Hypothesis_Testing_with_Insurance_Data_(Core).ipynb

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        "#Hypothesis Testing with Insurance Data"
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        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy.stats as stats"
      ],
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              "   age     sex     bmi  children smoker     region      charges\n",
              "0   19  female  27.900         0    yes  southwest  16884.92400\n",
              "1   18    male  33.770         1     no  southeast   1725.55230\n",
              "2   28    male  33.000         3     no  southeast   4449.46200\n",
              "3   33    male  22.705         0     no  northwest  21984.47061\n",
              "4   32    male  28.880         0     no  northwest   3866.85520"
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      "source": [
        "url = 'https://docs.google.com/spreadsheets/d/e/2PACX-1vQSg4M8Lo3z1C3-9ESRh3xeRnhVeZ_fUu8ts88_Tt3ksCuU8oZtslTumnmzZEZoZaO4N8Fm71nqMmz1/pub?output=csv'\n",
        "df = pd.read_csv(url)\n",
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      "source": [
        "##Do smokers have higher insurance charges than non-smokers?"
      ],
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        "id": "LWAQ0of96lpU"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "State the null and alternative hypothesis\n",
        "\n",
        "Null Hypothesis: There is no difference in insurance costs between smokers and non smokers\n",
        "\n",
        "Alternative hypothesis: There is a significant difference in insurance costs between smokers and n on smokers"
      ],
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        "id": "OWoWv3inGnDd"
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      "source": [
        "#separate smoker groups\n",
        "smoker = df.loc[df['smoker']=='yes', ['smoker', 'charges']]\n",
        "smoker.head()"
      ],
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            "text/plain": [
              "   smoker     charges\n",
              "0     yes  16884.9240\n",
              "11    yes  27808.7251\n",
              "14    yes  39611.7577\n",
              "19    yes  36837.4670\n",
              "23    yes  37701.8768"
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        "not_smoker = df.loc[df['smoker']=='no', ['smoker', 'charges']]\n",
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              "  smoker      charges\n",
              "1     no   1725.55230\n",
              "2     no   4449.46200\n",
              "3     no  21984.47061\n",
              "4     no   3866.85520\n",
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              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-01ef237b-7745-4a46-a1a0-819364ee1b8e button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-01ef237b-7745-4a46-a1a0-819364ee1b8e');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "        }\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#visualization\n",
        "plot_df = pd.concat([smoker, not_smoker])\n",
        "plot_df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 411
        },
        "id": "5noNM3TKJ4AT",
        "outputId": "f0342f3e-c435-40f4-abfb-3832bb75e940"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     smoker     charges\n",
              "0       yes  16884.9240\n",
              "11      yes  27808.7251\n",
              "14      yes  39611.7577\n",
              "19      yes  36837.4670\n",
              "23      yes  37701.8768\n",
              "...     ...         ...\n",
              "1332     no  11411.6850\n",
              "1333     no  10600.5483\n",
              "1334     no   2205.9808\n",
              "1335     no   1629.8335\n",
              "1336     no   2007.9450\n",
              "\n",
              "[1338 rows x 2 columns]"
            ],
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              "<style scoped>\n",
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              "      <th>charges</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
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              "      <th>0</th>\n",
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              "      <td>16884.9240</td>\n",
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              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>yes</td>\n",
              "      <td>27808.7251</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>yes</td>\n",
              "      <td>39611.7577</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>yes</td>\n",
              "      <td>36837.4670</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>yes</td>\n",
              "      <td>37701.8768</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1332</th>\n",
              "      <td>no</td>\n",
              "      <td>11411.6850</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1333</th>\n",
              "      <td>no</td>\n",
              "      <td>10600.5483</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1334</th>\n",
              "      <td>no</td>\n",
              "      <td>2205.9808</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1335</th>\n",
              "      <td>no</td>\n",
              "      <td>1629.8335</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1336</th>\n",
              "      <td>no</td>\n",
              "      <td>2007.9450</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1338 rows × 2 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c697aed3-8f80-4ed0-8280-d6528c617675')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
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              "\n",
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              "      padding: 0 0 0 0;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
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              "      fill: #174EA6;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-c697aed3-8f80-4ed0-8280-d6528c617675 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-c697aed3-8f80-4ed0-8280-d6528c617675');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sns.barplot(data=plot_df, x='smoker', y='charges', ci=68)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "2hHSRp8tJ_YE",
        "outputId": "011e1907-fffa-4ada-9d78-75567cb64d69"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fa4d2755dd0>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "display(len(smoker), len(not_smoker))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49
        },
        "id": "r0xHHTNlGh_z",
        "outputId": "626b81fe-2807-4285-83ad-b831ae791170"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "274"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "1064"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#test for outliers\n",
        "smoker_group = smoker['charges']\n",
        "not_smoker_group = not_smoker['charges']\n",
        "smoker_outliers = np.abs(stats.zscore(smoker_group)) > 3\n",
        "not_smoker_outliers = np.abs(stats.zscore(not_smoker_group)) > 3\n",
        "display(smoker_outliers.sum(), not_smoker_outliers.sum())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 49
        },
        "id": "0br8Q1Q3G6Z7",
        "outputId": "32139464-f3ea-4abd-ee63-30c38e5315ee"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "24"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#remove outliers for non_smoker group\n",
