From 899816d786b48eb05d4ac59af9a8eca49f17153d Mon Sep 17 00:00:00 2001
From: Nikola Grubor <nickgrubor@gmail.com>
Date: Wed, 20 Nov 2024 01:51:03 +0100
Subject: [PATCH] week 08

---
 docs/index.html                               |   70 +-
 docs/search.json                              |  107 +-
 docs/slides/08_rangovi/prezentacija.html      | 1130 +++++++++++++++++
 .../figure-revealjs/unnamed-chunk-2-1.png     |  Bin 0 -> 22298 bytes
 docs/slides/08_rangovi/slike/jenga.png        |  Bin 0 -> 128379 bytes
 docs/slides/08_rangovi/slike/logo.png         |  Bin 0 -> 5240 bytes
 docs/slides/08_rangovi/slike/mwu.jpg          |  Bin 0 -> 40249 bytes
 docs/slides/08_rangovi/slike/sumrank.png      |  Bin 0 -> 40066 bytes
 index.qmd                                     |    4 +-
 slides/08_rangovi/prezentacija.qmd            |  175 +++
 slides/08_rangovi/slike/jenga.png             |  Bin 0 -> 128379 bytes
 slides/08_rangovi/slike/logo.png              |  Bin 0 -> 5240 bytes
 slides/08_rangovi/slike/mwu.jpg               |  Bin 0 -> 40249 bytes
 slides/08_rangovi/slike/sumrank.png           |  Bin 0 -> 40066 bytes
 14 files changed, 1451 insertions(+), 35 deletions(-)
 create mode 100644 docs/slides/08_rangovi/prezentacija.html
 create mode 100644 docs/slides/08_rangovi/prezentacija_files/figure-revealjs/unnamed-chunk-2-1.png
 create mode 100644 docs/slides/08_rangovi/slike/jenga.png
 create mode 100644 docs/slides/08_rangovi/slike/logo.png
 create mode 100644 docs/slides/08_rangovi/slike/mwu.jpg
 create mode 100644 docs/slides/08_rangovi/slike/sumrank.png
 create mode 100644 slides/08_rangovi/prezentacija.qmd
 create mode 100644 slides/08_rangovi/slike/jenga.png
 create mode 100644 slides/08_rangovi/slike/logo.png
 create mode 100644 slides/08_rangovi/slike/mwu.jpg
 create mode 100644 slides/08_rangovi/slike/sumrank.png

diff --git a/docs/index.html b/docs/index.html
index 32c6766..62bb07c 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -131,10 +131,10 @@ <h3 id="lista-prezentacija">Lista prezentacija</h3>
   
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@@ -152,7 +152,7 @@ <h3 id="lista-prezentacija">Lista prezentacija</h3>
 
   
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-      <table class="table table-borderless" id="tinytable_i9539dfmhdsrv6qta809" style="width: auto; margin-left: auto; margin-right: auto;" data-quarto-disable-processing="true">
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         <thead>
         
               <tr>
@@ -192,10 +192,14 @@ <h3 id="lista-prezentacija">Lista prezentacija</h3>
                 </tr>
                 <tr>
                   <td>8</td>
-                  <td><a href="./slides/09_korelacija/prezentacija.html">Korelacija</a></td>
+                  <td><a href="./slides/08_rangovi/prezentacija.html">Testiranje hipoteza o rangovima</a></td>
                 </tr>
                 <tr>
                   <td>9</td>
+                  <td><a href="./slides/09_korelacija/prezentacija.html">Korelacija</a></td>
+                </tr>
+                <tr>
+                  <td>10</td>
                   <td><a href="./slides/10_regresija/prezentacija.html">Regresija</a></td>
                 </tr>
         </tbody>
@@ -203,12 +207,12 @@ <h3 id="lista-prezentacija">Lista prezentacija</h3>
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diff --git a/docs/search.json b/docs/search.json
index 68bfd95..5a9cb9c 100644
--- a/docs/search.json
+++ b/docs/search.json
@@ -1271,7 +1271,7 @@
     "href": "index.html",
     "title": "Osnovni kurs medicinske statistike i informatike",
     "section": "",
