statistics-part3.ipynb

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      "cell_type": "markdown",
      "source": [
        "# Significance Tests\n",
        "\n",
        "![](https://drive.google.com/uc?id=1AD3wA3QnMiBM1UI3KKoAv-WQopJT_3f4)"
      ],
      "metadata": {
        "id": "UbzP1Dw4zA1L"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "# Multiple Tests"
      ],
      "metadata": {
        "id": "c2fCd47s7BKI"
      }
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    {
      "cell_type": "code",
      "source": [
        "def mult_test_err(c: int) -> float:\n",
        "    return round((1 - (0.95) ** c) * 100, 1)\n",
        "\n",
        "\n",
        "# Test for c=3\n",
        "mult_test_err(c=3)"
      ],
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            "text/plain": [
              "14.3"
            ]
          },
          "metadata": {},
          "execution_count": 2
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    {
      "cell_type": "code",
      "source": [
        "# Test for c=5\n",
        "mult_test_err(c=5)"
      ],
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        "id": "dEvvxks177y8",
        "outputId": "f54f09be-2945-4c74-8283-151619794fe9"
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      "execution_count": null,
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          "data": {
            "text/plain": [
              "22.6"
            ]
          },
          "metadata": {},
          "execution_count": 3
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      ]
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    {
      "cell_type": "code",
      "source": [
        "# Bonferroni Approach 1\n",
        "print(round(0.05 / 3, 3))\n",
        "\n",
        "# Bonferroni Approach 2\n",
        "print(0.03 * 3)"
      ],
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        "id": "ienTYvN08ao2",
        "outputId": "29ace1fa-ff0a-45c2-c44b-ba8c525e9bcd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.017\n",
            "0.09\n"
          ]
        }
      ]
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        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/gdrive\n"
          ]
        }
      ],
      "source": [
        "# Mount Google Drive\n",
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import the modules\n",
        "import pandas as pd\n",
        "\n",
        "# Import the data\n",
        "# Source: https://www.kaggle.com/datasets/lsind18/weight-vs-age-of-chicks-on-different-diets\n",
        "data = pd.read_csv(\"/content/gdrive/MyDrive/YouTube/dataAnalysisPlaylist/practical-statistics-for-data-scientists/media/ChickWeight.csv\")\\\n",
        "            .drop(columns=[\"Unnamed: 0\"])\n",
        "# Trace\n",
        "data.sample(n=5, random_state=43)"
      ],
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          "height": 206
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              "     weight  Time  Chick  Diet\n",
              "309     114    10     28     2\n",
              "407     166    14     36     3\n",
              "35      202    21      3     1\n",
              "69      160    18      6     1\n",
              "553     322    21     48     4"
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      "cell_type": "code",
      "source": [
        "# Unmount the gdrive\n",
        "drive.flush_and_unmount()"
      ],
      "metadata": {
        "id": "O1xTiuiDVNeY"
      },
      "execution_count": null,
      "outputs": []
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      "source": [
        "def calc_missing(df: pd.DataFrame) -> pd.DataFrame:\n",
        "    \"\"\"Returns the missing percentages of the given frame.\n",
        "\n",
        "    Args:\n",
        "        df (pd.DataFrame): The Dataframe. \n",
        "\n",
        "    Returns:\n",
        "        pd.DataFrame: The missing percentages.\n",
        "    \"\"\"\n",
        "    # Calculate the number of missing values\n",
        "    missing = df.isnull().sum()\n",
        "    # Calculate the missing percentages\n",
        "    percent_missing = missing * 100 / len(df)\n",
        "    # Create a frame with dict format\n",
        "    missing_value_df = pd.DataFrame(\n",
        "        {\"num_missing\": missing, \"percent_missing\": percent_missing}\n",
        "    )\n",
        "    # Round the percentage values\n",
        "    missing_value_df = round(number=missing_value_df, ndigits=2)\n",
        "    # Sort from highest to lowest\n",
        "    missing_value_df.sort_values(\"percent_missing\", inplace=True)\n",
        "    # Return the missing value frame\n",
        "    return missing_value_df\n",
        "\n",
        "\n",
        "# Trace the missing values\n",
        "calc_missing(df=data)"
      ],
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              "        num_missing  percent_missing\n",
              "weight            0              0.0\n",
              "Time              0              0.0\n",
              "Chick             0              0.0\n",
              "Diet              0              0.0"
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      "cell_type": "code",
      "source": [
        "# Get dummies of the \"Diet\" feature\n",
        "data_dummies = pd.get_dummies(data=data, columns=[\"Diet\"])\n",
        "# Trace\n",
        "data_dummies.sample(n=5, random_state=43)"
      ],
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              "     weight  Time  Chick  Diet_1  Diet_2  Diet_3  Diet_4\n",
              "309     114    10     28       0       1       0       0\n",
              "407     166    14     36       0       0       1       0\n",
              "35      202    21      3       1       0       0       0\n",
              "69      160    18      6       1       0       0       0\n",
