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December 14, 2021 01:27
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ml_lab4.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "metadata": { | |
| "colab": { | |
| "name": "ml_lab4.ipynb", | |
| "provenance": [], | |
| "collapsed_sections": [], | |
| "authorship_tag": "ABX9TyOWv3aElXB0tnwovhKk/rQj", | |
| "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/gist/executed/9b0b673c8239febdf671bc93597c8956/ml_lab4.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Import libraries" | |
| ], | |
| "metadata": { | |
| "id": "8rASFPaZyXZ6" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 302, | |
| "metadata": { | |
| "id": "uchZSuNXxDa5" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import math\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "import pandas as pd\n", | |
| "import numpy as np\n", | |
| "from mpl_toolkits.mplot3d import Axes3D\n", | |
| "from sklearn import datasets\n", | |
| "from sklearn.decomposition import PCA\n", | |
| "from scipy.stats import shapiro\n", | |
| "from scipy.stats import ks_2samp\n", | |
| "from scipy.stats import chi2_contingency\n", | |
| "from scipy.optimize import curve_fit\n", | |
| "from scipy.stats import ttest_ind" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# Shapiro–Wilk test" | |
| ], | |
| "metadata": { | |
| "id": "cMerJiFAybt1" | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Load Iris dataset" | |
| ], | |
| "metadata": { | |
| "id": "A-F59CpKyfrO" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "iris = datasets.load_iris()\n", | |
| "\n", | |
| "data = pd.DataFrame(data= np.c_[iris['data'], iris['target']], columns= iris['feature_names'] + ['target'])\n", | |
| "\n", | |
| "data = data.loc[data['target'] == 0]\n", | |
| "\n", | |
| "data.head()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 206 | |
| }, | |
| "id": "-8M_zyUMyhoy", | |
| "outputId": "c7221cd5-a53d-4b7f-bae6-56e95f5e4898" | |
| }, | |
| "execution_count": 46, | |
| "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>sepal length (cm)</th>\n", | |
| " <th>sepal width (cm)</th>\n", | |
| " <th>petal length (cm)</th>\n", | |
| " <th>petal width (cm)</th>\n", | |
| " <th>target</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>5.1</td>\n", | |
| " <td>3.5</td>\n", | |
| " <td>1.4</td>\n", | |
| " <td>0.2</td>\n", | |
| " <td>0.0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>4.9</td>\n", | |
| " <td>3.0</td>\n", | |
| " <td>1.4</td>\n", | |
| " <td>0.2</td>\n", | |
| " <td>0.0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>4.7</td>\n", | |
| " <td>3.2</td>\n", | |
| " <td>1.3</td>\n", | |
| " <td>0.2</td>\n", | |
| " <td>0.0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>4.6</td>\n", | |
| " <td>3.1</td>\n", | |
| " <td>1.5</td>\n", | |
| " <td>0.2</td>\n", | |
| " <td>0.0</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>5.0</td>\n", | |
| " <td>3.6</td>\n", | |
| " <td>1.4</td>\n", | |
| " <td>0.2</td>\n", | |
| " <td>0.0</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " sepal length (cm) sepal width (cm) ... petal width (cm) target\n", | |
| "0 5.1 3.5 ... 0.2 0.0\n", | |
