper sourceCode" id="cb39">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -973,14 +1088,22 @@ <h3 id="background-on-compositional-effect">Background on compositional effect<a
 <p>As mentioned before, in DA we don’t normalize our data with
 <code>calcNormFactors</code> function, because this approach considers
 that most of the input features do not vary between conditions. This
-cannot be applied to this analysis because we have a small number of
-cell populations that all can change due to the treatment. Leaving us to
-normalize only for library depth, which in pseudo-bulk data means by the
-total number of cells in each sample (cell type).</p>
+cannot be applied to DA analysis because we have a small number of cell
+populations that all can change due to the treatment. This means that
+here we will normalize only for library depth, which in pseudo-bulk data
+means by the total number of cells in each sample (cell type).</p>
 <p>On the other hand, this can lead our data to be susceptible to
-compositional effect, that means that our conclusions can be biased by
-the amount of cells present in each cell type. And this amount of cells
-can be totally unbalanced between cell types.</p>
+compositional effect. “Compositional” refers to the fact that the
+cluster abundances in a sample are not independent of one another
+because each cell type is effectively competing for space in the sample.
+They behave like proportions. If cell type A abundance increases in a
+new condition, that means we’ll observe less of everything else, even if
+everything else is unaffected by the new condition.</p>
+<p>Compositionality means that our conclusions can be biased by the
+amount of cells present in each cell type. And this amount of cells can
+be totally unbalanced between cell types. This is particularly
+problematic for cell types that start at or end up near 0 or 100
+percent.</p>
 <p>For example, a specific cell type can be 40% of the total amount of
 cells present in the experiment, while another just the 3%. The
 differences in terms of abundance of these cell types are detected
@@ -997,7 +1120,7 @@ <h3 id="assuming-most-labels-do-not-change">Assuming most labels do not change<a
 <p>To do so, we first normalize the data with
 <code>calcNormFactors</code> and then we fit and estimate a QL-model for
 our abundance data.</p>
-<div class="codewrapper sourceCode" id="cb39">
+<div class="codewrapper sourceCode" id="cb40">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1009,14 +1132,17 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </h3>
 <pre class="output" tabindex="0"><code>[1] 1.1029040 1.0228173 1.0695358 0.7686501 1.0402941 1.0365354</code></pre>
 </div>
-<p>We then follow the already seen edgeR analysis steps.</p>
-<div class="codewrapper sourceCode" id="cb41">
+<p>We then use edgeR in a manner similar to what we ran before:</p>
+<div class="codewrapper sourceCode" id="cb42">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">y.ab2</span> <span class="op">&lt;-</span> <span class="fu">estimateDisp</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, trend<span class="op">=</span><span class="st">"none"</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">fit.ab2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFit</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, robust<span class="op">=</span><span class="cn">TRUE</span>, abundance.trend<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">res2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFTest</span><span class="op">(</span><span class="va">fit.ab2</span>, coef<span class="op">=</span><span class="fu">ncol</span><span class="op">(</span><span class="va">design</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="fu">summary</span><span class="op">(</span><span class="fu">decideTests</span><span class="op">(</span><span class="va">res2</span><span class="op">)</span><span class="op">)</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -1027,7 +1153,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 29
 Up                      1</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb43">
+<div class="codewrapper sourceCode" id="cb44">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1053,15 +1179,16 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <div class="section level3">
 <h3 id="testing-against-a-log-fold-change-threshold">Testing against a log-fold change threshold<a class="anchor" aria-label="anchor" href="#testing-against-a-log-fold-change-threshold"></a></h3>
 <p>This other approach assumes that the composition bias introduces a
-spurious log2-fold change of no more than a quantity for a non-DA label.
