comp.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyM1ipAz8ucK9ZHDc5B47mij",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/satuelisa/NLPF/blob/main/comp.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 176,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "T_I0nQsigW2p",
        "outputId": "2601d087-7b37-4b5c-bc36-739900783be2"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25., 39., 26., 23., 26., 34., 20., 38., 22., 31.])"
            ]
          },
          "metadata": {},
          "execution_count": 176
        }
      ],
      "source": [
        "import numpy as np\n",
        "\n",
        "ss = 10000\n",
        "d1 = np.random.poisson(lam = 30.32, size = ss) + np.round(5 * np.random.normal(size = ss))\n",
        "d2 = np.random.poisson(lam = 24.36, size = ss)\n",
        "d2r = np.random.poisson(lam = 24.34, size = ss)\n",
        "d1[:10]"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "pos = [1, 2, 3] # d1 and d2, d2r\n",
        "fig = plt.violinplot([d1, d2, d2r], pos,\n",
        "                     showmeans = True, \n",
        "                     showextrema = True, \n",
        "                     showmedians = True)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "5JxfmU2fhDDy",
        "outputId": "def6cf94-3c33-4f10-e680-7c59acc792b5"
      },
      "execution_count": 177,
      "outputs": [
        {
          "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": [
        "import pandas as pd\n",
        "pct = pd.DataFrame()\n",
        "pct['d1'] = np.percentile(d1, range(100))\n",
        "pct['d2'] = np.percentile(d2, range(100))\n",
        "pct['d2r'] = np.percentile(d2r, range(100))\n",
        "pct['quantile'] = range(100)\n",
        "pct.head()\n",
        "print(pct.loc[pct['quantile'] == 50])\n",
        "pct.tail()\n",
        "print(sum(d1) / ss)\n",
        "print(np.mean(d1))\n",
        "print(sum(d2) / ss)\n",
        "print(np.mean(d2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F-7ZMJXai5Rt",
        "outputId": "2a3a4955-e330-400c-81e1-bf8b556b7b4e"
      },
      "execution_count": 178,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "      d1    d2   d2r  quantile\n",
            "50  30.0  24.0  24.0        50\n",
            "30.4863\n",
            "30.4863\n",
            "24.3329\n",
            "24.3329\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import seaborn as sns\n",
        "plt.figure(figsize=(8, 8))\n",
        "plt.scatter(x = 'd1', y = 'd2', data = pct, label='Quantiles');\n",
        "sns.lineplot(x = 'd1', y = 'd1', data = pct, color='r', label='Perfect fit');\n",
        "sns.lineplot(x = 'd2', y = 'd2', data = pct, color='g');\n",
        "plt.xlabel('Quantiles of d1')\n",
        "plt.ylabel('Quantiles of d2')\n",
        "plt.legend()\n",
        "plt.title(\"QQ plot (different)\");"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "J7jJFy60ilf4",
        "outputId": "43a51850-ba83-4f0a-fe7d-40837cf03798"
      },
      "execution_count": 179,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(8, 8))\n",
        "plt.scatter(x = 'd2', y = 'd2r', data = pct, label='Quantiles');\n",
        "sns.lineplot(x = 'd2', y = 'd2', data = pct, color='r', label='Perfect fit');\n",
        "sns.lineplot(x = 'd2r', y = 'd2r', data = pct, color='g');\n",
        "plt.xlabel('Quantiles of d2')\n",
        "plt.ylabel('Quantiles of d2r')\n",
        "plt.legend()\n",
        "plt.title(\"QQ plot (sameish)\");"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "id": "6w4StsJjqXJ-",
        "outputId": "90eeee01-57a9-4499-e94b-9ffbcad34484"
      },
      "execution_count": 180,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df_bins = pd.DataFrame()\n",
        "_, bins = pd.qcut(d1, q = 5, retbins = True)\n",
        "df_bins['bin'] = pd.cut(d1, bins = bins).value_counts().index\n",
        "df_bins['d1_observed'] = pd.cut(d1, bins = bins).value_counts().values\n",
        "df_bins['d2_observed'] = pd.cut(d2, bins = bins).value_counts().values\n",
        "df_bins['d2_expected'] = df_bins['d1_observed'] / np.sum(df_bins['d1_observed']) * np.sum(df_bins['d2_observed'])\n",
        "\n",
        "print(sum(df_bins['d2_observed']))\n",
        "print(sum(df_bins['d2_expected']))\n",
        "df_bins"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "id": "wX-zUYUXlpG4",
        "outputId": "41a44502-c98e-4023-c25a-9a343ea2b8ff"
      },
      "execution_count": 182,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10000\n",
            "10000.0\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "            bin  d1_observed  d2_observed  d2_expected\n",
              "0   (4.0, 24.0]         2113         5286  2113.211321\n",
              "1  (24.0, 29.0]         2394         3249  2394.239424\n",
              "2  (29.0, 32.0]         1620          918  1620.162016\n",
              "3  (32.0, 37.0]         2156          480  2156.215622\n",
              "4  (37.0, 64.0]         1716           67  1716.171617"
            ],
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              "      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-6c6e4104-a985-41cb-a565-3861b7c9bbb1 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-6c6e4104-a985-41cb-a565-3861b7c9bbb1');\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": 182