| "1 4.9 3.0 ... 0.2 0.0\n", | |
| "2 4.7 3.2 ... 0.2 0.0\n", | |
| "3 4.6 3.1 ... 0.2 0.0\n", | |
| "4 5.0 3.6 ... 0.2 0.0\n", | |
| "\n", | |
| "[5 rows x 5 columns]" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 46 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Check features distributions on histograms" | |
| ], | |
| "metadata": { | |
| "id": "piy9Br6ny-TE" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "target_feature_name = 'sepal length (cm)'\n", | |
| "\n", | |
| "plt.hist(data[target_feature_name])\n", | |
| "plt.xlabel(target_feature_name)\n", | |
| "plt.ylabel('Amount of values per range')\n", | |
| "plt.show()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 279 | |
| }, | |
| "id": "HM24aKn2zDhP", | |
| "outputId": "934f2d1f-6bef-40f4-efd6-e321ece5678f" | |
| }, | |
| "execution_count": 66, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Shapiro–Wilk test on the specific feature data" | |
| ], | |
| "metadata": { | |
| "id": "OxAVey-R1wav" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "stat, p = shapiro(data[target_feature_name])\n", | |
| "print('Statistics=%.3f, p=%.3f' % (stat, p))\n", | |
| "\n", | |
| "alpha = 0.05\n", | |
| "if p > alpha:\n", | |
| "\tprint('Sample looks Gaussian (fail to reject H0)')\n", | |
| "else:\n", | |
| "\tprint('Sample does not look Gaussian (reject H0)')" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "ZJbFYLaW1392", | |
| "outputId": "afac74a8-5737-4d83-b567-d9d23458be8e" | |
| }, | |
| "execution_count": 67, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "Statistics=0.978, p=0.460\n", | |
| "Sample looks Gaussian (fail to reject H0)\n" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# Kolmogorov–Smirnov test on generated data" | |
| ], | |
| "metadata": { | |
| "id": "5PnXRefj48XN" | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Generate Normal distribution" | |
| ], | |
| "metadata": { | |
| "id": "FcctJ38f65f-" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "x1 = np.random.normal(loc=10,scale=math.sqrt(10),size=40)\n", | |
| "x2 = np.random.normal(loc=15,scale=math.sqrt(15),size=40)\n", | |
| "x3 = np.random.normal(loc=20,scale=math.sqrt(20),size=40)\n", | |
| "x4 = np.random.normal(loc=25,scale=math.sqrt(25),size=40)\n", | |
| "x5 = np.random.normal(loc=30,scale=math.sqrt(30),size=40)\n", | |
| "\n", | |
| "x = np.append(np.append(np.append(x1, x1), np.append(x3, x4)), x5)\n", | |
| "\n", | |
| "plt.hist(x)\n", | |
| "plt.title('Normal distribution with given mean and std deviation')\n", | |
| "plt.show()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 281 | |
| }, | |
| "id": "jhs-mBve5BPO", | |
| "outputId": "0a955591-529f-4f73-e63c-7aa2d18c5014" | |
| }, | |
| "execution_count": 149, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Generate Chi-squarred distribution" | |
| ], | |
| "metadata": { | |
| "id": "4Byjyjwk68QZ" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "y1 = np.random.chisquare(10,40)\n", | |
| "y2 = np.random.chisquare(15,40)\n", | |
| "y3 = np.random.chisquare(20,40)\n", | |
| "y4 = np.random.chisquare(25,40)\n", | |
| "y5 = np.random.chisquare(30,40)\n", | |
| "\n", | |