-In other words, we interpret this as the maximum log-fold change in the
-total number of cells given by DA in other labels. On the other hand,
-when choosing , we should not consider fold-differences in the totals
-due to differences in capture efficiency or the size of the original
-cell population are not attributable to composition bias. We then
-mitigate the effect of composition biases by testing each label for
+spurious log2-fold change of no more than a quantity for a non-DA
+label.</p>
+<p>In other words, we interpret this as the maximum log-fold change in
+the total number of cells given by DA in other labels. On the other
+hand, when choosing , we should not consider fold-differences in the
+totals due to differences in capture efficiency or the size of the
+original cell population are not attributable to composition bias. We
+then mitigate the effect of composition biases by testing each label for
 changes in abundance beyond .</p>
-<div class="codewrapper sourceCode" id="cb45">
+<div class="codewrapper sourceCode" id="cb46">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1076,7 +1203,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 32
 Up                      0</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb47">
+<div class="codewrapper sourceCode" id="cb48">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1114,7 +1241,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </div>
 </section><section><h2 class="section-heading" id="session-info">Session Info<a class="anchor" aria-label="anchor" href="#session-info"></a>
 <a class="anchor" aria-label="anchor" href="#session-info"></a></h2>
-<hr class="half-width"><div class="codewrapper sourceCode" id="cb49">
+<hr class="half-width"><div class="codewrapper sourceCode" id="cb50">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1233,33 +1360,47 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
-
+<p>Remember, you can subset SingleCellExperiments with logical indices,
+just like a matrix. You can also access their column data with the
+<code>$</code> accessor, like a data frame.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution4" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
-  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
+  <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb52">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
+<span></span>
+<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span><span class="va">summed.filt.subset</span>, </span>
+<span>    label<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design<span class="op">=</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
+<span>    coef<span class="op">=</span><span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span></code></pre>
+</div>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-muscat" class="callout challenge">
+<div id="exercise-2" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-muscat" class="callout-inner">
-<h3 class="callout-title">Exercise 2: <code>muscat</code><a class="anchor" aria-label="anchor" href="#exercise-2-muscat"></a>
+<div id="exercise-2" class="callout-inner">
+<h3 class="callout-title">Exercise 2:<a class="anchor" aria-label="anchor" href="#exercise-2"></a>
 </h3>
 <div class="callout-content">
-<p>Test differential expressed genes computed with <code>muscat</code>
-package and check for differences in the results.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -1270,19 +1411,33 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" aria-labelledby="headingHint2" data-bs-parent="#accordionHint2">
 <div class="accordion-body">
-
+<p>You can just hand <code>pheatmap()</code> a matrix as its only
+argument. It has a million options, but the defaults are usually pretty
+good.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution5" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
-  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution5" aria-expanded="false" aria-controls="collapseSolution5">
+  <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution5" class="accordion-collapse collapse" aria-labelledby="headingSolution5" data-bs-parent="#accordionSolution5">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb53">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">library</span><span class="op">(</span><span class="va">pheatmap</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="../fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
@@ -1397,8 +1552,8 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/multi-sample.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/multi-sample.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/profiles.html b/instructor/profiles.html
index 3ee3744..aedd197 100644
--- a/instructor/profiles.html
+++ b/instructor/profiles.html
@@ -352,8 +352,8 @@ <h1>Learner Profiles</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/instructor/profiles.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/profiles.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/instructor/reference.html b/instructor/reference.html
index 8ee11fb..95844c2 100644
--- a/instructor/reference.html
+++ b/instructor/reference.html
@@ -414,7 +414,7 @@ <h1>Reference</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/instructor/reference.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/intro-sce.html b/intro-sce.html
index 4c4386b..d7c616f 100644
--- a/intro-sce.html
+++ b/intro-sce.html
@@ -540,7 +540,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
   <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" data-bs-parent="#accordionSolution1" aria-labelledby="headingSolution1">
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
 <div class="accordion-body">
 <ol style="list-style-type: decimal"><li><p>You have to do tons of book-keeping! If you perform a QC step
 that removes dead cells, now you also have to remember to remove that
@@ -680,7 +680,7 @@ <h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#
 <button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
