30_3_ttest,_ANOVA,_resampling.ipynb

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  "metadata": {
    "colab": {
      "name": "30.3. ttest, ANOVA, resampling.ipynb",
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      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nmningmei/LevelUpPythonTutorial/blob/master/30_3_ttest%2C_ANOVA%2C_resampling.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dhfqOvbpi-vh",
        "colab_type": "text"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZW51Ed04ESeZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy import stats\n",
        "from matplotlib import pyplot as plt\n",
        "%matplotlib inline\n",
        "import seaborn as sns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mhmScwEgEZm4",
        "colab_type": "text"
      },
      "source": [
        "# T-tests"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "enYZqnMrEcaA",
        "colab_type": "text"
      },
      "source": [
        "## one-sample t-test"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Dl0HxyCNEgux",
        "colab_type": "text"
      },
      "source": [
        "### generate the data from normal distribution"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4g1gvQLRE1gy",
        "colab_type": "code",
        "outputId": "87409c0f-054b-4c2c-fd6d-0fa1e6f232f5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "mean = 100\n",
        "standard_deviation = 18\n",
        "n_samples = 78\n",
        "theoretic_standard_error = standard_deviation / np.sqrt(n_samples)\n",
        "print(f'mean = {mean:.4f},standard error = {theoretic_standard_error:.4f}')\n",
        "np.random.seed(12345)\n",
        "samples = np.random.normal(loc = mean, scale = standard_deviation, size = n_samples)\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples,bins = 5,alpha = 0.7,color = 'blue')\n",
        "_ = ax.axvline(samples.mean(),linestyle = '--',color = 'black',alpha = 1.,label = f'mean = {samples.mean():.4f}')\n",
        "_ = ax.axvspan(samples.mean() - samples.std()/np.sqrt(n_samples),\n",
        "               samples.mean() + samples.std() / np.sqrt(n_samples), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples.std() / np.sqrt(n_samples):.4f}')\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "mean = 100.0000,standard error = 2.0381\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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LF/LWW2/xwQcfkJiYGJlbGCAhIaHS51udczz88MP079+/xPscPzFERSeKOFGOyk6fuGfP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\nRETEAxVgERERD/4/ZJuiS4ldd24AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CG-kHM94FZqZ",
        "colab_type": "code",
        "outputId": "0ce8efd8-4365-4670-ba06-20fab78805af",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.ttest_1samp(samples,100,)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=-0.5251460594920753, pvalue=0.6009905475805698)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 175
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gOJxPrt7Gvik",
        "colab_type": "code",
        "outputId": "a1a9bb4f-a1aa-457f-c2ac-7ea3c982245b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "mean = 106\n",
        "standard_deviation = 18\n",
        "n_samples = 78\n",
        "theoretic_standard_error = standard_deviation / np.sqrt(n_samples)\n",
        "print(f'mean = {mean:.4f},standard error = {theoretic_standard_error:.4f}')\n",
        "np.random.seed(12345)\n",
        "samples = np.random.normal(loc = mean, scale = standard_deviation, size = n_samples)\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples,bins = 5,alpha = 0.7,color = 'blue')\n",
        "_ = ax.axvline(samples.mean(),linestyle = '--',color = 'black',alpha = 1.,label = f'mean = {samples.mean():.4f}')\n",
        "_ = ax.axvspan(samples.mean() - samples.std()/np.sqrt(n_samples),\n",
        "               samples.mean() + samples.std() / np.sqrt(n_samples), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples.std() / np.sqrt(n_samples):.4f}')\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "mean = 106.0000,standard error = 2.0381\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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iIiJSjuoU4GVAqpm1M7NzgJuAV4OJJSIiUrtVeQjaOXfUzH4FvAXUAaY553Kq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\nVIBFREQ8UAEWERHx4P8DRZSntffWlH4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Vk0i-hU3G08U",
        "colab_type": "code",
        "outputId": "c24bf2a2-b56d-4f8d-954d-f1c65b69b6b1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.ttest_1samp(samples,100,)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=2.2459567903320825, pvalue=0.027573833297004427)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 177
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4niyqn7UHL8z",
        "colab_type": "text"
      },
      "source": [
        "### generate from non-normal distribution: exponential\n",
        "\n",
        "$$P(X \\leq x) = 1 - e^{\\lambda x}$$\n",
        "$$E[x] = 1/\\lambda$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WORi5UNaG6b0",
        "colab_type": "code",
        "outputId": "03cb8ae8-d5a9-48e7-c3ae-52b680256691",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "mean = 117\n",
        "n_samples = 78\n",
        "np.random.seed(12345)\n",
        "samples = np.random.exponential(scale = mean, size = n_samples)\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples,bins = 5,alpha = 0.7,color = 'blue')\n",
        "_ = ax.axvline(samples.mean(),linestyle = '--',color = 'black',alpha = 1.,label = f'mean = {samples.mean():.4f}')\n",