        "not_smoker_group = not_smoker_group.loc[~not_smoker_outliers]"
      ],
      "metadata": {
        "id": "kn5eQiNhHjG8"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#test for normality\n",
        "result = stats.normaltest(smoker_group)\n",
        "result.pvalue"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "npfMwQ7MI4gN",
        "outputId": "84924515-91e2-47f1-c5fa-19c8b411418c"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5.564930630036463e-14"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "result = stats.normaltest(not_smoker_group)\n",
        "result.pvalue"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0aJL7JJ0I-Mv",
        "outputId": "aae76a41-0c01-44e3-d543-843ce8f6d0d3"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.6945416315543976e-36"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We have a large enough group size that we can safely disregard the assumption of normality"
      ],
      "metadata": {
        "id": "ndRgxJ5ZIEvc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#test for equal variance\n",
        "result = stats.levene(smoker_group, not_smoker_group)\n",
        "print(result)\n",
        "if result.pvalue < 0.05:\n",
        "  print('The groups do NOT have equal variance')\n",
        "else: \n",
        "  print ('The groups DO have equal variance')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iEess6fQI12v",
        "outputId": "a03f5fe1-d8fa-4a44-c79a-afa78db6236c"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "LeveneResult(statistic=520.7468821724297, pvalue=2.4247238784347824e-97)\n",
            "The groups do NOT have equal variance\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Since the groups do not have equal variance, the welch's t-test will be run instead"
      ],
      "metadata": {
        "id": "SPZN7jQxJUWv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#final hypothesis\n",
        "result = stats.ttest_ind(smoker_group, not_smoker_group, equal_var=False)\n",
        "print(result)\n",
        "result.pvalue < 0.05"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P_rANh3rJdFl",
        "outputId": "e98f6dcc-3a4d-4eb3-936d-c763828bddc6"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ttest_indResult(statistic=33.732305987092516, pvalue=2.575322662587431e-104)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The p value was less than 0.05 for the Welch's t test, meaning we reject the null hypothesis and support the alternative hypothesis. There is a significant difference in insurance costs between smokers and non-smokers. "
      ],
      "metadata": {
        "id": "bCLEITF_JplS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Are men more likely to smoke than women?"
      ],
      "metadata": {
        "id": "EexLBYuZ6qWQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "State the null and alternative hypothesis\n",
        "\n",
        "Null Hypothesis: There is no difference between men and women who smoke\n",
        "\n",
        "Alternative hypothesis: There is a significant difference between men and women who smoke"
      ],
      "metadata": {
        "id": "-Us9arMMMJEB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This is categorical, chi-test, and 4 sample groups"
      ],
      "metadata": {
        "id": "VRNfcuVFNF23"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#separate smoker groups\n",
        "male = df.loc[df['sex']=='male', ['sex', 'smoker']]\n",
        "male.head()"
      ],
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      "execution_count": 14,
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        {
          "output_type": "execute_result",
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            "text/plain": [
              "    sex smoker\n",
              "1  male     no\n",
              "2  male     no\n",
              "3  male     no\n",
              "4  male     no\n",
              "8  male     no"
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      "cell_type": "code",
      "source": [
        "#separate smoker groups\n",
        "female = df.loc[df['sex']=='female', ['sex', 'smoker']]\n",
        "female.head()"
      ],
      "metadata": {
        "colab": {
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        {
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          "data": {
            "text/plain": [
              "      sex smoker\n",
              "0  female    yes\n",
              "5  female     no\n",
              "6  female     no\n",
              "7  female     no\n",
              "9  female     no"
            ],
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              "                                                     [key], {});\n",
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ax = sns.countplot(data = df, x='sex', hue='smoker')\n",
        "ax.set_title('Numer of Smokers by Sex')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 310
        },
        "id": "FIFcOGXuMbBZ",
        "outputId": "1571b0ce-ca06-459a-c7d6-aea5ad33bfe2"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Numer of Smokers by Sex')"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#calculate the contigency table with pd.cross-tab\n",
        "table = pd.crosstab(df['sex'],df['smoker'])\n",
        "table"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "id": "V_mpKTZJOI9i",
        "outputId": "177dbf32-3d17-4017-e965-3b2a0428231f"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "smoker   no  yes\n",
              "sex             \n",
              "female  547  115\n",
              "male    517  159"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-97987937-1434-4069-ae49-ca2f63672dea\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>smoker</th>\n",
              "      <th>no</th>\n",
              "      <th>yes</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sex</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>female</th>\n",
              "      <td>547</td>\n",
              "      <td>115</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>male</th>\n",
              "      <td>517</td>\n",
              "      <td>159</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-97987937-1434-4069-ae49-ca2f63672dea')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-97987937-1434-4069-ae49-ca2f63672dea button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-97987937-1434-4069-ae49-ca2f63672dea');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#run the test and save the output\n",
        "result = stats.chi2_contingency(table)\n",
        "chi2, p, deg_free, expected_vals = result"
      ],
      "metadata": {
        "id": "3qYaRAh1OSFy"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#p-value\n",
        "print(p)\n",
        "p<0.05"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AqdgZyksOZqa",
        "outputId": "2322fee9-48bd-4045-fb5f-51754b526b43"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.006548143503580696\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The p-value is less than 0.05. We reject the null and support the alternative hypothesis. There is a difference between men and women who smoke. "
      ],
      "metadata": {
        "id": "nbuU3NilOz7E"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Do different regions have different charges on average?"