   <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" data-bs-parent="#accordionSolution2" aria-labelledby="headingSolution2">
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
 <div class="accordion-body">
 <p>Here we add a column called “conservation” that is just an integer
 sequence from 1 to the number of genes.</p>
@@ -756,7 +756,7 @@ <h3 class="callout-title">Exercise 1<a class="anchor" aria-label="anchor" href="
 <button class="accordion-button hint-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseHint1" aria-expanded="false" aria-controls="collapseHint1">
   <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
-<div id="collapseHint1" class="accordion-collapse collapse" data-bs-parent="#accordionHint1" aria-labelledby="headingHint1">
+<div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
 <p>The <code>SingleCellExperiment</code> constructor function can be
 used to create a new <code>SingleCellExperiment</code> object.</p>
@@ -876,7 +876,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/intro-sce.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-08-12",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/key-points.html b/key-points.html
index de09efc..27e3a95 100644
--- a/key-points.html
+++ b/key-points.html
@@ -538,8 +538,8 @@ <h2 class="accordion-header" id="flush-headingTwelve">
   "url": "https://ccb-hms.github.io/osca-carpentries/key-points.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/key-points.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/large_data.html b/large_data.html
index 943a02b..b773e91 100644
--- a/large_data.html
+++ b/large_data.html
@@ -1401,7 +1401,7 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "identifier": "https://ccb-hms.github.io/osca-carpentries/large_data.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/md5sum.txt b/md5sum.txt
index dc3af05..189f3ea 100644
--- a/md5sum.txt
+++ b/md5sum.txt
@@ -7,7 +7,7 @@
 "episodes/intro-sce.Rmd" "43e8d9965c505108e386dffb0f011697" "site/built/intro-sce.md" "2024-08-12"
 "episodes/eda_qc.Rmd" "07eec916cc6aff0c5dcd6ec463b66e75" "site/built/eda_qc.md" "2024-08-12"
 "episodes/cell_type_annotation.Rmd" "fa2333e4c8aa876394327610eb650e8b" "site/built/cell_type_annotation.md" "2024-08-12"
-"episodes/multi-sample.Rmd" "75798a2bb3500220ff7b3c1d88cadf41" "site/built/multi-sample.md" "2024-07-02"
+"episodes/multi-sample.Rmd" "e33ec8bf5cfd26471d17fce4d6af9281" "site/built/multi-sample.md" "2024-08-19"
 "episodes/large_data.Rmd" "6b413ccf15bea3e70c6dd75432d3914d" "site/built/large_data.md" "2024-07-02"
 "episodes/hca.Rmd" "09e4390a2d357fdb950d663f3d3fcd7a" "site/built/hca.md" "2024-07-02"
 "instructors/instructor-notes.md" "cae72b6712578d74a49fea7513099f8c" "site/built/instructor-notes.md" "2024-07-02"
diff --git a/multi-sample.html b/multi-sample.html
index 13c2603..a627dcd 100644
--- a/multi-sample.html
+++ b/multi-sample.html
@@ -331,7 +331,7 @@ <h2 class="accordion-header" id="flush-headingTwelve">
       </div>
       <hr></nav><main id="main-content" class="main-content"><div class="container lesson-content">
         <h1>Multi-sample analyses</h1>
-        <p>Last updated on 2024-07-02 |
+        <p>Last updated on 2024-08-19 |
 
         <a href="https://github.com/ccb-hms/osca-carpentries/edit/main/episodes/multi-sample.Rmd" class="external-link">Edit this page <i aria-hidden="true" data-feather="edit"></i></a></p>
 
@@ -350,12 +350,12 @@ <h2 class="card-header">Overview</h2>
 <div class="card-body">
 <div class="inner">
 <h3 class="card-title">Questions</h3>
-<ul><li>How to integrate data from multiple batches, samples, and
+<ul><li>How can we integrate data from multiple batches, samples, and
 studies?</li>
-<li>How to identify differentially expressed genes between experimental
-conditions for each cell type?</li>
-<li>How to identify changes in cell type abundance between experimental
-conditions?</li>
+<li>How can we identify differentially expressed genes between
+experimental conditions for each cell type?</li>
+<li>How can we identify changes in cell type abundance between
+experimental conditions?</li>
 </ul></div>
 </div>
 </div>
@@ -375,7 +375,7 @@ <h3 class="card-title">Objectives</h3>
 </div>
 <section><h2 class="section-heading" id="setup-and-data-exploration">Setup and data exploration<a class="anchor" aria-label="anchor" href="#setup-and-data-exploration"></a>
 <a class="anchor" aria-label="anchor" href="#setup-and-data-exploration"></a></h2>
-<hr class="half-width"><p>As said, we will use the the wild-type data from the Tal1 chimera
+<hr class="half-width"><p>As before, we will use the the wild-type data from the Tal1 chimera
 experiment:</p>
 <ul><li>Sample 5: E8.5 injected cells (tomato positive), pool 3</li>
 <li>Sample 6: E8.5 host cells (tomato negative), pool 3</li>
@@ -517,6 +517,44 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 method, one may want to remove the sample effects with “batch effect”
 correction methods.</p>
 <p>For now, let’s assume that we want to remove this effect.</p>
+<div id="challenge1" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge1"></a>
+</h3>
+<div class="callout-content">
+<p>It seems like samples 5 and 6 are separated off from the others in
+gene expression space. Given the group of cells in each sample, why
+might this make sense versus some other pair of samples? What is the
+factor presumably leading to this difference?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
+  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+</button>
+<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div class="accordion-body">
+<p>Samples 5 and 6 were from the same “pool” of cells. Looking at the
+documentation for the dataset under <code>?WTChimeraData</code> we see
+that the pool variable is defined as: “Integer, embryo pool from which
+cell derived; samples with same value are matched.” So samples 5 and 6
+have an experimental factor in common which causes a shared, systematic
+difference in gene expression profiles compared to the other samples.