        "_ = ax.axvspan(samples.mean() - samples.std()/np.sqrt(n_samples),\n",
        "               samples.mean() + samples.std() / np.sqrt(n_samples), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples.std() / np.sqrt(n_samples):.4f}')\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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fdQq/jh07UlBQwJrgy/S0adPKfNzAgQOZMGFC7CjilStXsnPnzmPmy8rKYu7cuWzatImD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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jp74HrY9IPHM",
        "colab_type": "code",
        "outputId": "d5b2d0bf-d234-4b8f-d7d7-835ff98f2b07",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.ttest_1samp(samples,100)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_1sampResult(statistic=2.2858733668219404, pvalue=0.025012543966142314)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 179
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kKyaQSAiIeWe",
        "colab_type": "text"
      },
      "source": [
        "### [generate from more distributions if you like](https://docs.scipy.org/doc/numpy-1.14.1/reference/routines.random.html)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GJUh2E7WImKE",
        "colab_type": "text"
      },
      "source": [
        "## paired 2-sample t-test"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f6nhT2kdI22v",
        "colab_type": "text"
      },
      "source": [
        "### generate from normal distribution and kinda equal variance, they have to have the same sample size"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UfhxSBakIZjB",
        "colab_type": "code",
        "outputId": "96331a9b-96f3-4d9c-87ed-19c83d7495f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "sample_mean1 = 0.52\n",
        "sample_mean2 = 0.75\n",
        "sample_sd1 = 0.15\n",
        "sample_sd2 = 0.19\n",
        "sample_size1 = 30\n",
        "sample_size2 = 30\n",
        "\n",
        "np.random.seed(12345)\n",
        "samples1 = np.random.normal(sample_mean1,sample_sd1,sample_size1)\n",
        "samples2 = np.random.normal(sample_mean2,sample_sd2,sample_size2)\n",
        "\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples1,color = 'red',label='sample1',alpha = 0.4)\n",
        "_ = ax.hist(samples2,color = 'blue',label='sample2',alpha = 0.4)\n",
        "\n",
        "_ = ax.axvline(samples1.mean(),linestyle = '--',color = 'red',alpha = 1.,label = f'mean = {samples1.mean():.4f}')\n",
        "_ = ax.axvspan(samples1.mean() - samples1.std()/np.sqrt(sample_size1),\n",
        "               samples1.mean() + samples1.std() / np.sqrt(sample_size1), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples1.std() / np.sqrt(sample_size1):.4f}')\n",
        "\n",
        "_ = ax.axvline(samples2.mean(),linestyle = '--',color = 'blue',alpha = 1.,label = f'mean = {samples2.mean():.4f}')\n",
        "_ = ax.axvspan(samples2.mean() - samples2.std()/np.sqrt(sample_size2),\n",
        "               samples2.mean() + samples2.std() / np.sqrt(sample_size2), \n",
        "               color = 'blue', alpha = 0.7,label = f'standard error = {samples2.std() / np.sqrt(sample_size2):.4f}')\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LGOjVy7OISPX8OaNtD7zl7eaLAl6x1lYe6VJHQa6SpzJ5Y8Z4yuT94hfcMGJE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\naEVERBz0/wHDeLTVutBsWAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Ek7QG8aJm7g",
        "colab_type": "code",
        "outputId": "a223b73e-bbc6-46a3-a5ad-638df359965f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.ttest_rel(samples1,samples2,)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_relResult(statistic=-2.1049874165929663, pvalue=0.044072222303606606)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 181
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lsv-Gs1YKcRs",
        "colab_type": "text"
      },
      "source": [
        "## independent 2-sample t-test"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vZKcjVgTKTTF",
        "colab_type": "text"
      },
      "source": [
        "### generate from normal distribution and kinda equal variance and unequal sample size"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T6mqLixBKKz2",
        "colab_type": "code",
        "outputId": "26716eb8-8a55-46d4-9177-ef858d2c6ab5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "sample_mean1 = 0.52\n",
        "sample_mean2 = 0.75\n",
        "sample_sd1 = 0.15\n",
        "sample_sd2 = 0.19\n",
        "sample_size1 = 30\n",
        "sample_size2 = 60 # only change from above\n",
        "\n",
        "np.random.seed(12345)\n",
        "samples1 = np.random.normal(sample_mean1,sample_sd1,sample_size1)\n",
        "samples2 = np.random.normal(sample_mean2,sample_sd2,sample_size2)\n",
        "\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples1,color = 'red',label='sample1',alpha = 0.4)\n",
        "_ = ax.hist(samples2,color = 'blue',label='sample2',alpha = 0.4)\n",
        "\n",
        "_ = ax.axvline(samples1.mean(),linestyle = '--',color = 'red',alpha = 1.,label = f'mean = {samples1.mean():.4f}')\n",
        "_ = ax.axvspan(samples1.mean() - samples1.std()/np.sqrt(sample_size1),\n",
        "               samples1.mean() + samples1.std() / np.sqrt(sample_size1), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples1.std() / np.sqrt(sample_size1):.4f}')\n",
        "\n",
        "_ = ax.axvline(samples2.mean(),linestyle = '--',color = 'blue',alpha = 1.,label = f'mean = {samples2.mean():.4f}')\n",
        "_ = ax.axvspan(samples2.mean() - samples2.std()/np.sqrt(sample_size2),\n",
        "               samples2.mean() + samples2.std() / np.sqrt(sample_size2), \n",