| "y = np.append(np.append(np.append(y1, y2), np.append(y3, y4)), y5)\n", | |
| "\n", | |
| "plt.hist(y)\n", | |
| "plt.title('Chi-squarred distribution with given degrees of freedom')\n", | |
| "plt.show()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 281 | |
| }, | |
| "id": "w6YzAx4C8J7v", | |
| "outputId": "5e0a45e6-8a8c-42cc-8e17-f4686867f39c" | |
| }, | |
| "execution_count": 144, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Kolmogorov–Smirnov test on 2 distributions" | |
| ], | |
| "metadata": { | |
| "id": "P-4wteSe90E5" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "stat, p = ks_2samp(x, y)\n", | |
| "print('Statistics=%.3f, p=%.3f' % (stat, p))\n", | |
| "\n", | |
| "alpha = 0.05\n", | |
| "if p >= alpha:\n", | |
| "\tprint('2 distributions are probably similar')\n", | |
| "else:\n", | |
| "\tprint('2 distributions are probably different')" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "aLuTSiiW97IG", | |
| "outputId": "3340d122-e467-45ff-eaf6-042ba37382fc" | |
| }, | |
| "execution_count": 150, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "Statistics=0.125, p=0.088\n", | |
| "2 distributions are probably similar\n" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# Kolmogorov–Smirnov test on data from dataset" | |
| ], | |
| "metadata": { | |
| "id": "303-rJJPAYOj" | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Reading the dataset" | |
| ], | |
| "metadata": { | |
| "id": "wONarAtMAlWH" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "data = pd.read_csv(\"https://drive.google.com/uc?id=1od2L_Iokq5UPkq6Lv4DWWquC4xtqsHh-\", delimiter=r\"\\s+\", header=0)\n", | |
| "\n", | |
| "data = pd.DataFrame(data, columns=['country', 'population', 'area', 'gdp', 'ind'])\n", | |
| "\n", | |
| "data = data.loc[data['area'].notnull()].loc[data['area'] > 10].loc[data['population'].notnull()]\n", | |
| "\n", | |
| "data.head()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 225 | |
| }, | |
| "id": "Ab1NfmGbAakx", | |
| "outputId": "b08bad41-d85b-4dc2-b594-fcd1836d036f" | |
| }, | |
| "execution_count": 196, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "1105\n" | |
| ] | |
| }, | |
| { | |
| "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>country</th>\n", | |
| " <th>population</th>\n", | |
| " <th>area</th>\n", | |
| " <th>gdp</th>\n", | |
| " <th>ind</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>China</td>\n", | |
| " <td>1319498000</td>\n", | |
| " <td>9640821.0</td>\n", | |
| " <td>2630113.0</td>\n", | |
| " <td>ind</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>India</td>\n", | |
| " <td>1169016000</td>\n", | |
| " <td>3287263.0</td>\n", | |
| " <td>886867.0</td>\n", | |
| " <td>ind</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>USA</td>\n", | |
| " <td>302425000</td>\n", | |
| " <td>9629091.0</td>\n", | |
| " <td>13244550.0</td>\n", | |
| " <td>ind</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>Indonesia</td>\n", | |
| " <td>231627000</td>\n", | |
| " <td>1904569.0</td>\n", | |
| " <td>364239.0</td>\n", | |
| " <td>ind</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>Brazil</td>\n", | |
| " <td>186736000</td>\n", | |