-    "text": "Osnovni kurs medicinske statistike i informatike\n\n\n\n\n\n\n\n\n\nDobrodošli na kurs medicinske statistike i informatike! Sve informacije vezane za kurs i termine polaganja možete pronaći na sajtu instituta. Ova web stranica služi kao lični repozitorijum kako bi prezentacije sa vežbi bile uvek dostupne onima koji to žele.\nLista prezentacija\n\n\n \n\n  \n    \n    \n    tinytable_i9539dfmhdsrv6qta809\n    \n    \n    \n    \n  \n\n  \n    \n      \n        \n        \n              \n                Nedelja\n                Tema\n              \n        \n        \n        \n                \n                  1\n                  Uvod u medicinsku statistiku (eng)\n                \n                \n                  2\n                  Sređivanje podataka\n                \n                \n                  3\n                  Statističko opisivanje podataka\n                \n                \n                  4\n                  Verovatnoća i raspodele verovatnoća (eng)\n                \n                \n                  5\n                  Populacija i uzorak\n                \n                \n                  6\n                  Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama\n                \n                \n                  7\n                  Testiranje hipoteza o učestalostima\n                \n                \n                  8\n                  Korelacija\n                \n                \n                  9\n                  Regresija"
+    "text": "Osnovni kurs medicinske statistike i informatike\n\n\n\n\n\n\n\n\n\nDobrodošli na kurs medicinske statistike i informatike! Sve informacije vezane za kurs i termine polaganja možete pronaći na sajtu instituta. Ova web stranica služi kao lični repozitorijum kako bi prezentacije sa vežbi bile uvek dostupne onima koji to žele.\nLista prezentacija\n\n\n \n\n  \n    \n    \n    tinytable_vuyeoonzm8rpdjw6zfn9\n    \n    \n    \n    \n  \n\n  \n    \n      \n        \n        \n              \n                Nedelja\n                Tema\n              \n        \n        \n        \n                \n                  1\n                  Uvod u medicinsku statistiku (eng)\n                \n                \n                  2\n                  Sređivanje podataka\n                \n                \n                  3\n                  Statističko opisivanje podataka\n                \n                \n                  4\n                  Verovatnoća i raspodele verovatnoća (eng)\n                \n                \n                  5\n                  Populacija i uzorak\n                \n                \n                  6\n                  Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama\n                \n                \n                  7\n                  Testiranje hipoteza o učestalostima\n                \n                \n                  8\n                  Testiranje hipoteza o rangovima\n                \n                \n                  9\n                  Korelacija\n                \n                \n                  10\n                  Regresija"
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@@ -2847,5 +2847,110 @@
     "title": "Testiranje hipoteza o učestalostima",
     "section": "Primer biranja testa",
     "text": "Primer biranja testa"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#parametarski-i-neparametarski-testovi",
+    "href": "slides/08_rangovi/prezentacija.html#parametarski-i-neparametarski-testovi",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Parametarski i neparametarski testovi",
+    "text": "Parametarski i neparametarski testovi\n\n\n\nTestovi koji porede artmetičke sredine pretpostavljaju normalnu distribuciju\nNormalna raspodela definisana je parametrima: arit. sred. i standard. devijacijom\nTestovi koji se ne oslanjaju na raspodele su neparametarski"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#koraci-u-statističkom-zaključivanju",
+    "href": "slides/08_rangovi/prezentacija.html#koraci-u-statističkom-zaključivanju",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Koraci u statističkom zaključivanju",
+    "text": "Koraci u statističkom zaključivanju"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#statistički-testovi-do-sad",