        "               color = 'blue', alpha = 0.7,label = f'standard error = {samples2.std() / np.sqrt(sample_size2):.4f}')\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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al+2gfdkO1zGc2r3bs4iI7wIqwMaYdsaY140x240x24wxVwYrmEikiK09QWxt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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "osdz1te9Ki1T",
        "colab_type": "code",
        "outputId": "b33d4dff-5d01-40c9-badf-f0f5351d0c63",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.ttest_ind(samples1,samples2,equal_var = True)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_indResult(statistic=-3.5176311972648056, pvalue=0.0006912109659667991)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 183
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sMmjjkBMK3I3",
        "colab_type": "text"
      },
      "source": [
        "### generate from normal distribution and unequal vairance and unequal sample size"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oMh0n0o4Ko6o",
        "colab_type": "code",
        "outputId": "5ae464fd-e0d6-4b74-84e6-6486ad21459c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "sample_mean1 = 0.52\n",
        "sample_mean2 = 1.03\n",
        "sample_sd1 = 0.15 * 5\n",
        "sample_sd2 = 0.15 #\n",
        "sample_size1 = 30\n",
        "sample_size2 = 60 #\n",
        "\n",
        "np.random.seed(12345)\n",
        "samples1 = np.random.normal(sample_mean1,sample_sd1,sample_size1)\n",
        "samples2 = np.random.normal(sample_mean2,sample_sd2,sample_size2)\n",
        "\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples1,color = 'red',label='sample1',alpha = 0.4)\n",
        "_ = ax.hist(samples2,color = 'blue',label='sample2',alpha = 0.4)\n",
        "\n",
        "_ = ax.axvline(samples1.mean(),linestyle = '--',color = 'red',alpha = 1.,label = f'mean = {samples1.mean():.4f}')\n",
        "_ = ax.axvspan(samples1.mean() - samples1.std()/np.sqrt(sample_size1),\n",
        "               samples1.mean() + samples1.std() / np.sqrt(sample_size1), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples1.std() / np.sqrt(sample_size1):.4f}')\n",
        "\n",
        "_ = ax.axvline(samples2.mean(),linestyle = '--',color = 'blue',alpha = 1.,label = f'mean = {samples2.mean():.4f}')\n",
        "_ = ax.axvspan(samples2.mean() - samples2.std()/np.sqrt(sample_size2),\n",
        "               samples2.mean() + samples2.std() / np.sqrt(sample_size2), \n",
        "               color = 'blue', alpha = 0.7,label = f'standard error = {samples2.std() / np.sqrt(sample_size2):.4f}')\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wnLW2H3AKeLBiI2vtPGttlrU2q7RIs4h4ERfnWkIrtIj4qD5bwIVAobV2rfvx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\n4P8ARai8awCZAygAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gXGRm6rjLEEL",
        "colab_type": "code",
        "outputId": "40cab042-e84a-40b3-b56c-2f80bf48c346",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.ttest_ind(samples1,samples2,equal_var = False)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Ttest_indResult(statistic=-1.5454099912243922, pvalue=0.1327234442423455)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 185
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D935FI3-LoUS",
        "colab_type": "text"
      },
      "source": [
        "# ANOVA"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Zws7d7AsLrZ-",
        "colab_type": "text"
      },
      "source": [
        "## one-way ANOVA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OszWVZz4LIz1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.datasets import load_iris"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "drr8KlmgL_0s",
        "colab_type": "code",
        "outputId": "eecc0b65-3621-4f01-fb8b-03a1a0b622ca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 246
        }
      },
      "source": [
        "data,groups = load_iris(return_X_y=True)\n",
        "print(data[:,0],groups)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[5.1 4.9 4.7 4.6 5.  5.4 4.6 5.  4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4 5.1\n",
            " 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.  5.  5.2 5.2 4.7 4.8 5.4 5.2 5.5 4.9 5.\n",
            " 5.5 4.9 4.4 5.1 5.  4.5 4.4 5.  5.1 4.8 5.1 4.6 5.3 5.  7.  6.4 6.9 5.5\n",
            " 6.5 5.7 6.3 4.9 6.6 5.2 5.  5.9 6.  6.1 5.6 6.7 5.6 5.8 6.2 5.6 5.9 6.1\n",
            " 6.3 6.1 6.4 6.6 6.8 6.7 6.  5.7 5.5 5.5 5.8 6.  5.4 6.  6.7 6.3 5.6 5.5\n",
            " 5.5 6.1 5.8 5.  5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8 7.1 6.3 6.5 7.6 4.9 7.3\n",
            " 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7 6.  6.9 5.6 7.7 6.3 6.7 7.2\n",
            " 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7 6.3 6.4 6.  6.9 6.7 6.9 5.8 6.8\n",
            " 6.7 6.7 6.3 6.5 6.2 5.9] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
            " 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
            " 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\n",
            " 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n",
            " 2 2]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ck5x4utXMLhm",
        "colab_type": "code",
        "outputId": "9daf3beb-8a3d-46d8-c1b4-b5ae937b706f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 417
        }
      },
      "source": [
        "df = pd.DataFrame(np.vstack([data[:,0],groups]).T,columns = ['measures','groups'])\n",
        "df"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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></th>\n",