| " <td>8514877.0</td>\n", | |
| " <td>1067706.0</td>\n", | |
| " <td>ind</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " country population area gdp ind\n", | |
| "0 China 1319498000 9640821.0 2630113.0 ind\n", | |
| "1 India 1169016000 3287263.0 886867.0 ind\n", | |
| "2 USA 302425000 9629091.0 13244550.0 ind\n", | |
| "3 Indonesia 231627000 1904569.0 364239.0 ind\n", | |
| "4 Brazil 186736000 8514877.0 1067706.0 ind" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 196 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "population_log = np.log10(np.log10(data['population']))\n", | |
| "area_log = np.log10(np.log10(data['area']))\n", | |
| "\n", | |
| "\n", | |
| "def func(x, a, b):\n", | |
| " y = a*x + b\n", | |
| " return y\n", | |
| "\n", | |
| "alpha = curve_fit(func, xdata = area_log, ydata = population_log)[0]\n", | |
| "b1 = alpha[0]\n", | |
| "b2 = alpha[1]\n", | |
| "\n", | |
| "cst_fun = lambda t: t*b1 + b2\n", | |
| "vfunc = np.vectorize(cst_fun)\n", | |
| "f_area_log = vfunc(area_log)\n", | |
| "\n", | |
| "plt.hist(population_log)\n", | |
| "plt.title('log10(log10(population))')\n", | |
| "plt.show()\n", | |
| "\n", | |
| "plt.hist(f_area_log)\n", | |
| "plt.title('least squares population_log to area_log')\n", | |
| "plt.show()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 545 | |
| }, | |
| "id": "c10pW4ITJraQ", | |
| "outputId": "1ac917df-7b68-4776-8471-2272f0f6be5b" | |
| }, | |
| "execution_count": 249, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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qvqnezMxaazhdKHOB7jTcDcwbfjlmZlZV1QAP4GZJayQtTNOmRsT2NLwDmNr06szMrF9Vv5X+jyJiq6TnArdI+mV5ZkSEpKi3Ygr8hQDHHnvssIo1M7N9Kl2BR8TW9LgLuAk4DdgpaRpAetzVz7pLIqIrIro6OjqaU7WZmTUOcElHShrfNwy8GvgFsBKYnxabD6xoVZFmZnagKl0oU4GbJPUtf0NEfF/SHcAySQuAB4ELW1emmZnVahjgEbEJeHGd6Y8A57aiKDMza8yfxDQzy5QD3MwsU1XfRmhmB5nORd9pdwk2TL4CNzPLlAPczCxTDnAzs0w5wM3MMuUANzPLlAPczCxTDnAzs0w5wM3MMuUANzPLlAPczCxTDnAzs0w5wM3MMuUANzPLlAPczCxTlQNc0hhJayV9O43PlHSbpI2SbpQ0rnVlmplZrcFcgV8KbCiNfx64MiKOBx4DFjSzMDMzG1ilAJc0A7gAuCaNCzgHWJ4W6QbmtaJAMzOrr+oV+FXAZcDv0/gUYHdE7E3jW4Dp9VaUtFBSj6Se3t7eYRVrZmb7NAxwSa8FdkXEmqHsICKWRERXRHR1dHQMZRNmZlZHle/EPAN4naQ5wOHAUcDVwERJY9NV+Axga+vKNDOzWg2vwCPiwxExIyI6gYuAH0TEm4HVwBvTYvOBFS2r0szMDjCc94F/CHi/pI0UfeLXNqckMzOrokoXyrMi4lbg1jS8CTit+SWZmVkV/iSmmVmmHOBmZplygJuZZcoBbmaWKQe4mVmmHOBmZplygJuZZcoBbmaWKQe4mVmmHOBmZplygJuZZcoBbmaWKQe4mVmmHOBmZplygJuZZcoBbmaWqSpfany4pNsl3SXpHkmfStNnSrpN0kZJN0oa1/pyzcysT5Ur8KeAcyLixcCpwGxJpwOfB66MiOOBx4AFrSvTzMxqVflS44iIPWn00PQTwDnA8jS9G5jXkgrNzKyuSn3gksZIWgfsAm4B7gd2R8TetMgWYHo/6y6U1COpp7e3txk1m5kZFQM8Ip6JiFOBGRRfZHxy1R1ExJKI6IqIro6OjiGWaWZmtQb1LpSI2A2sBl4BTJTU9632M4CtTa7NzMwGMLbRApI6gKcjYrekI4BXUdzAXA28Efg6MB9Y0cpCzcyGq3PRd9qy382LL2jJdhsGODAN6JY0huKKfVlEfFvSeuDrkj4NrAWubUmFZmZWV8MAj4ifAy+pM30TRX+4mZm1gT+JaWaWKQe4mVmmHOBmZplygJuZZcoBbmaWKQe4mVmmHOBmZplygJuZZcoBbmaWKQe4mVmmHOBmZplygJuZZcoBbmaWKQe4mVmmHOBmZplygJuZZaphgEt6nqTVktZLukfSpWn6ZEm3SLovPU5qfblmZtanyhX4XuADETELOB34n5JmAYuAVRFxArAqjZuZ2QhpGOARsT0i7kzDTwAbgOnAXKA7LdYNzGtVkWZmdqBB9YFL6qT4fszbgKkRsT3N2gFM7WedhZJ6JPX09vYOo1QzMyurHOCS/gD4JvC+iHi8PC8iAoh660XEkojoioiujo6OYRVrZmb7VApwSYdShPfXIuJbafJOSdPS/GnArtaUaGZm9VR5F4qAa4ENEfGF0qyVwPw0PB9Y0fzyzMysP2MrLHMG8Bbgbknr0rSPAIuBZZIWAA8CF7amRDMzq6dhgEfEjwH1M/vc5pZjZmZV+ZOYZmaZcoCbmWWqSh+42YjpXPSdtux38+IL2rJfs+HwFbiZWaYc4GZmmXKAm5llygFuZpYpB7iZWaYc4GZmmfLbCM3arF1vnbT8+QrczCxTDnAzs0w5wM3MMuUANzPLlG9imuEbiZYnX4GbmWWqyleqfUXSLkm/KE2bLOkWSfelx0mtLdPMzGpVuQK/DphdM20RsCoiTgBWpXEzMxtBDQM8In4EPFozeS7QnYa7gXlNrsvMzBoYah/41IjYnoZ3AFObVI+ZmVU07JuYERFA9Ddf0kJJPZJ6ent7h7s7MzNLhhrgOyVNA0iPu/pbMCKWRERXRHR1dHQMcXdmZlZrqO8DXwnMBxanxxVNq8jazu+JNstDlbcRLgV+CpwkaYukBRTB/SpJ9wHnpXEzMxtBDa/AI+Lifmad2+RazMxsEPxJTDOzTDnAzcwy5QA3M8uUA9zMLFMOcDOzTDnAzcwy5QA3M8uUA9zMLFMOcDOzTDnAzcwy5QA3M8uUA9zMLFND/XeyNgL8b13NbCC+Ajczy5QD3MwsU+5CacDdGGY2WvkK3MwsU8O6Apc0G7gaGANcExEt+2o1Xwmbme1vyFfgksYAfw+cD8wCLpY0q1mFmZnZwIbThXIasDEiNkXE74CvA3ObU5aZmTUynC6U6cBDpfEtwMtrF5K0EFiYRvdIurc0+2jg4WHU0EqubWhc2+CN1rrAtQ3VfrXp88Pe3nH1Jrb8XSgRsQRYUm+epJ6I6Gp1DUPh2obGtQ3eaK0LXNtQjVRtw+lC2Qo8rzQ+I00zM7MRMJwAvwM4QdJMSeOAi4CVzSnLzMwaGXIXSkTslfQe4F8p3kb4lYi4Z5Cbqdu1Mkq4tqFxbYM3WusC1zZUI1KbImIk9mNmZk3mT2KamWXKAW5mlqmWBbik2ZLulbRR0qI68y+R1CtpXfp5e2nefEn3pZ/5o6y2Z0rTm37TtlFtaZkLJa2XdI+kG0rTW9Zuw6yrrW0m6crS/n8laXdpXrvPtYFqa3e7HStptaS1kn4uaU5p3ofTevdKes1oqEtSp6T/V2qzLzWzroq1HSdpVarrVkkzSvOaf65FRNN/KG5q3g88HxgH3AXMqlnmEuDv6qw7GdiUHiel4UmjobY0b08r2mwQtZ0ArO1rE+C5rW634dQ1GtqsZvn3UtxwHxXnWn+1jYZ2o7gR9+40PAvYXBq+CzgMmJm2M2YU1NUJ/KLNbfYNYH4aPgf451aea626Ah/Ox+xfA9wSEY9GxGPALcDsUVJbq1Wp7R3A36e2ISJ2pemtbLfh1NVqg30+LwaWpuHRdq6Va2u1KrUFcFQangBsS8Nzga9HxFMR8QCwMW2v3XW1WpXaZgE/SMOrS/Nbcq61KsDrfcx+ep3l3pBeaiyX1PehoKrrtqM2gMMl9Uj6maR5Tayram0nAidK+kmqYfYg1m1HXdD+NgOKl7cUV4x9v2Cj5VyrVxu0v90uB/5M0hbguxSvEKqu2466AGamrpUfSjqzSTUNpra7gNen4T8BxkuaUnHdQWvnTcz/A3RGxIso/hp1t7GWWgPVdlwUH5F9E3CVpBeMcG1jKborzqa4YvuypIkjXEM9A9XV7jbrcxGwPCKeadP+B1Kvtna328XAdRExA5gD/LOk0fDGh/7q2g4cGxEvAd4P3CDpqAG20wofBM6StBY4i+LT6S0731r1ZDT8mH1EPBIRT6XRa4CXVV23jbUREVvT4ybgVuAlI1kbxV/ulRHxdHr5+iuK4Gxluw2nrtHQZn0uYv8uirafawPUNhrabQGwLNXwU+Bwin/S1O5zrW5dqUvnkTR9DUV/9YlNqqtSbRGxLSJen/6IfDRN211l3SFpUWf/WIpO+pns6+w/pWaZaaXhPwF+Vursf4Cio39SGp48SmqbBByWho8G7mOAm1Itqm020F2q4SFgSivbbZh1tb3N0nInA5tJH14bLefaALW1vd2A7wGXpOH/TNHXLOAU9r+JuYnm3cQcTl0dfXVQ3GjcOtLPZ3quDknDnwGuaOW51pQD6+dg51Bchd0PfDRNuwJ4XRr+HHBPaoTVwMmldd9GcWNkI/DW0VIb8Erg7jT9bmBBG2oT8AVgfarhopFot6HWNRraLI1fDiyus25bz7X+ahsN7UZxQ+4nqYZ1wKtL6340rXcvcP5oqAt4Q/q9XQfcCfy3NrTZGyn+2P6K4tX7Ya081/xRejOzTI2GGxJmZjYEDnAzs0w5wM3MMuUANzPLlAPczCxTDnAzs0w5wM3MMvX/AS/f5OTBzjbeAAAAAElFTkSuQmCC\n", | |
| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Kolmogorov–Smirnov test on 2 distributions" | |
| ], | |
| "metadata": { | |
| "id": "W6f4YoEERbDG" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "stat, p = ks_2samp(population_log, f_area_log)\n", | |
| "print('Statistics=%.3f, p=%.3f' % (stat, p))\n", | |
| "\n", | |
| "alpha = 0.05\n", | |
| "if p >= alpha:\n", | |
| "\tprint('2 distributions are probably similar')\n", | |
| "else:\n", | |
| "\tprint('2 distributions are probably different')" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "fjAFX7q4RdtH", | |
| "outputId": "a3cf19c6-f3a7-4e6d-d756-76c38ebbd1f6" | |
| }, | |
| "execution_count": 250, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "Statistics=0.116, p=0.111\n", | |