+    "href": "slides/08_rangovi/prezentacija.html#statistički-testovi-do-sad",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Statistički testovi do sad",
+    "text": "Statistički testovi do sad"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#zašto-rangovi",
+    "href": "slides/08_rangovi/prezentacija.html#zašto-rangovi",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Zašto rangovi?",
+    "text": "Zašto rangovi?\n\n\n\nManje pretpostavki je bolje\nPodaci uglavnom nisu normalno raspodeljeni\nGubimo statističku moć ukoliko podaci zapravo ispunjavaju uslove za parametrijski (npr. Studentov) test"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#test-sume-rangova",
+    "href": "slides/08_rangovi/prezentacija.html#test-sume-rangova",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Test sume rangova",
+    "text": "Test sume rangova\nMann-Whitney U / Wilcoxon rank-sum test"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#provera-normalnosti-numeričkih-podataka",
+    "href": "slides/08_rangovi/prezentacija.html#provera-normalnosti-numeričkih-podataka",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Provera normalnosti numeričkih podataka",
+    "text": "Provera normalnosti numeričkih podataka\n\nKoeficijent varijacije\nSkew i Kurtosis\nQQ Plot\nHistogram\nStatističkim testovima za normalnost"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#vežba-mmw-test",
+    "href": "slides/08_rangovi/prezentacija.html#vežba-mmw-test",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Vežba: MMW Test",
+    "text": "Vežba: MMW Test\n\nIspitati da li se osobe sa različitim\nnadmorskim visinama prebivališta\nrazlikuju prema koncentraciji fibrinogena."
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#test-ekvivalentnih-parova",
+    "href": "slides/08_rangovi/prezentacija.html#test-ekvivalentnih-parova",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Test ekvivalentnih parova",
+    "text": "Test ekvivalentnih parova\nWilcoxon signed rank test\nTip podataka:\n\nNumerički ne-normalni podaci, ordinalni podaci\n\nUslovi:\n\nUzorak čine zavisne jedinice\nPodaci mogu da se rangiraju"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#vežba-test-ekvivalentnih-parova",
+    "href": "slides/08_rangovi/prezentacija.html#vežba-test-ekvivalentnih-parova",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Vežba: Test ekvivalentnih parova",
+    "text": "Vežba: Test ekvivalentnih parova\n\nU bazi Aritmije MW W McN.xlsx date su\nvrednosti Lp(a) pre početka terapije i\nmesec dana posle započete terapije.\nCilj istraživača bio je da ispita da li dolazi\ndo promene vrednosti Lp(a) posle davanja antilipemika."
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#izbor-testa",
+    "href": "slides/08_rangovi/prezentacija.html#izbor-testa",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Izbor testa",
+    "text": "Izbor testa\n\nJedan ili dva uzorka\nPonovljena merenja ili ne\nTip podataka (numerički, ordinalni, kategorije)\nNa osnovu deskriptivnih mera određujemo da li podaci ispunjavaju uslov normalnosti"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#struktura-kursa",
+    "href": "slides/08_rangovi/prezentacija.html#struktura-kursa",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Struktura kursa",
+    "text": "Struktura kursa\n\n\n \n\n  \n    \n    \n    tinytable_i0bb5u4a7ekszse4uemu\n    \n    \n    \n    \n  \n\n  \n    \n      \n        \n        \n              \n                Nedelja\n                Tema\n              \n        \n        \n        \n                \n                   1\n                  Uvod u medicinsku statistiku                                           \n                \n                \n                   2\n                  Sređivanje podataka                                                    \n                \n                \n                   3\n                  Statističko opisivanje podataka                                        \n                \n                \n                   4\n                  Verovatnoća i raspodele verovatnoća                                    \n                \n                \n                   5\n                  Populacija i uzorak                                                    \n                \n                \n                   6\n                  Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama\n                \n                \n                   7\n                  Testiranje hipoteza o učestalostima                                    \n                \n                \n                   8\n                  Testiranje hipoteza o rangovima                                        \n                \n                \n                   9\n                  Korelacija                                                             \n                \n                \n                  10\n                  Regresija / Kolokvijum                                                 \n                \n                \n                  11\n                  Podaci, informacije i znanje                                           \n                \n                \n                  12\n                  Zdravstveni informacioni sistem                                        \n                \n                \n                  13\n                  Mere dijagnostičke tačnosti                                            \n                \n                \n                  14\n                  Medicinsko odlučivanje                                                 \n                \n                \n                  15\n                  Bioinformatika"
+  },
+  {
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+    "href": "slides/08_rangovi/prezentacija.html#recept-za-testiranje-nulte-hipoteze",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Recept za testiranje nulte hipoteze",
+    "text": "Recept za testiranje nulte hipoteze\n\nFormiranje hipoteze koja predstavlja naše mišljenje (pre nego što smo videli podatke)\nOdređivanje nulte i alternativne hipoteze\nPrikupljanje podataka relevantnih za našu hipotezu\nNapraviti model koji predstavlja podatke i izračunati test statistiku\nIzračunati verovatnoću da naši podaci daju dobijenu test statistiku ako je nulta hipoteza tačna\nProceniti “statističku značajnost”"
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#uslovi-za-test-sume-rangova",
+    "href": "slides/08_rangovi/prezentacija.html#uslovi-za-test-sume-rangova",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Uslovi za test sume rangova",
+    "text": "Uslovi za test sume rangova\nTip podataka:\n\nNumerički ne-normalni podaci, ordinalni podaci\n\nUslovi:\n\nUzorak čine nezavisne jedinice\nPodaci mogu da se rangiraju\n\n\n\n\n\n\n\nUpozorenje\n\n\nIma manju statističku moć od parametarskih, ako su uslovi za parametarske testove ispunjeni."
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#vežba-mww-test",
+    "href": "slides/08_rangovi/prezentacija.html#vežba-mww-test",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Vežba: MWW test",
+    "text": "Vežba: MWW test\n\nIspitati da li se osobe sa različitim\nnadmorskim visinama prebivališta\nrazlikuju prema koncentraciji fibrinogena."
+  },
+  {
+    "objectID": "slides/08_rangovi/prezentacija.html#test-ekvivalentnih-parova-wilcoxon-signed-rank-test",
+    "href": "slides/08_rangovi/prezentacija.html#test-ekvivalentnih-parova-wilcoxon-signed-rank-test",
+    "title": "Testiranje hipoteza o rangovima",
+    "section": "Test ekvivalentnih parova Wilcoxon signed rank test)",
+    "text": "Test ekvivalentnih parova Wilcoxon signed rank test)\nTip podataka:\n\nNumerički ne-normalni podaci, ordinalni podaci\n\nUslovi:\n\nUzorak čine zavisne jedinice\nPodaci mogu da se rangiraju\n\n\n\n\n\n\n\nUpozorenje\n\n\nIma manju statističku moć od parametarskih, ako su uslovi za parametarske testove ispunjeni."