              "      <th>measures</th>\n",
              "      <th>groups</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>6.7</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>6.3</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>6.5</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>6.2</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>149</th>\n",
              "      <td>5.9</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>150 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "     measures  groups\n",
              "0         5.1     0.0\n",
              "1         4.9     0.0\n",
              "2         4.7     0.0\n",
              "3         4.6     0.0\n",
              "4         5.0     0.0\n",
              "..        ...     ...\n",
              "145       6.7     2.0\n",
              "146       6.3     2.0\n",
              "147       6.5     2.0\n",
              "148       6.2     2.0\n",
              "149       5.9     2.0\n",
              "\n",
              "[150 rows x 2 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ji-Fqu2uMYq6",
        "colab_type": "code",
        "outputId": "f58c23ff-ffe1-4222-92a0-e3cd69e91d82",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        }
      },
      "source": [
        "df['x'] = 0\n",
        "sns.barplot(x = 'x',\n",
        "            y = 'measures',\n",
        "            hue = 'groups',\n",
        "            data = df,\n",
        "            )"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f2dc2440c88>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 189
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dw5UFAGirpDP4a1SzF/wCdy+TlCfpp8GqAgC0WdK7aMokPVDveK9YgweAk1rSu2guNrNN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\n/7wshWmDAxncAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lrFllZHsnQ9m",
        "colab_type": "code",
        "outputId": "7e824519-f4ec-4f36-a257-c736bcc91be0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        }
      },
      "source": [
        "df[df['groups'] == 0]['measures'].values"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([5.1, 4.9, 4.7, 4.6, 5. , 5.4, 4.6, 5. , 4.4, 4.9, 5.4, 4.8, 4.8,\n",
              "       4.3, 5.8, 5.7, 5.4, 5.1, 5.7, 5.1, 5.4, 5.1, 4.6, 5.1, 4.8, 5. ,\n",
              "       5. , 5.2, 5.2, 4.7, 4.8, 5.4, 5.2, 5.5, 4.9, 5. , 5.5, 4.9, 4.4,\n",
              "       5.1, 5. , 4.5, 4.4, 5. , 5.1, 4.8, 5.1, 4.6, 5.3, 5. ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0LMi6DnunQ7g",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LslZtkNCMw0_",
        "colab_type": "code",
        "outputId": "ce31651d-fc9d-4963-990d-a21ab6580fe6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "stats.f_oneway(df[df['groups'] == 0]['measures'].values,\n",
        "               df[df['groups'] == 1]['measures'].values,\n",
        "               df[df['groups'] == 2]['measures'].values,)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "F_onewayResult(statistic=119.26450218450468, pvalue=1.6696691907693826e-31)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 190
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9k1kKJRmNA15",
        "colab_type": "code",
        "outputId": "b65d06de-0fb3-43f9-a7dc-06602eef2a22",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "import statsmodels.api as sm\n",
        "from statsmodels.formula.api import ols\n",
        "\n",
        "mod = ols('measures ~ C(groups)',\n",
        "                data=df).fit()\n",
        "                \n",
        "aov_table = sm.stats.anova_lm(mod, typ=2)\n",
        "esq_sm = aov_table['sum_sq'][0]/(aov_table['sum_sq'][0]+aov_table['sum_sq'][1])\n",
        "aov_table['EtaSq'] = [esq_sm, 'NaN']\n",
        "print(aov_table)\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "              sum_sq     df           F        PR(>F)     EtaSq\n",
            "C(groups)  63.212133    2.0  119.264502  1.669669e-31  0.618706\n",
            "Residual   38.956200  147.0         NaN           NaN       NaN\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OtwVosonO8M1",
        "colab_type": "text"
      },
      "source": [
        "### multiple comparison"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qJycbNhJPbgn",
        "colab_type": "code",
        "outputId": "7eb44271-9faa-471f-8da4-4db11267c777",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        }
      },
      "source": [
        "pair_t = mod.t_test_pairwise('C(groups)')\n",
        "print(pair_t.result_frame)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "          coef   std err          t  ...  Conf. Int. Upp.     pvalue-hs  reject-hs\n",
            "1.0-0.0  0.930  0.102958   9.032819  ...         1.133469  1.776357e-15       True\n",
            "2.0-0.0  1.582  0.102958  15.365506  ...         1.785469  0.000000e+00       True\n",
            "2.0-1.0  0.652  0.102958   6.332686  ...         0.855469  2.765638e-09       True\n",
            "\n",
            "[3 rows x 8 columns]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TuMuKxvSOIlj",
        "colab_type": "text"
      },
      "source": [
        "## 2-way ANOVA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IknIpEEhNj1M",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df = pd.read_csv(\"https://raw.githubusercontent.com/Opensourcefordatascience/Data-sets/master/crop_yield.csv\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g1Yg2xIbORLK",
        "colab_type": "code",
        "outputId": "8c378848-1d23-4f99-e754-b462c11ddf82",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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></th>\n",