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import chisquare\n",
        "\n",
        "stat, p_value = chisquare(df_bins['d2_observed'], df_bins['d2_expected'])\n",
        "print(f\"Chi-squared Test: statistic = {stat:.4f}, p-value = {p_value:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iZXSlgR6ldE4",
        "outputId": "cc14bdc7-0cb8-4ab1-d9cc-b5fa634a2b92"
      },
      "execution_count": 183,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Chi-squared Test: statistic = 8260.9672, p-value = 0.0000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df_bins = pd.DataFrame()\n",
        "_, bins = pd.qcut(d2, q = 5, retbins = True)\n",
        "df_bins['bin'] = pd.cut(d1, bins = bins).value_counts().index\n",
        "df_bins['d2_observed'] = pd.cut(d2, bins = bins).value_counts().values\n",
        "df_bins['d2r_observed'] = pd.cut(d2r, bins = bins).value_counts().values\n",
        "df_bins['d2r_expected'] = df_bins['d2_observed'] / np.sum(df_bins['d2_observed']) * np.sum(df_bins['d2r_observed'])\n",
        "\n",
        "print(sum(df_bins['d2r_observed']))\n",
        "print(sum(df_bins['d2r_expected']))\n",
        "stat, p_value = chisquare(df_bins['d2r_observed'], df_bins['d2r_expected'])\n",
        "print(f\"Chi-squared Test: statistic = {stat:.4f}, p-value = {p_value:.4f}\")\n",
        "df_bins"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 258
        },
        "id": "1bdecgFAqson",
        "outputId": "91933e17-fc94-4baf-c3d3-2988ed7fef98"
      },
      "execution_count": 184,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "9996\n",
            "9996.0\n",
            "Chi-squared Test: statistic = 3.6273, p-value = 0.4588\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "            bin  d2_observed  d2r_observed  d2r_expected\n",
              "0   (9.0, 20.0]         2193          2181   2192.780634\n",
              "1  (20.0, 23.0]         2251          2217   2250.774832\n",
              "2  (23.0, 25.0]         1651          1610   1650.834850\n",
              "3  (25.0, 28.0]         1971          2003   1970.802841\n",
              "4  (28.0, 46.0]         1931          1985   1930.806842"
            ],
            "text/html": [
              "\n",
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              "    <div class=\"colab-df-container\">\n",
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              "<style scoped>\n",
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              "        vertical-align: middle;\n",
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              "\n",
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>bin</th>\n",
              "      <th>d2_observed</th>\n",
              "      <th>d2r_observed</th>\n",
              "      <th>d2r_expected</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>(9.0, 20.0]</td>\n",
              "      <td>2193</td>\n",
              "      <td>2181</td>\n",
              "      <td>2192.780634</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>(20.0, 23.0]</td>\n",
              "      <td>2251</td>\n",
              "      <td>2217</td>\n",
              "      <td>2250.774832</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>(23.0, 25.0]</td>\n",
              "      <td>1651</td>\n",
              "      <td>1610</td>\n",
              "      <td>1650.834850</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>(25.0, 28.0]</td>\n",
              "      <td>1971</td>\n",
              "      <td>2003</td>\n",
              "      <td>1970.802841</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>(28.0, 46.0]</td>\n",
              "      <td>1931</td>\n",
              "      <td>1985</td>\n",
              "      <td>1930.806842</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "              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",
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              "  </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",
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              "    }\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-2ec1b7e7-b1f3-40c9-9c62-b93087e37428 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-2ec1b7e7-b1f3-40c9-9c62-b93087e37428');\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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              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 184
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import mannwhitneyu\n",
        "\n",
        "stat, p_value = mannwhitneyu(d1, d2)\n",
        "print(f\" Mann–Whitney U Test: statistic={stat:.4f}, p-value={p_value:.4f}\")\n",
        "\n",
        "stat, p_value = mannwhitneyu(d2, d2r)\n",
        "print(f\" Mann–Whitney U Test: statistic={stat:.4f}, p-value={p_value:.4f}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gbg0xUILpBHF",
        "outputId": "875accdd-ecfd-47c1-be1b-6b0853721c56"
      },
      "execution_count": 185,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " Mann–Whitney U Test: statistic=75565933.5000, p-value=0.0000\n",
            " Mann–Whitney U Test: statistic=49518334.5000, p-value=0.2372\n"
          ]
        }
      ]
    }
  ]
}