   }
 ]
\ No newline at end of file
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+<body class="quarto-dark">
+  <div class="reveal">
+    <div class="slides">
+
+<section id="title-slide" class="quarto-title-block center">
+  <h1 class="title">Testiranje hipoteza o rangovima</h1>
+
+<div class="quarto-title-authors">
+<div class="quarto-title-author">
+<div class="quarto-title-author-name">
+Dr Nikola Grubor 
+</div>
+</div>
+</div>
+
+  <p class="date">2024-11-20</p>
+</section>
+<section id="parametarski-i-neparametarski-testovi" class="slide level2 smaller">
+<h2>Parametarski i neparametarski testovi</h2>
+<div class="columns">
+<div class="column">
+<ul>
+<li>Testovi koji porede artmetičke sredine pretpostavljaju normalnu distribuciju</li>
+<li>Normalna raspodela definisana je <span class="yellow">parametrima</span>: arit. sred. i standard. devijacijom</li>
+<li>Testovi koji se ne oslanjaju na raspodele su <span class="yellow">neparametarski</span></li>
+</ul>
+</div><div class="column">
+<div class="cell">
+<div class="cell-output-display">
+<div>
+<figure>
+<p><img data-src="prezentacija_files/figure-revealjs/unnamed-chunk-2-1.png" width="960"></p>
+</figure>
+</div>
+</div>
+</div>
+</div>
+</div>
+</section>
+<section id="recept-za-testiranje-nulte-hipoteze" class="slide level2">
+<h2>Recept za testiranje nulte hipoteze</h2>
+<ol type="1">
+<li>Formiranje <span class="yellow">hipoteze</span> koja predstavlja naše mišljenje (pre nego što smo videli podatke)</li>
+<li>Određivanje nulte i alternativne hipoteze</li>
+<li>Prikupljanje podataka <em>relevantnih</em> za našu hipotezu</li>
+<li>Napraviti model koji predstavlja podatke i izračunati <span class="yellow">test statistiku</span></li>
+<li>Izračunati verovatnoću da naši podaci daju dobijenu test statistiku ako je nulta hipoteza tačna</li>
+<li>Proceniti “statističku značajnost”</li>
+</ol>
+</section>
+<section id="zašto-rangovi" class="slide level2">
+<h2>Zašto rangovi?</h2>
+<div class="columns">
+<div class="column">
+<ul>
+<li>Manje pretpostavki je bolje</li>
+<li>Podaci uglavnom nisu normalno raspodeljeni</li>
+<li>Gubimo statističku moć ukoliko podaci zapravo ispunjavaju uslove za parametrijski (npr. Studentov) test</li>
+</ul>
+</div><div class="column">
+<p><img data-src="slike/jenga.png"></p>
+</div>
+</div>
+</section>
+<section id="test-sume-rangova" class="slide level2">
+<h2>Test sume rangova</h2>
+<p>Mann-Whitney U / Wilcoxon rank-sum test</p>
+
+<img data-src="slike/sumrank.png" class="quarto-figure quarto-figure-center r-stretch"></section>
+<section id="uslovi-za-test-sume-rangova" class="slide level2">
+<h2>Uslovi za test sume rangova</h2>
+<p>Tip podataka:</p>
+<ul>
+<li>Numerički ne-normalni podaci, ordinalni podaci</li>
+</ul>
+<p>Uslovi:</p>
+<ul>
+<li>Uzorak čine nezavisne jedinice</li>
+<li>Podaci mogu da se rangiraju</li>
+</ul>
+<div class="callout callout-warning callout-titled callout-style-default">
+<div class="callout-body">
+<div class="callout-title">
+<div class="callout-icon-container">
+<i class="callout-icon"></i>
+</div>
+<p><strong>Upozorenje</strong></p>
+</div>
+<div class="callout-content">
+<p>Ima manju statističku moć od parametarskih, ako su uslovi za parametarske testove ispunjeni.</p>
+</div>
+</div>
+</div>
+</section>
+<section id="provera-normalnosti-numeričkih-podataka" class="slide level2">
+<h2>Provera normalnosti numeričkih podataka</h2>
+<ul>
+<li><span class="yellow">Koeficijent varijacije</span></li>
+<li>Skew i Kurtosis</li>
+<li>QQ Plot</li>
+<li><span class="yellow">Histogram</span></li>
+<li>Statističkim testovima za normalnost</li>
+</ul>
+</section>
+<section id="vežba-mww-test" class="slide level2">
+<h2>Vežba: MWW test</h2>
+<div class="r-fit-text">