              "      <th>Fert</th>\n",
              "      <th>Water</th>\n",
              "      <th>Yield</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>A</td>\n",
              "      <td>High</td>\n",
              "      <td>27.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>A</td>\n",
              "      <td>High</td>\n",
              "      <td>33.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>A</td>\n",
              "      <td>High</td>\n",
              "      <td>29.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>A</td>\n",
              "      <td>High</td>\n",
              "      <td>35.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>A</td>\n",
              "      <td>High</td>\n",
              "      <td>33.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  Fert Water  Yield\n",
              "0    A  High   27.4\n",
              "1    A  High   33.6\n",
              "2    A  High   29.8\n",
              "3    A  High   35.2\n",
              "4    A  High   33.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 194
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BoRRQWxMOStr",
        "colab_type": "code",
        "outputId": "191aa6dd-1e38-4acd-e792-6e0e5058c634",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        }
      },
      "source": [
        "import statsmodels.api as sm\n",
        "from statsmodels.formula.api import ols\n",
        "import statsmodels.stats.multicomp\n",
        "\"Yield ~ C(Fert) + C(Water) + C(Fert):C(Water)\"\n",
        "model = ols('Yield ~ C(Fert)*C(Water)', df).fit() # with interaction\n",
        "print(f\"Overall model F({model.df_model: .0f},{model.df_resid: .0f}) = {model.fvalue: .3f}, p = {model.f_pvalue: .4f}\")\n",
        "print()\n",
        "print(model.summary())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overall model F( 3, 16) =  4.112, p =  0.0243\n",
            "\n",
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                  Yield   R-squared:                       0.435\n",
            "Model:                            OLS   Adj. R-squared:                  0.330\n",
            "Method:                 Least Squares   F-statistic:                     4.112\n",
            "Date:                Sun, 24 Nov 2019   Prob (F-statistic):             0.0243\n",
            "Time:                        16:52:02   Log-Likelihood:                -50.996\n",
            "No. Observations:                  20   AIC:                             110.0\n",
            "Df Residuals:                      16   BIC:                             114.0\n",
            "Df Model:                           3                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "================================================================================================\n",
            "                                   coef    std err          t      P>|t|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------------------------\n",
            "Intercept                       31.8000      1.549     20.527      0.000      28.516      35.084\n",
            "C(Fert)[T.B]                    -1.9600      2.191     -0.895      0.384      -6.604       2.684\n",
            "C(Water)[T.Low]                 -1.8000      2.191     -0.822      0.423      -6.444       2.844\n",
            "C(Fert)[T.B]:C(Water)[T.Low]    -3.5200      3.098     -1.136      0.273     -10.088       3.048\n",
            "==============================================================================\n",
            "Omnibus:                        3.427   Durbin-Watson:                   2.963\n",
            "Prob(Omnibus):                  0.180   Jarque-Bera (JB):                1.319\n",
            "Skew:                          -0.082   Prob(JB):                        0.517\n",
            "Kurtosis:                       1.752   Cond. No.                         6.85\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j8wIURL_OfCj",
        "colab_type": "code",
        "outputId": "0093009c-99fa-4c6f-eaa0-4e035c5f5023",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 104
        }
      },
      "source": [
        "res = sm.stats.anova_lm(model, typ= 2)\n",
        "print(res)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "                   sum_sq    df         F    PR(>F)\n",
            "C(Fert)            69.192   1.0  5.766000  0.028847\n",
            "C(Water)           63.368   1.0  5.280667  0.035386\n",
            "C(Fert):C(Water)   15.488   1.0  1.290667  0.272656\n",
            "Residual          192.000  16.0       NaN       NaN\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h_k77U73OlCm",
        "colab_type": "code",
        "outputId": "fe47ae20-239b-42de-aa4f-3ca28ddca8cc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        }
      },
      "source": [
        "model2 = ols('Yield ~ C(Fert)+ C(Water)', df).fit() # without interaction\n",
        "print(f\"Overall model F({model2.df_model: .0f},{model2.df_resid: .0f}) = {model2.fvalue: .3f}, p = {model2.f_pvalue: .4f}\")\n",
        "print()\n",
        "print(model2.summary())\n",
        "res2 = sm.stats.anova_lm(model2, typ= 2)\n",
        "print(res2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Overall model F( 2, 17) =  5.430, p =  0.0150\n",
            "\n",
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:                  Yield   R-squared:                       0.390\n",
            "Model:                            OLS   Adj. R-squared:                  0.318\n",
            "Method:                 Least Squares   F-statistic:                     5.430\n",