+That’s why you can see many of isolated blue/orange clusters on the
+first TSNE plot. If you were developing single-cell library preparation
+protocols you might want to preserve this effect to understand how
+variation in pools leads to variation in expression, but for now, given
+that we’re investigate other effects, we’ll want to remove this as
+undesired technical variation.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="correcting-batch-effects">Correcting batch effects<a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a>
 <a class="anchor" aria-label="anchor" href="#correcting-batch-effects"></a></h2>
 <hr class="half-width"><p>We correct the effect of samples by aid of the
@@ -545,6 +583,45 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="fig/multi-sample-rendered-unnamed-chunk-3-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Once we removed the sample batch effect, we can proceed with the
 Differential Expression Analysis.</p>
+<div id="challenge2" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge2"></a>
+</h3>
+<div class="callout-content">
+<p>Having multiple independent samples in each experimental group is
+always helpful, but it particularly important when it comes to batch
+effect correction. Why?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
+  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+</button>
+<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div class="accordion-body">
+<p>It’s important to have multiple samples within each experimental
+group because it helps the batch effect correction algorithm distinguish
+differences due to batch effects (uninteresting) from differences due to
+biology (interesting).</p>
+<p>Imagine you had one sample that received a drug treatment and one
+that did not, each with 10,000 cells. They differ substantially in
+expression of gene X. Is that an important scientific finding? You can’t
+tell for sure, because the effect of drug is indistinguishable from a
+sample-wise batch effect. But if the difference in gene X holds up when
+you have five treated samples and five untreated samples, now you can be
+a bit more confident. Many batch effect correction methods will take
+information on experimental factors as additional arguments, which they
+can use to help remove batch effects while retaining experimental
+differences.</p>
+</div>
+</div>
+</div>
+</div>
 </section><section><h2 class="section-heading" id="differential-expression">Differential Expression<a class="anchor" aria-label="anchor" href="#differential-expression"></a>
 <a class="anchor" aria-label="anchor" href="#differential-expression"></a></h2>
 <hr class="half-width"><p>In order to perform a Differential Expression Analysis, we need to
@@ -739,16 +816,23 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow<span class="op">=</span><span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">2</span>,<span class="fl">3</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="kw">for</span> <span class="op">(</span><span class="va">i</span> <span class="kw">in</span> <span class="fu">seq_len</span><span class="op">(</span><span class="fu">ncol</span><span class="op">(</span><span class="va">y</span><span class="op">)</span><span class="op">)</span><span class="op">)</span> <span class="op">{</span></span>
 <span>    <span class="fu">plotMD</span><span class="op">(</span><span class="va">y</span>, column<span class="op">=</span><span class="va">i</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre>
 </div>
-<figure><img src="fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>Furthermore, we want to check if the samples cluster together based
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-9-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><div class="codewrapper sourceCode" id="cb20">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu">par</span><span class="op">(</span>mfrow <span class="op">=</span> <span class="fu">c</span><span class="op">(</span><span class="fl">1</span>,<span class="fl">1</span><span class="op">)</span><span class="op">)</span></span></code></pre>
+</div>
+<p>Furthermore, we want to check if the samples cluster together based
 on their known factors (like the tomato injection in this case).</p>
 <p>To do so, we use the MDS plot, which is very close to a PCA
 representation.</p>
-<div class="codewrapper sourceCode" id="cb20">
+<div class="codewrapper sourceCode" id="cb21">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -759,11 +843,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 tomato as factors. This design indicates which samples belong to which
 pool and condition, so we can use it in the next step of the
 analysis.</p>
-<div class="codewrapper sourceCode" id="cb21">
+<div class="codewrapper sourceCode" id="cb22">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>, <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
+<code class="sourceCode R"><span><span class="va">design</span> <span class="op">&lt;-</span> <span class="fu">model.matrix</span><span class="op">(</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="fu">factor</span><span class="op">(</span><span class="va">tomato</span><span class="op">)</span>,</span>