+<p>Ispitati da li se osobe sa različitim</p>
+<p>nadmorskim visinama prebivališta</p>
+<p>razlikuju prema koncentraciji fibrinogena.</p>
+</div>
+
+<img data-src="slike/mwu.jpg" class="quarto-figure quarto-figure-center r-stretch"></section>
+<section id="test-ekvivalentnih-parova" class="slide level2">
+<h2>Test ekvivalentnih parova</h2>
+<h3 id="wilcoxon-signed-rank-test">Wilcoxon signed rank test</h3>
+<p>Tip podataka:</p>
+<ul>
+<li>Numerički ne-normalni podaci, ordinalni podaci</li>
+</ul>
+<p>Uslovi:</p>
+<ul>
+<li>Uzorak čine <span class="yellow">zavisne</span> jedinice</li>
+<li>Podaci mogu da se rangiraju</li>
+</ul>
+</section>
+<section id="vežba-test-ekvivalentnih-parova" class="slide level2">
+<h2>Vežba: Test ekvivalentnih parova</h2>
+<div class="r-fit-text">
+<p>U bazi <span class="yellow">Aritmije MW W McN.xlsx</span> date su</p>
+<p>vrednosti Lp(a) pre početka terapije i</p>
+<p>mesec dana posle započete terapije.</p>
+<p>Cilj istraživača bio je da ispita da li dolazi</p>
+<p>do promene vrednosti Lp(a) posle davanja antilipemika.</p>
+</div>
+</section>
+<section id="izbor-testa" class="slide level2">
+<h2>Izbor testa</h2>
+<ul>
+<li>Jedan ili dva uzorka</li>
+<li>Ponovljena merenja ili ne</li>
+<li>Tip podataka (numerički, ordinalni, kategorije)</li>
+<li>Na osnovu deskriptivnih mera određujemo da li podaci ispunjavaju uslov normalnosti</li>
+</ul>
+</section>
+<section id="struktura-kursa" class="slide level2">
+<h2>Struktura kursa</h2>
+<div class="cell">
+<div class="cell-output-display">
+ 
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+        <thead>
+        
+              <tr>
+                <th scope="col">Nedelja</th>
+                <th scope="col">Tema</th>
+              </tr>
+        </thead>
+        
+        <tbody>
+                <tr>
+                  <td> 1</td>
+                  <td>Uvod u medicinsku statistiku                                           </td>
+                </tr>
+                <tr>
+                  <td> 2</td>
+                  <td>Sređivanje podataka                                                    </td>
+                </tr>
+                <tr>
+                  <td> 3</td>
+                  <td>Statističko opisivanje podataka                                        </td>
+                </tr>
+                <tr>
+                  <td> 4</td>
+                  <td>Verovatnoća i raspodele verovatnoća                                    </td>
+                </tr>
+                <tr>
+                  <td> 5</td>
+                  <td>Populacija i uzorak                                                    </td>
+                </tr>
+                <tr>
+                  <td> 6</td>
+                  <td>Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama</td>
+                </tr>
+                <tr>
+                  <td> 7</td>
+                  <td>Testiranje hipoteza o učestalostima                                    </td>
+                </tr>
+                <tr>
+                  <td> 8</td>
+                  <td>Testiranje hipoteza o rangovima                                        </td>
+                </tr>
+                <tr>
+                  <td> 9</td>
+                  <td>Korelacija                                                             </td>
+                </tr>
+                <tr>
+                  <td>10</td>
+                  <td>Regresija / Kolokvijum                                                 </td>
+                </tr>
+                <tr>
+                  <td>11</td>
+                  <td>Podaci, informacije i znanje                                           </td>
+                </tr>
+                <tr>
+                  <td>12</td>