            "Date:                Sun, 24 Nov 2019   Prob (F-statistic):             0.0150\n",
            "Time:                        16:52:02   Log-Likelihood:                -51.772\n",
            "No. Observations:                  20   AIC:                             109.5\n",
            "Df Residuals:                      17   BIC:                             112.5\n",
            "Df Model:                           2                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "===================================================================================\n",
            "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
            "-----------------------------------------------------------------------------------\n",
            "Intercept          32.6800      1.353     24.153      0.000      29.825      35.535\n",
            "C(Fert)[T.B]       -3.7200      1.562     -2.381      0.029      -7.016      -0.424\n",
            "C(Water)[T.Low]    -3.5600      1.562     -2.279      0.036      -6.856      -0.264\n",
            "==============================================================================\n",
            "Omnibus:                        1.169   Durbin-Watson:                   2.736\n",
            "Prob(Omnibus):                  0.557   Jarque-Bera (JB):                0.820\n",
            "Skew:                          -0.081   Prob(JB):                        0.664\n",
            "Kurtosis:                       2.022   Cond. No.                         3.19\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
            "           sum_sq    df         F    PR(>F)\n",
            "C(Fert)    69.192   1.0  5.669070  0.029228\n",
            "C(Water)   63.368   1.0  5.191895  0.035887\n",
            "Residual  207.488  17.0       NaN       NaN\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h0bwtD6BO1CO",
        "colab_type": "text"
      },
      "source": [
        "### multiple comparison"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7gtkvXe5Ov8i",
        "colab_type": "code",
        "outputId": "c958fa51-1111-4d80-bcb8-55540dfb08ba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        }
      },
      "source": [
        "mc = statsmodels.stats.multicomp.MultiComparison(df['Yield'], df['Fert'])\n",
        "mc_results = mc.tukeyhsd()\n",
        "print(mc_results)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Multiple Comparison of Means - Tukey HSD, FWER=0.05 \n",
            "====================================================\n",
            "group1 group2 meandiff p-adj   lower   upper  reject\n",
            "----------------------------------------------------\n",
            "     A      B    -3.72 0.0459 -7.3647 -0.0753   True\n",
            "----------------------------------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ycc1FOIZO3Qp",
        "colab_type": "code",
        "outputId": "280bfe90-d118-4011-fd22-76f23e756aeb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        }
      },
      "source": [
        "mc = statsmodels.stats.multicomp.MultiComparison(df['Yield'], df['Water'])\n",
        "mc_results = mc.tukeyhsd()\n",
        "print(mc_results)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Multiple Comparison of Means - Tukey HSD, FWER=0.05\n",
            "===================================================\n",
            "group1 group2 meandiff p-adj   lower  upper  reject\n",
            "---------------------------------------------------\n",
            "  High    Low    -3.56 0.0574 -7.2436 0.1236  False\n",
            "---------------------------------------------------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hYMkHyHsPMK3",
        "colab_type": "text"
      },
      "source": [
        "# resampling"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rsv1mpGDPfdI",
        "colab_type": "text"
      },
      "source": [
        "## remember this?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z17vBMg3PFU0",
        "colab_type": "code",
        "outputId": "125af9d3-19b5-4ae2-fb39-4d52f9b0657e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "mean = 117\n",
        "n_samples = 78\n",
        "np.random.seed(12345)\n",
        "samples = np.random.exponential(scale = mean, size = n_samples)\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples,bins = 5,alpha = 0.7,color = 'blue')\n",
        "_ = ax.axvline(samples.mean(),linestyle = '--',color = 'black',alpha = 1.,label = f'mean = {samples.mean():.4f}')\n",
        "_ = ax.axvspan(samples.mean() - samples.std()/np.sqrt(n_samples),\n",
        "               samples.mean() + samples.std() / np.sqrt(n_samples), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples.std() / np.sqrt(n_samples):.4f}')\n",
        "_ = ax.legend()\n",
        "print(stats.ttest_1samp(samples,100))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ttest_1sampResult(statistic=2.2858733668219404, pvalue=0.025012543966142314)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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fdQq/jh07UlBQwJrgy/S0adPKfNzAgQOZMGFC7CjilStXsnPnzmPmy8rKYu7cuWzatImD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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "808TgPNcPg7t",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n_sim = 1000\n",
        "results = []\n",
        "for _ in range(n_sim):\n",
        "    resampled = np.random.choice(samples,\n",
        "                                 size = n_samples,\n",
        "                                 replace = True, #\n",
        "                                 )\n",