+<span>                       data <span class="op">=</span> <span class="va">y</span><span class="op">$</span><span class="va">samples</span><span class="op">)</span></span>
 <span><span class="va">design</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -787,7 +872,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </div>
 <p>Now we can estimate the Negative Binomial (NB) overdispersion
 parameter, to model the mean-variance trend.</p>
-<div class="codewrapper sourceCode" id="cb23">
+<div class="codewrapper sourceCode" id="cb24">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -804,7 +889,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 Biological Coefficient of Variation and the Average log CPM for each
 gene. Additionally, the Common and Trend BCV are shown in
 <code>red</code> and <code>blue</code>.</p>
-<div class="codewrapper sourceCode" id="cb25">
+<div class="codewrapper sourceCode" id="cb26">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -812,12 +897,12 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 </div>
 <figure><img src="fig/multi-sample-rendered-unnamed-chunk-13-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>We then fit a Quasi-Likelihood (QL) negative binomial generalized
 linear model for each gene. The <code>robust=TRUE</code> parameter
-avoids distorsions from highly variable clusters. The QL method includes
+avoids distortions from highly variable clusters. The QL method includes
 an additional dispersion parameter, useful to handle the uncertainty and
 variability of the per-gene variance, which is not well estimated by the
 NB dispersions, so the two dispersion types complement each other in the
 final analysis.</p>
-<div class="codewrapper sourceCode" id="cb26">
+<div class="codewrapper sourceCode" id="cb27">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -830,7 +915,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <pre class="output" tabindex="0"><code>   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
  0.3189  0.9705  1.0901  1.0251  1.1486  1.2151 </code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb28">
+<div class="codewrapper sourceCode" id="cb29">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -845,7 +930,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>QL dispersion estimates for each gene as a function of abundance. Raw
 estimates (black) are shrunk towards the trend (blue) to yield squeezed
 estimates (red).</p>
-<div class="codewrapper sourceCode" id="cb30">
+<div class="codewrapper sourceCode" id="cb31">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -856,7 +941,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 False Discovery Rate (FDR) of 5%. The low amount of DGEs highlights that
 the tomato injection effect has a low influence on the mesenchyme
 cells.</p>
-<div class="codewrapper sourceCode" id="cb31">
+<div class="codewrapper sourceCode" id="cb32">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -871,7 +956,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig               4510
 Up                      5</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb33">
+<div class="codewrapper sourceCode" id="cb34">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -896,7 +981,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <p>All the previous steps can be easily performed with the following
 function for each cell type, thanks to the <code>pseudoBulkDGE</code>
 function in the <code>scran</code> package.</p>
-<div class="codewrapper sourceCode" id="cb35">
+<div class="codewrapper sourceCode" id="cb36">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -914,7 +999,7 @@ <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i
 the results for a cell type. Each of these contains also the
 intermediate results in <code>edgeR</code> format to perform any
 intermediate plot or diagnostic.</p>
-<div class="codewrapper sourceCode" id="cb36">
+<div class="codewrapper sourceCode" id="cb37">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -939,19 +1024,49 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 ENSMUSG00000096730        NA        NA        NA          NA          NA
 ENSMUSG00000095742        NA        NA        NA          NA          NA</code></pre>
 </div>
+<div id="challenge3" class="callout challenge">
+<div class="callout-square">
+<i class="callout-icon" data-feather="zap"></i>
+</div>
+<div class="callout-inner">
+<h3 class="callout-title">Challenge<a class="anchor" aria-label="anchor" href="#challenge3"></a>
+</h3>
+<div class="callout-content">
+<p>Clearly some of the results have low p-values. What about the effect
+sizes? What does <code>logFC</code> stand for?</p>
+</div>
+</div>
+</div>
+<div id="accordionSolution3" class="accordion challenge-accordion accordion-flush">
+<div class="accordion-item">
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution3" aria-expanded="false" aria-controls="collapseSolution3">
+  <h4 class="accordion-header" id="headingSolution3"> Show me the solution </h4>
+</button>
+<div id="collapseSolution3" class="accordion-collapse collapse" aria-labelledby="headingSolution3" data-bs-parent="#accordionSolution3">
+<div class="accordion-body">
+<p>“logFC” stands for log fold-change. Rather than reporting e.g. a
+5-fold increase, it’s better to report a logFC of log(5) = 1.61.