+                  <td>Zdravstveni informacioni sistem                                        </td>
+                </tr>
+                <tr>
+                  <td>13</td>
+                  <td>Mere dijagnostičke tačnosti                                            </td>
+                </tr>
+                <tr>
+                  <td>14</td>
+                  <td>Medicinsko odlučivanje                                                 </td>
+                </tr>
+                <tr>
+                  <td>15</td>
+                  <td>Bioinformatika                                                         </td>
+                </tr>
+        </tbody>
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diff --git a/index.qmd b/index.qmd
index 20c9f20..b17c998 100644
--- a/index.qmd
+++ b/index.qmd
@@ -30,7 +30,7 @@ Dobrodošli na kurs medicinske statistike i informatike! Sve informacije vezane
 #| echo: false
 
 dat <- data.frame(
-  Nedelja = 1:9,
+  Nedelja = 1:10,
   Tema = c(
     "[Uvod u medicinsku statistiku](slides/01_uvod/prezentacija.qmd) ([eng](slides/01_uvod/pres.qmd))",
     "[Sređivanje podataka](slides/02_sredjivanje/prezentacija.qmd)",
@@ -39,7 +39,7 @@ dat <- data.frame(
     "[Populacija i uzorak](slides/05_uzorak/prezentacija.qmd)",
     "[Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama](slides/06_hipoteze/prezentacija.qmd)",
     "[Testiranje hipoteza o učestalostima](slides/07_hi_kvadrat/prezentacija.qmd)",
-    # "[Testiranje hipoteza o rangovima]()",
+    "[Testiranje hipoteza o rangovima](slides/08_rangovi/prezentacija.qmd)",
     "[Korelacija](slides/09_korelacija/prezentacija.qmd)",
     "[Regresija](slides/10_regresija/prezentacija.qmd)"
     # "[Podaci, informacije i znanje]()",
diff --git a/slides/08_rangovi/prezentacija.qmd b/slides/08_rangovi/prezentacija.qmd
new file mode 100644
index 0000000..6a68393
--- /dev/null
+++ b/slides/08_rangovi/prezentacija.qmd
@@ -0,0 +1,175 @@
+---
+title: "Testiranje hipoteza o rangovima"
+date: last-modified
+author: "Dr Nikola Grubor"
+# institute: "Institut za Medicinsku Statistiku i Informatiku"
+logo: "slike/logo.png"
+lang: sr-Latn
+---
+```{r}
+library(glue)
+library(here)
+library(tidyverse)
+library(tinytable)
+library(gtsummary)
+source(file = here("slides", "theme", "ggthemes.R"))
+```
+
+## Parametarski i neparametarski testovi {.smaller}
+
+:::: columns
+
+::: {.column}
+
+- Testovi koji porede artmetičke sredine pretpostavljaju normalnu distribuciju
+- Normalna raspodela definisana je [parametrima]{.yellow}: arit. sred. i standard. devijacijom
+- Testovi koji se ne oslanjaju na raspodele su [neparametarski]{.yellow}
+
+:::
+
+::: {.column}
+
+```{r}
+#| fig-asp: 1
+p1 <- ggplot(data = data.frame(x = c(-5, 5)), aes(x)) +
+  stat_function(fun = dnorm, n = 101, args = list(mean = 0, sd = 1),
+                col = "#F4BA02", linewidth = 1) +
+  stat_function(fun = dnorm, n = 101, args = list(mean = 0, sd = 2),
+                col = "#F4BA02", linetype = 2, linewidth = 1) +
+  stat_function(fun = dnorm, n = 101, args = list(mean = 0, sd = 3),
+                col = "#F4BA02", linetype = 3, linewidth = 1) +
+  ylab("") +
+  scale_y_continuous(breaks = NULL) +
+  ggdist::theme_ggdist(base_size = 18) +
+  theme_blue()
+p1
+```
+
+
+:::
+
+::::
+
+## Recept za testiranje nulte hipoteze
+
+1. Formiranje [hipoteze]{.yellow} koja predstavlja naše mišljenje (pre nego što smo videli podatke)
+2. Određivanje nulte i alternativne hipoteze
+3. Prikupljanje podataka *relevantnih* za našu hipotezu
+4. Napraviti model koji predstavlja podatke i izračunati [test statistiku]{.yellow}
+5. Izračunati verovatnoću da naši podaci daju dobijenu test statistiku ako je nulta hipoteza tačna
+6. Proceniti "statističku značajnost"
+
+## Zašto rangovi?