| "2 distributions are probably similar\n" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# Chi-squarred test" | |
| ], | |
| "metadata": { | |
| "id": "4evN5WFTTw8G" | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Loading dataset" | |
| ], | |
| "metadata": { | |
| "id": "qdJwQGkcT4na" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "data = pd.read_csv(\"https://drive.google.com/uc?id=1CfnyUBYOvRNMG8tUqqr1BUbTkwjANe3H\", header=0)\n", | |
| "\n", | |
| "data = pd.DataFrame(data, columns=['Hair', 'Eye', 'Sex', 'Freq'])\n", | |
| "\n", | |
| "data = data.loc[data['Eye'].notnull()].loc[data['Sex'] == 'Female'].loc[data['Hair'].notnull()]\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "data.head()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 206 | |
| }, | |
| "id": "L_ZVlOxJT4L9", | |
| "outputId": "9dddee02-1682-4b7e-ec4a-31b8dba92c72" | |
| }, | |
| "execution_count": 268, | |
| "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>Hair</th>\n", | |
| " <th>Eye</th>\n", | |
| " <th>Sex</th>\n", | |
| " <th>Freq</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>16</th>\n", | |
| " <td>Black</td>\n", | |
| " <td>Brown</td>\n", | |
| " <td>Female</td>\n", | |
| " <td>36</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>17</th>\n", | |
| " <td>Brown</td>\n", | |
| " <td>Brown</td>\n", | |
| " <td>Female</td>\n", | |
| " <td>66</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>18</th>\n", | |
| " <td>Red</td>\n", | |
| " <td>Brown</td>\n", | |
| " <td>Female</td>\n", | |
| " <td>16</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>19</th>\n", | |
| " <td>Blond</td>\n", | |
| " <td>Brown</td>\n", | |
| " <td>Female</td>\n", | |
| " <td>4</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>20</th>\n", | |
| " <td>Black</td>\n", | |
| " <td>Blue</td>\n", | |
| " <td>Female</td>\n", | |
| " <td>9</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " Hair Eye Sex Freq\n", | |
| "16 Black Brown Female 36\n", | |
| "17 Brown Brown Female 66\n", | |
| "18 Red Brown Female 16\n", | |
| "19 Blond Brown Female 4\n", | |
| "20 Black Blue Female 9" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 268 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Transform strings to numbers" | |
| ], | |
| "metadata": { | |
| "id": "cGNOuoDKXSJ4" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "color_dict =\t{\n", | |
| " \"Brown\": 1,\n", | |
| " \"Blue\": 2,\n", | |
| " \"Hazel\": 3,\n", | |
| " \"Green\": 4,\n", | |
| " \"Black\": 5,\n", | |
| " \"Red\": 6,\n", | |
| " \"Blond\": 7\n", | |
| "}\n", | |
| "\n", | |
| "eye_df = data['Eye'].apply(lambda x: color_dict[x])\n", | |
| "hair_df = data['Hair'].apply(lambda x: color_dict[x])" | |
| ], | |
| "metadata": { | |
| "id": "av72pi-3XV2M" | |
| }, | |
| "execution_count": 276, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Test contingency" | |
| ], | |
| "metadata": { | |
| "id": "N587t7-AWQOU" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "info = [eye_df, hair_df]\n", | |
| "\n", | |
| "stat, p_value, dof = chi2_contingency(hair_and_eye_mx)[0:3]\n", | |
| " \n", | |
| "significance_level = 0.05\n", | |
| "print(\"p value: \" + str(p_value)) \n", | |