        "    resampled_mean = resampled.mean()\n",
        "    results.append(resampled_mean)\n",
        "results = np.array(results)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QCwEGzn4P_fm",
        "colab_type": "code",
        "outputId": "aff7f733-ba1f-4614-c951-caf86641affc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        }
      },
      "source": [
        "fig,ax = plt.subplots(figsize = (8,6))\n",
        "_ = ax.hist(results,color = 'blue',bins = 25,alpha = 0.4)\n",
        "_ = ax.axvline(100,linestyle = '--',color = 'black',label = 'what we want to compare against to')\n",
        "_ = ax.axvline(mean,linestyle = '--',color = 'red',label = f'true mean = {mean:.4f}')\n",
        "_ = ax.axvline(results.mean(),linestyle = '--',color = 'blue',label = f'average of resampled means = {results.mean():.4f}')\n",
        "_ = ax.axvline(samples.mean(),linestyle = '--',color = 'yellow',label = f'sample mean = {samples.mean():.4f}')\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CO2nSJKxatQrx8fGIj4/Hrl27AAALFixAz549ER8fj549e2LBggUAlCsa5j525cqVmDRp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\nrkJggg==\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q2uWndDiP_5P",
        "colab_type": "code",
        "outputId": "9f40d0b0-2220-4f4a-f50f-3f81d3d09325",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "p = (np.sum(results < mean) + 1) / (n_sim + 1)\n",
        "p / 2"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.07642357642357642"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 203
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7847bhjzTNd2",
        "colab_type": "text"
      },
      "source": [
        "## and this?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6pHc2ytMS-gl",
        "colab_type": "code",
        "outputId": "3d477c72-074f-46d1-e0ce-e65e6592c33a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "sample_mean1 = 0.52\n",
        "sample_mean2 = 1.03\n",
        "sample_sd1 = 0.15 * 5\n",
        "sample_sd2 = 0.15 #\n",
        "sample_size1 = 30\n",
        "sample_size2 = 60 #\n",
        "\n",
        "np.random.seed(12345)\n",
        "samples1 = np.random.normal(sample_mean1,sample_sd1,sample_size1)\n",
        "samples2 = np.random.normal(sample_mean2,sample_sd2,sample_size2)\n",
        "\n",
        "fig,ax = plt.subplots(figsize = (8,4))\n",
        "_ = ax.hist(samples1,color = 'red',label='sample1',alpha = 0.4)\n",
        "_ = ax.hist(samples2,color = 'blue',label='sample2',alpha = 0.4)\n",
        "\n",
        "_ = ax.axvline(samples1.mean(),linestyle = '--',color = 'red',alpha = 1.,label = f'mean = {samples1.mean():.4f}')\n",
        "_ = ax.axvspan(samples1.mean() - samples1.std()/np.sqrt(sample_size1),\n",
        "               samples1.mean() + samples1.std() / np.sqrt(sample_size1), \n",
        "               color = 'red', alpha = 0.7,label = f'standard error = {samples1.std() / np.sqrt(sample_size1):.4f}')\n",
        "\n",
        "_ = ax.axvline(samples2.mean(),linestyle = '--',color = 'blue',alpha = 1.,label = f'mean = {samples2.mean():.4f}')\n",
        "_ = ax.axvspan(samples2.mean() - samples2.std()/np.sqrt(sample_size2),\n",
        "               samples2.mean() + samples2.std() / np.sqrt(sample_size2), \n",
        "               color = 'blue', alpha = 0.7,label = f'standard error = {samples2.std() / np.sqrt(sample_size2):.4f}')\n",
        "_ = ax.legend()\n",
        "\n",
        "print(stats.ttest_ind(samples1,samples2,equal_var=False))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Ttest_indResult(statistic=-1.5454099912243922, pvalue=0.1327234442423455)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wnLW2H3AKeLBiI2vtPGttlrU2q7RIs4h4ERfnWkIrtIj4qD5bwIVAobV2rfvx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\n4P8ARai8awCZAygAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BUCm6ZoQtLfh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(12345)\n",
        "diffs = []\n",
        "for _ in range(100):\n",
        "    group1_ = np.random.choice(samples1,size = 1000, replace = True)\n",
        "    group2_ = np.random.choice(samples2,size = 1000, replace = True)\n",
        "\n",
        "    diff = group1_.mean() - group2_.mean()\n",
        "    diffs.append(diff)\n",
        "diffs = np.array(diffs)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BnA_0tj4t-MX",
        "colab_type": "code",
        "outputId": "3016d0c5-016a-4a0e-cb22-4d74df1d1f2a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 353
        }
      },
      "source": [
        "plt.hist(diffs)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 2.,  1.,  5., 11., 11., 22., 18., 13., 13.,  4.]),\n",
              " array([-0.30468451, -0.29166492, -0.27864533, -0.26562574, -0.25260615,\n",
              "        -0.23958656, -0.22656697, -0.21354738, -0.20052779, -0.18750819,\n",
              "        -0.1744886 ]),\n",
              " <a list of 10 Patch objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "N347AJgpTUhi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "mean_difference_between_samples = samples1.mean() - samples2.mean()\n",
        "\n",
        "pool = np.concatenate([samples1,samples2])\n",
        "np.random.seed(12345)\n",
        "results = []\n",
        "for _ in range(n_sim):\n",
        "    np.random.shuffle(pool)\n",
        "    new_samples1 = pool[:samples1.shape[0]]\n",
        "    new_samples2 = pool[samples1.shape[0]:]\n",
        "\n",
        "    new_mean_difference_between_samples = new_samples1.mean() - new_samples2.mean()\n",
        "    results.append(new_mean_difference_between_samples)\n",