+
+:::: columns
+
+::: {.column}
+
+- Manje pretpostavki je bolje
+- Podaci uglavnom nisu normalno raspodeljeni
+- Gubimo statističku moć ukoliko podaci zapravo ispunjavaju uslove za parametrijski (npr. Studentov) test
+
+:::
+
+::: {.column}
+
+![](slike/jenga.png)
+
+:::
+
+::::
+
+## Test sume rangova
+
+Mann-Whitney U / Wilcoxon rank-sum test
+
+![](slike/sumrank.png){fig-align="center"}
+
+## Uslovi za test sume rangova
+
+Tip podataka:
+
+- Numerički ne-normalni podaci, ordinalni podaci
+
+Uslovi:
+
+- Uzorak čine nezavisne jedinice
+- Podaci mogu da se rangiraju
+
+::: {.callout-warning}
+Ima manju statističku moć od parametarskih, ako su uslovi za parametarske testove ispunjeni.
+:::
+
+## Provera normalnosti numeričkih podataka
+
+- [Koeficijent varijacije]{.yellow}
+- Skew i Kurtosis
+- QQ Plot
+- [Histogram]{.yellow}
+- Statističkim testovima za normalnost
+
+## Vežba: MWW test
+
+::: {.r-fit-text}
+
+Ispitati da li se osobe sa različitim
+
+nadmorskim visinama prebivališta
+
+razlikuju prema koncentraciji fibrinogena.
+
+:::
+
+![](slike/mwu.jpg){fig-align="center"}
+
+## Test ekvivalentnih parova 
+
+### Wilcoxon signed rank test
+
+Tip podataka:
+
+- Numerički ne-normalni podaci, ordinalni podaci
+
+Uslovi:
+
+- Uzorak čine [zavisne]{.yellow} jedinice
+- Podaci mogu da se rangiraju
+
+## Vežba: Test ekvivalentnih parova
+
+::: {.r-fit-text}
+
+U bazi [Aritmije MW W McN.xlsx]{.yellow} date su 
+
+vrednosti Lp(a) pre početka terapije i 
+
+mesec dana posle započete terapije. 
+
+Cilj istraživača bio je da ispita da li dolazi 
+
+do promene vrednosti Lp(a) posle davanja antilipemika.
+
+:::
+
+## Izbor testa
+
+- Jedan ili dva uzorka
+- Ponovljena merenja ili ne
+- Tip podataka (numerički, ordinalni, kategorije)
+- Na osnovu deskriptivnih mera određujemo da li podaci ispunjavaju uslov normalnosti
+
+## Struktura kursa
+
+```{r}
+teme <- c(
+  "Uvod u medicinsku statistiku", "Sređivanje podataka",
+  "Statističko opisivanje podataka", "Verovatnoća i raspodele verovatnoća",
+  "Populacija i uzorak", "Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama",
+  "Testiranje hipoteza o učestalostima", "Testiranje hipoteza o rangovima", "Korelacija",
+  "Regresija / Kolokvijum", "Podaci, informacije i znanje", "Zdravstveni informacioni sistem",
+  "Mere dijagnostičke tačnosti", "Medicinsko odlučivanje", "Bioinformatika"
+)
+
+kurs <- tibble(Nedelja = 1:15, Tema = teme)
+tt(kurs) |> style_tt(j = 1:2, fontsize = 0.55)
+```
diff --git a/slides/08_rangovi/slike/jenga.png b/slides/08_rangovi/slike/jenga.png
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diff --git a/slides/08_rangovi/slike/mwu.jpg b/slides/08_rangovi/slike/mwu.jpg
new file mode 100644
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GIT binary patch
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