              "553     322    21     48       0       0       0       1"
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              "    <tr>\n",
              "      <th>407</th>\n",
              "      <td>166</td>\n",
              "      <td>14</td>\n",
              "      <td>36</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>35</th>\n",
              "      <td>202</td>\n",
              "      <td>21</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>69</th>\n",
              "      <td>160</td>\n",
              "      <td>18</td>\n",
              "      <td>6</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>553</th>\n",
              "      <td>322</td>\n",
              "      <td>21</td>\n",
              "      <td>48</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ad7ae9a0-e2ea-4bd3-8f00-b008234a8bea')\"\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-ad7ae9a0-e2ea-4bd3-8f00-b008234a8bea 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-ad7ae9a0-e2ea-4bd3-8f00-b008234a8bea');\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": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Observed results\n",
        "for i in range(1, 5):\n",
        "    # Calculate the mean of the given diet\n",
        "    diet_mean = round(\n",
        "        data_dummies.loc[getattr(data_dummies, f\"Diet_{i}\") == 1, \"weight\"].mean(), 3\n",
        "    )\n",
        "    # Trace\n",
        "    print(f\"Diet {i}: {diet_mean}\")\n",
        "\n",
        "# Delete not needed objects\n",
        "del diet_mean"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4CCV8ypMXVHY",
        "outputId": "f73cac7d-1ba4-4483-95e8-9176a77ca655"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Diet 1: 102.645\n",
            "Diet 2: 122.617\n",
            "Diet 3: 142.95\n",
            "Diet 4: 135.263\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data.groupby(\"Diet\").weight.mean()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AUHxGd2rYeEM",
        "outputId": "e81c50a8-64c8-496a-ebb6-58cca0af43f5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Diet\n",
              "1    102.645455\n",
              "2    122.616667\n",
              "3    142.950000\n",
              "4    135.262712\n",
              "Name: weight, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import the modules\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from scipy.stats import norm\n",
        "from seaborn import histplot\n",
        "from statsmodels.api import ProbPlot\n",
        "\n",
        "# Declare the weight values\n",
        "weights = data.weight.values\n",
        "# Declare a Probability Plot object\n",
        "pplot = ProbPlot(data=weights,\n",
        "                 dist=norm, fit=True)\n",
        "\n",
        "# Figure setup\n",
        "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))\n",
        "# Histogram of the original data\n",
        "histplot(x=weights, kde=True, stat=\"density\", bins=50, ax=axes[0])\n",
        "# X and y lims\n",
        "axes[0].set_xlim(xmin=weights.min() - 10, xmax=weights.max() + 10)\n",
        "axes[0].set_ylim(ymin=0., ymax=0.0125)\n",
        "# X label\n",
        "axes[0].set_xlabel(xlabel=\"Data\")\n",
        "# Title\n",
        "axes[0].set_title(label=\"Histogram w/ density function\")\n",
        "# QQ plot\n",
        "pplot.qqplot(line=\"45\", ax=axes[1])\n",
        "# Title\n",
        "axes[1].set_title(label=\"QQ Plot\")\n",
        "\n",
        "# Show the plots\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "4q8Y2kEEc1Tg",
        "outputId": "bff2a882-2f69-4dbc-d8cb-e2e72a07504f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x288 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import the modules\n",
        "import numpy as np\n",
        "\n",
        "\n",
        "def permutation_test(df: pd.DataFrame) -> np.float64:\n",
        "    # Copy the frame\n",
        "    df_cp = df.copy()\n",
        "    # Permute the weights\n",
        "    df_cp.loc[:, \"weight\"] = np.random.permutation(weights)\n",
        "    # Return the variance\n",
        "    return df_cp.groupby(\"Diet\").weight.mean().var()"
      ],
      "metadata": {
        "id": "dcWZlPcyh4vD"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Observed variance\n",
        "obs_var = data.groupby(\"Diet\").weight.mean().var()\n",
        "\n",
        "# Permutation test\n",
        "perm_variance = [permutation_test(df=data) for _ in range(3000)]\n",
        "# Trace\n",
        "print('Pr(Prob)', np.mean([var > obs_var for var in perm_variance]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZkzMVEw338HA",
        "outputId": "716b5c2b-7f1b-4c2a-da47-c91306a8caaf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Pr(Prob) 0.0003333333333333333\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Import the modules\n",
        "from scipy.stats import f_oneway\n",
        "\n",
        "# Extract groups from the data\n",
        "groups = [\n",
        "    data_dummies.loc[data_dummies.Diet_1 == 1, \"weight\"].values,\n",
        "    data_dummies.loc[data_dummies.Diet_2 == 1, \"weight\"].values,\n",
        "    data_dummies.loc[data_dummies.Diet_3 == 1, \"weight\"].values,\n",
        "    data_dummies.loc[data_dummies.Diet_4 == 1, \"weight\"].values,\n",
        "]\n",
        "# One-way ANOVA test\n",
        "f_statistic, p_value = f_oneway(*groups)\n",
        "# Trace the results\n",
        "print(\"F-statistic:\", round(f_statistic, 3))\n",
        "print(\"p-value:\", round(p_value, 5), p_value < 0.05)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YHdtptKbjQlX",
        "outputId": "e3f2346e-9207-4103-e50e-a07f3cda057f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "F-statistic: 10.81\n",
            "p-value: 0.0 True\n"
          ]
        }
      ]
    }
  ]
}