| "if p_value <= significance_level: \n", | |
| " print('Values are dependent') \n", | |
| "else: \n", | |
| " print('Values are independent') " | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "ehW4PzyBWTsS", | |
| "outputId": "85199485-db8c-484b-d60b-5989a10f6638" | |
| }, | |
| "execution_count": 292, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "p value: 1.0\n", | |
| "Values are independent\n" | |
| ] | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "# T-student test" | |
| ], | |
| "metadata": { | |
| "id": "9WcplqDVeAsb" | |
| } | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Loading dataset" | |
| ], | |
| "metadata": { | |
| "id": "AXh1U6fNeERj" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "data = pd.read_csv(\"https://drive.google.com/uc?id=170LKMRahhjDYcEB9DzdJY9X1lqNTOZPk\", delimiter=r\"\\s+\", header=0)\n", | |
| " \n", | |
| "\n", | |
| "data = pd.DataFrame(data, columns=['Score', 'LearningType'])\n", | |
| "\n", | |
| "draDf = data.loc[data['LearningType'] == 'DRA']['Score']\n", | |
| "scDf = data.loc[data['LearningType'] == 'SC']['Score']\n", | |
| "\n", | |
| "data.head()" | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 206 | |
| }, | |
| "id": "EWORJmSFeD4k", | |
| "outputId": "47c832d4-141a-4624-85e2-612749734222" | |
| }, | |
| "execution_count": 300, | |
| "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>Score</th>\n", | |
| " <th>LearningType</th>\n", | |
| " </tr>\n", | |
| " </thead>\n", | |
| " <tbody>\n", | |
| " <tr>\n", | |
| " <th>0</th>\n", | |
| " <td>24</td>\n", | |
| " <td>DRA</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>1</th>\n", | |
| " <td>43</td>\n", | |
| " <td>DRA</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>2</th>\n", | |
| " <td>58</td>\n", | |
| " <td>DRA</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>3</th>\n", | |
| " <td>71</td>\n", | |
| " <td>DRA</td>\n", | |
| " </tr>\n", | |
| " <tr>\n", | |
| " <th>4</th>\n", | |
| " <td>43</td>\n", | |
| " <td>DRA</td>\n", | |
| " </tr>\n", | |
| " </tbody>\n", | |
| "</table>\n", | |
| "</div>" | |
| ], | |
| "text/plain": [ | |
| " Score LearningType\n", | |
| "0 24 DRA\n", | |
| "1 43 DRA\n", | |
| "2 58 DRA\n", | |
| "3 71 DRA\n", | |
| "4 43 DRA" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 300 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "source": [ | |
| "Perform t-student test" | |
| ], | |
| "metadata": { | |
| "id": "nJjsqdFGfK9Z" | |
| } | |
| }, | |
| { | |
| "cell_type": "code", | |
| "source": [ | |
| "t_stat, p = ttest_ind(draDf, scDf)\n", | |
| "\n", | |
| "alpha = 0.05\n", | |
| "\n", | |
| "print(\"p value: \" + str(p)) \n", | |
| "if p < alpha: \n", | |
| " print('Values are different') \n", | |
| "else: \n", | |
| " print('Values may be similar') " | |
| ], | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "5hT-AAU4fNIS", | |
| "outputId": "72ebdbd9-a94a-4215-ec62-4986841e42a2" | |
| }, | |
| "execution_count": 309, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "p value: 0.028629482832245753\n", | |
| "Values are different\n" | |
| ] | |
| } | |
| ] | |
| } | |
| ] | |
| } |
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