      ],
      "metadata": {
        "id": "dsLnSZ3b6srC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "State the null and alternative hypothesis\n",
        "\n",
        "Null Hypothesis: There is no difference in charges between regions\n",
        "\n",
        "Alternative hypothesis: There is a significant difference in charges between regions"
      ],
      "metadata": {
        "id": "nqnhpl9oM8Zm"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This is multiple samples/groups and numerical"
      ],
      "metadata": {
        "id": "XTJzhcIlNKIQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#separate into appropriate groups\n",
        "groups = {}\n",
        "for region in df['region'].unique():\n",
        "  temp_df = df.loc[df['region']==region, 'charges']\n",
        "  groups[region] = temp_df\n",
        "groups.keys()"
      ],
      "metadata": {
        "id": "FGJko9SrM71h",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "86c73a0c-d736-447a-d34c-39e8f9f52d0a"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_keys(['southwest', 'southeast', 'northwest', 'northeast'])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#graph and visualize the results\n",
        "sns.barplot(data = df, x='region', y='charges', ci=68)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "SYvsA1pgxlXr",
        "outputId": "84c7bd01-ee2c-4a51-db71-0e225e324633"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fa4b90dec10>"
            ]
          },
          "metadata": {},
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#calculate outliers\n",
        "for region, data in groups.items():\n",
        "  outliers = np.abs(stats.zscore(data)) > 3\n",
        "  print(f'{outliers.sum()} outliers were removed from the {region} group')\n",
        "  groups[region] = data.loc[~outliers]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kWywNWJYXP5-",
        "outputId": "4f73f367-db2b-48c9-ee94-e0f85bb3a5ef"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "8 outliers were removed from the southwest group\n",
            "2 outliers were removed from the southeast group\n",
            "7 outliers were removed from the northwest group\n",
            "4 outliers were removed from the northeast group\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#test for normality\n",
        "norm_results = {}\n",
        "for i, data in groups.items():\n",
        "  stat, p = stats.normaltest(data)\n",
        "  norm_results[i] = {'n':len(data),\n",
        "                     'p':p}"
      ],
      "metadata": {
        "id": "-j85WMHpXnh6"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#display dataframe created from the norm results\n",
        "pd.DataFrame(norm_results).T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "id": "hswlEBZIX4sK",
        "outputId": "9005b745-b1d3-4179-8338-3afda1a36c11"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               n             p\n",
              "southwest  317.0  7.728611e-22\n",
              "southeast  362.0  1.936990e-13\n",
              "northwest  318.0  2.940543e-19\n",
              "northeast  320.0  3.557877e-17"
            ],
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            ]
          },
          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#display dataframe created from norm_results\n",
        "norm_df = pd.DataFrame(norm_results).T\n",
        "norm_df['sig?'] = norm_df['p'] < 0.05\n",
        "norm_df"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        },
        "id": "odCmgnzHX-mX",
        "outputId": "61b6f161-81d2-4683-99b8-b26315dcb7e6"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "               n             p  sig?\n",
              "southwest  317.0  7.728611e-22  True\n",
              "southeast  362.0  1.936990e-13  True\n",
              "northwest  318.0  2.940543e-19  True\n",
              "northeast  320.0  3.557877e-17  True"
            ],
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-e093a688-75ed-4006-afc3-16fe2bfafbec');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "No need for normality testing as we have large groups. The groups do not come from normal distributions"
      ],
      "metadata": {
        "id": "3m0iMKUivdYg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#equal variance\n",
        "statistic, pvalue = stats.levene(*groups.values())\n",
        "print(statistic, pvalue)\n",
        "if pvalue < 0.05:\n",
        "  print('The groups do NOT have equal variance')\n",
        "else: \n",
        "  print ('The groups DO have equal variance')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qw8wF3Jar7Vd",
        "outputId": "b9a53ac3-7390-4ca5-8b51-b4134e320fec"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "9.518349004554441 3.2035503711783993e-06\n",
            "The groups do NOT have equal variance\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The groups do not have equal variance, therefore we will use the Kruskal test. "
      ],
      "metadata": {
        "id": "ST1Qh8zYwd-r"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#final hypothesis\n",
        "statistic, pvalue = stats.kruskal(*groups.values())\n",
        "print(statistic, pvalue)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "28RsIb3iwOHf",
        "outputId": "f59bcc0f-1c39-46b7-83b3-a856043b36fe"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6.914045702545643 0.07468847911322242\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The p-value is greater than 0.05. We failed to reject the null and support the null hypothesis. There is no significant difference in charges between regions "
      ],
      "metadata": {
        "id": "q2AiykbFw9LI"
      }
    }
  ]
}