+Additive log scales are easier to work with than multiplicative identity
+scales, once you get used to it.</p>
+<p><code>ENSMUSG00000037664</code> seems to have an estimated logFC of
+about -8. That’s a big difference if it’s real.</p>
+</div>
+</div>
+</div>
+</div>
 </div>
 </section><section><h2 class="section-heading" id="differential-abundance">Differential Abundance<a class="anchor" aria-label="anchor" href="#differential-abundance"></a>
 <a class="anchor" aria-label="anchor" href="#differential-abundance"></a></h2>
-<hr class="half-width"><p>With DA we test for differences between clusters across conditions,
-to investigate which clusters change accordingly to the treatment (the
-tomato injection in our case).</p>
+<hr class="half-width"><p>With DA we look for differences in cluster <em>abundance</em> across
+conditions (the tomato injection in our case), rather than differences
+in gene expression.</p>
 <p>We first setup some code and variables for further analysis, like
 quantifying the number of cells per each cell type and fit a model to
 catch differences between the injected cells and the background.</p>
-<p>The performed steps are very similar to the ones for DEGs analysis,
-but this time we start our analysis on the computed abundances and
-without normalizing the data with TMM.</p>
-<div class="codewrapper sourceCode" id="cb38">
+<p>The steps are very similar to the ones for DEGs analysis, but this
+time we start our analysis on the computed abundances and without
+normalizing the data with TMM.</p>
+<div class="codewrapper sourceCode" id="cb39">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -971,14 +1086,22 @@ <h3 id="background-on-compositional-effect">Background on compositional effect<a
 <p>As mentioned before, in DA we don’t normalize our data with
 <code>calcNormFactors</code> function, because this approach considers
 that most of the input features do not vary between conditions. This
-cannot be applied to this analysis because we have a small number of
-cell populations that all can change due to the treatment. Leaving us to
-normalize only for library depth, which in pseudo-bulk data means by the
-total number of cells in each sample (cell type).</p>
+cannot be applied to DA analysis because we have a small number of cell
+populations that all can change due to the treatment. This means that
+here we will normalize only for library depth, which in pseudo-bulk data
+means by the total number of cells in each sample (cell type).</p>
 <p>On the other hand, this can lead our data to be susceptible to
-compositional effect, that means that our conclusions can be biased by
-the amount of cells present in each cell type. And this amount of cells
-can be totally unbalanced between cell types.</p>
+compositional effect. “Compositional” refers to the fact that the
+cluster abundances in a sample are not independent of one another
+because each cell type is effectively competing for space in the sample.
+They behave like proportions. If cell type A abundance increases in a
+new condition, that means we’ll observe less of everything else, even if
+everything else is unaffected by the new condition.</p>
+<p>Compositionality means that our conclusions can be biased by the
+amount of cells present in each cell type. And this amount of cells can
+be totally unbalanced between cell types. This is particularly
+problematic for cell types that start at or end up near 0 or 100
+percent.</p>
 <p>For example, a specific cell type can be 40% of the total amount of
 cells present in the experiment, while another just the 3%. The
 differences in terms of abundance of these cell types are detected
@@ -995,7 +1118,7 @@ <h3 id="assuming-most-labels-do-not-change">Assuming most labels do not change<a
 <p>To do so, we first normalize the data with
 <code>calcNormFactors</code> and then we fit and estimate a QL-model for
 our abundance data.</p>
-<div class="codewrapper sourceCode" id="cb39">
+<div class="codewrapper sourceCode" id="cb40">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1007,14 +1130,17 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </h3>
 <pre class="output" tabindex="0"><code>[1] 1.1029040 1.0228173 1.0695358 0.7686501 1.0402941 1.0365354</code></pre>
 </div>
-<p>We then follow the already seen edgeR analysis steps.</p>
-<div class="codewrapper sourceCode" id="cb41">
+<p>We then use edgeR in a manner similar to what we ran before:</p>
+<div class="codewrapper sourceCode" id="cb42">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">y.ab2</span> <span class="op">&lt;-</span> <span class="fu">estimateDisp</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, trend<span class="op">=</span><span class="st">"none"</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">fit.ab2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFit</span><span class="op">(</span><span class="va">y.ab2</span>, <span class="va">design</span>, robust<span class="op">=</span><span class="cn">TRUE</span>, abundance.trend<span class="op">=</span><span class="cn">FALSE</span><span class="op">)</span></span>
+<span></span>
 <span><span class="va">res2</span> <span class="op">&lt;-</span> <span class="fu">glmQLFTest</span><span class="op">(</span><span class="va">fit.ab2</span>, coef<span class="op">=</span><span class="fu">ncol</span><span class="op">(</span><span class="va">design</span><span class="op">)</span><span class="op">)</span></span>
+<span></span>
 <span><span class="fu">summary</span><span class="op">(</span><span class="fu">decideTests</span><span class="op">(</span><span class="va">res2</span><span class="op">)</span><span class="op">)</span></span></code></pre>
 </div>
 <div class="codewrapper">
@@ -1025,7 +1151,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 29
 Up                      1</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb43">
+<div class="codewrapper sourceCode" id="cb44">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1051,15 +1177,16 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 <div class="section level3">
 <h3 id="testing-against-a-log-fold-change-threshold">Testing against a log-fold change threshold<a class="anchor" aria-label="anchor" href="#testing-against-a-log-fold-change-threshold"></a></h3>
 <p>This other approach assumes that the composition bias introduces a
-spurious log2-fold change of no more than a quantity for a non-DA label.