        "results = np.array(results)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9xmyQEMrT1JM",
        "colab_type": "code",
        "outputId": "31715e32-e5fb-4e5c-fe52-c7542d946913",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 374
        }
      },
      "source": [
        "fig,ax = plt.subplots(figsize = (8,6))\n",
        "_ = ax.hist(results,bins = 25,alpha = 0.4,color = 'blue')\n",
        "_ = ax.axvline(mean_difference_between_samples,linestyle = '--', color = 'black',label = 'experiment difference')\n",
        "\n",
        "_ = ax.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AkEExJ6ysrCx0BABABkvZCVu2bJmWLVsWOgYAIA8z5oTdeuutkqQRI0YETgIA2I0ZMwAA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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a6Na2hO_UYUp",
        "colab_type": "code",
        "outputId": "5066e5ac-6e23-4ec0-dc09-34384f7dff99",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "p = (np.sum(results < mean_difference_between_samples) + 1) / (n_sim + 1)\n",
        "p / 2"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.01048951048951049"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 207
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2Xmx9I_BUwSV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "np.random.seed(12345)\n",
        "responses = np.random.choice([0,1],size = 25, )\n",
        "corrects = np.random.choice([0,1],size = 25)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GTFDL7YEuoM3",
        "colab_type": "code",
        "outputId": "513be6c6-6c44-4a5c-da06-45d0571469a5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "performance = np.sum(responses == corrects) / len(responses)\n",
        "print(performance)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.6\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nQaciqeJvfe2",
        "colab_type": "code",
        "outputId": "ff6ebcf8-53d5-4783-a2f6-13ec8978d14e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 819
        }
      },
      "source": [
        "import pandas as pd\n",
        "\n",
        "df = pd.DataFrame(np.vstack([responses,corrects]).T,columns = ['response','corrects'])\n",
        "df"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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></th>\n",
              "      <th>response</th>\n",
              "      <th>corrects</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    response  corrects\n",
              "0          0         0\n",
              "1          1         1\n",
              "2          1         0\n",
              "3          1         0\n",
              "4          0         1\n",
              "5          1         1\n",
              "6          0         1\n",
              "7          0         1\n",
              "8          1         1\n",
              "9          0         0\n",
              "10         1         1\n",
              "11         1         1\n",
              "12         0         1\n",
              "13         1         1\n",
              "14         1         1\n",
              "15         0         1\n",
              "16         1         0\n",
              "17         1         0\n",
              "18         1         1\n",
              "19         0         1\n",
              "20         0         0\n",
              "21         0         0\n",
              "22         1         1\n",
              "23         1         1\n",
              "24         1         1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uvt8bDJnwoGT",
        "colab_type": "code",
        "outputId": "5673294f-cde5-406f-d0db-c471dcb37f31",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 123
        }
      },
      "source": [
        "np.arange(len(responses))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
              "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
              "       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,\n",
              "       51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,\n",
              "       68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84,\n",
              "       85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W5cAkjBXw2Ev",
        "colab_type": "code",
        "outputId": "8f113d96-68b6-4dcf-fe2b-2ab2d175f3c2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "range(len(responses))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "range(0, 100)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UPs57Srtuwd3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "res = []\n",
        "for _ in range(100):\n",
        "    idx = np.random.choice(np.arange(len(responses)),size = 1000, replace = True)\n",
        "    reps = responses[idx]\n",
        "    corr = corrects[idx]\n",
        "    res.append( np.sum(reps == corr) / 1000)\n",
        "res = np.array(res)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zF8pwMlIvRml",
        "colab_type": "code",
        "outputId": "a96c65d8-deee-4e16-d2a6-9790d236e64b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        }
      },
      "source": [
        "plt.hist(res,alpha = 0.3)\n",
        "plt.axvline(res.mean())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.lines.Line2D at 0x7f56cf38ddd8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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em+S67mf5piRvm4+8I6mqx8yFqSeNvws8AzgIuB5YPW3OG4Cz97GdpzD15PITF2NW4HeA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\nA4mcLKZ+ZCnSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CZYjvBTUxL0Y",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}