-In other words, we interpret this as the maximum log-fold change in the
-total number of cells given by DA in other labels. On the other hand,
-when choosing , we should not consider fold-differences in the totals
-due to differences in capture efficiency or the size of the original
-cell population are not attributable to composition bias. We then
-mitigate the effect of composition biases by testing each label for
+spurious log2-fold change of no more than a quantity for a non-DA
+label.</p>
+<p>In other words, we interpret this as the maximum log-fold change in
+the total number of cells given by DA in other labels. On the other
+hand, when choosing , we should not consider fold-differences in the
+totals due to differences in capture efficiency or the size of the
+original cell population are not attributable to composition bias. We
+then mitigate the effect of composition biases by testing each label for
 changes in abundance beyond .</p>
-<div class="codewrapper sourceCode" id="cb45">
+<div class="codewrapper sourceCode" id="cb46">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1074,7 +1201,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 NotSig                 32
 Up                      0</code></pre>
 </div>
-<div class="codewrapper sourceCode" id="cb47">
+<div class="codewrapper sourceCode" id="cb48">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1112,7 +1239,7 @@ <h3 class="code-label">OUTPUT<i aria-hidden="true" data-feather="chevron-left"><
 </div>
 </section><section><h2 class="section-heading" id="session-info">Session Info<a class="anchor" aria-label="anchor" href="#session-info"></a>
 <a class="anchor" aria-label="anchor" href="#session-info"></a></h2>
-<hr class="half-width"><div class="codewrapper sourceCode" id="cb49">
+<hr class="half-width"><div class="codewrapper sourceCode" id="cb50">
 <h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
 </h3>
 <pre class="downlit sourceCode r">
@@ -1231,33 +1358,47 @@ <h4 class="accordion-header" id="headingHint1"> Give me a hint </h4>
 </button>
 <div id="collapseHint1" class="accordion-collapse collapse" aria-labelledby="headingHint1" data-bs-parent="#accordionHint1">
 <div class="accordion-body">
-
+<p>Remember, you can subset SingleCellExperiments with logical indices,
+just like a matrix. You can also access their column data with the
+<code>$</code> accessor, like a data frame.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution1" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution4" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution1" aria-expanded="false" aria-controls="collapseSolution1">
-  <h4 class="accordion-header" id="headingSolution1"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution4" aria-expanded="false" aria-controls="collapseSolution4">
+  <h4 class="accordion-header" id="headingSolution4"> Show me the solution </h4>
 </button>
-<div id="collapseSolution1" class="accordion-collapse collapse" aria-labelledby="headingSolution1" data-bs-parent="#accordionSolution1">
+<div id="collapseSolution4" class="accordion-collapse collapse" aria-labelledby="headingSolution4" data-bs-parent="#accordionSolution4">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb52">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">summed.filt.subset</span> <span class="op">=</span> <span class="va">summed.filt</span><span class="op">[</span>,<span class="va">summed.filt</span><span class="op">$</span><span class="va">pool</span> <span class="op">!=</span> <span class="fl">3</span><span class="op">]</span></span>
+<span></span>
+<span><span class="va">de.results</span> <span class="op">&lt;-</span> <span class="fu">pseudoBulkDGE</span><span class="op">(</span><span class="va">summed.filt.subset</span>, </span>
+<span>    label<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">celltype.mapped</span>,</span>
+<span>    design<span class="op">=</span><span class="op">~</span><span class="fu">factor</span><span class="op">(</span><span class="va">pool</span><span class="op">)</span> <span class="op">+</span> <span class="va">tomato</span>,</span>
+<span>    coef<span class="op">=</span><span class="st">"tomatoTRUE"</span>,</span>
+<span>    condition<span class="op">=</span><span class="va">summed.filt.subset</span><span class="op">$</span><span class="va">tomato</span> </span>
+<span><span class="op">)</span></span></code></pre>
+</div>
 </div>
 </div>
 </div>
 </div>
-<div id="exercise-2-muscat" class="callout challenge">
+<div id="exercise-2" class="callout challenge">
 <div class="callout-square">
 <i class="callout-icon" data-feather="zap"></i>
 </div>
-<div id="exercise-2-muscat" class="callout-inner">
-<h3 class="callout-title">Exercise 2: <code>muscat</code><a class="anchor" aria-label="anchor" href="#exercise-2-muscat"></a>
+<div id="exercise-2" class="callout-inner">
+<h3 class="callout-title">Exercise 2:<a class="anchor" aria-label="anchor" href="#exercise-2"></a>
 </h3>
 <div class="callout-content">
-<p>Test differential expressed genes computed with <code>muscat</code>
-package and check for differences in the results.</p>
+<p>Use the <code>pheatmap</code> package to create a heatmap of the
+abundances table. Does it comport with the model results?</p>
 </div>
 </div>
 </div>
@@ -1268,19 +1409,33 @@ <h4 class="accordion-header" id="headingHint2"> Give me a hint </h4>
 </button>
 <div id="collapseHint2" class="accordion-collapse collapse" aria-labelledby="headingHint2" data-bs-parent="#accordionHint2">
 <div class="accordion-body">
-
+<p>You can just hand <code>pheatmap()</code> a matrix as its only
+argument. It has a million options, but the defaults are usually pretty
+good.</p>
 </div>
 </div>
 </div>
 </div>
-<div id="accordionSolution2" class="accordion challenge-accordion accordion-flush">
+<div id="accordionSolution5" class="accordion challenge-accordion accordion-flush">
 <div class="accordion-item">
-<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution2" aria-expanded="false" aria-controls="collapseSolution2">
-  <h4 class="accordion-header" id="headingSolution2"> Show me the solution </h4>
+<button class="accordion-button solution-button collapsed" type="button" data-bs-toggle="collapse" data-bs-target="#collapseSolution5" aria-expanded="false" aria-controls="collapseSolution5">
+  <h4 class="accordion-header" id="headingSolution5"> Show me the solution </h4>
 </button>
-<div id="collapseSolution2" class="accordion-collapse collapse" aria-labelledby="headingSolution2" data-bs-parent="#accordionSolution2">
+<div id="collapseSolution5" class="accordion-collapse collapse" aria-labelledby="headingSolution5" data-bs-parent="#accordionSolution5">
 <div class="accordion-body">
-<p>TODO</p>
+<div class="codewrapper sourceCode" id="cb53">
+<h3 class="code-label">R<i aria-hidden="true" data-feather="chevron-left"></i><i aria-hidden="true" data-feather="chevron-right"></i>
+</h3>
+<pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="kw">library</span><span class="op">(</span><span class="va">pheatmap</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">pheatmap</span><span class="op">(</span><span class="va">y.ab</span><span class="op">$</span><span class="va">counts</span><span class="op">)</span></span></code></pre>
+</div>
+<figure><img src="fig/multi-sample-rendered-unnamed-chunk-25-1.png" style="display: block; margin: auto;" class="figure mx-auto d-block"></figure><p>The top DA result was a decrease in ExE ectoderm in the tomato
+condition, which you can sort of see, especially if you
+<code>log1p()</code> the counts or discard rows that show much higher
+values. ExE ectoderm counts were much higher in samples 8 and 10
+compared to 5, 7, and 9.</p>
 </div>
 </div>
 </div>
@@ -1395,8 +1550,8 @@ <h3 class="callout-title">Key Points<a class="anchor" aria-label="anchor" href="
   "url": "https://ccb-hms.github.io/osca-carpentries/multi-sample.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/multi-sample.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/pkgdown.yml b/pkgdown.yml
index 302bf31..9abdc02 100644
--- a/pkgdown.yml
+++ b/pkgdown.yml
@@ -2,4 +2,4 @@ pandoc: 3.1.11
 pkgdown: 2.1.0
 pkgdown_sha: ~
 articles: {}
-last_built: 2024-08-13T01:11Z
+last_built: 2024-08-19T18:01Z
diff --git a/profiles.html b/profiles.html
index cc02fb6..f2ccf77 100644
--- a/profiles.html
+++ b/profiles.html
@@ -352,8 +352,8 @@ <h1>Learner Profiles</h1>
   "url": "https://ccb-hms.github.io/osca-carpentries/profiles.html",
   "identifier": "https://ccb-hms.github.io/osca-carpentries/profiles.html",
   "dateCreated": "2024-01-10",
-  "dateModified": "2024-08-13",
-  "datePublished": "2024-08-13"
+  "dateModified": "2024-08-19",
+  "datePublished": "2024-08-19"
 }
 
   </script><script>
diff --git a/reference.html b/reference.html
index 09eb1b2..4576422 100644
--- a/reference.html
+++ b/reference.html
@@ -412,7 +412,7 @@ <h1>Reference</h1>
   "identifier": "https://ccb-hms.github.io/osca-carpentries/reference.html",
   "dateCreated": "2024-01-10",
   "dateModified": "2024-07-02",
-  "datePublished": "2024-08-13"
+  "datePublished": "2024-08-19"
 }
 
   </script><script>