{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean=50.303 stdv=4.426\n" ] } ], "source": [ "# From: https://machinelearningmastery.com/a-gentle-introduction-to-normality-tests-in-python/\n", "# generate gaussian data\n", "from numpy.random import seed\n", "from numpy.random import randn\n", "from numpy import mean\n", "from numpy import std\n", "# seed the random number generator\n", "seed(1)\n", "# generate univariate observations\n", "data = 5 * randn(100) + 50\n", "# summarize\n", "print('mean=%.3f stdv=%.3f' % (mean(data), std(data)))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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60nUsF26P3bk9duf22N1y3R59TvXcBhyX5HlJDgTOA65f0Od64IJu+rXAl6pq4BG/JGlpjHzEX1U7k7wNuAnYD1hfVXcleR8wU1XXA1cCn0hyP3NH+ueNo2hJ0uh63Za5qjYAGxa0vWfe9P8Cf9BnjGVg2Z1+mjC3x+7cHrtze+xuWW6PeOZFktriLRskqTEG/wJJ9kvyrST/1s0/r7vdxH3d7ScOnHSNS2nA9rgqyX8m2dy9Vk26xqWSZEuS73Q/90zXdliSjd3+sTHJoZOuc6kM2R7vTfL9efvHmknXuVSSHJLkM0nuSXJ3kpcv1/3D4H+ytwN3z5v/AHBpVR0HPMrcbShasnB7APxFVa3qXpsnUdQEndL93Lsu0bsIuKXbP27p5luycHvA3O/Lrv1jw9A1n37+Abixql4AnMjc782y3D8M/nmSHAOcDVzRzQc4lbnbTcDc7SdePZnqlt7C7aGB5t+WpKn9Q7+Q5NeAVzB3JSNV9dOq+iHLdP8w+Hf398BfAj/v5p8F/LC73QQMvi3F09nC7bHL3yb5dpJLkzxjAnVNSgE3J9nUfdMc4Miq2gbQvR8xseqW3qDtAfC2bv9Yv1xObSyB3wB2AB/rTo1ekeQglun+YfB3kpwDbK+qTfObB3Rt4jKoIdsD4N3AC4DfAQ4D3rXUtU3QSVX1EubuSPvWJK+YdEETNmh7fAR4PrAK2AZ8cIL1LaX9gZcAH6mqFwP/wzI5rTOIwf8LJwGvSrKFuTuNnsrcEe8h3e0mYPBtKZ6unrQ9kvxzVW2rOf8HfIy5u7Q2oaq2du/bgeuY+9kfSnIUQPe+fXIVLq1B26OqHqqqn1XVz4GP0s7+MQvMVtU3uvnPMPeHYFnuHwZ/p6reXVXHVNVK5r5h/KWqeh3wZeZuNwFzt5/4woRKXFJDtscfz9uJw9z5yjsnWOaSSXJQkoN3TQNnMPezz78tSTP7x7DtsWv/6LyGRvaPqvpv4MEkx3dNpwHfZZnuH72+uduIdwGfSvI3wLfo/nnTsGuSTDF3Gmwz8OYJ17NUjgSu6x4nsT/wyaq6McltwL8kuRD4L57631RfrGHb4xPdJb4FbAHeNLkSl9yfM/f7cSDwAPAG5g6ul93+4Td3JakxnuqRpMYY/JLUGINfkhpj8EtSYwx+SWqMwS9JjTH4JakxBr8kNeb/AewD/UIL3FA3AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from matplotlib import pyplot\n", "# histogram plot\n", "pyplot.hist(data)\n", "pyplot.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from statsmodels.graphics.gofplots import qqplot\n", "# q-q plot\n", "qqplot(data, line='s')\n", "pyplot.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statistics=0.992, p=0.822\n", "Sample looks Gaussian (fail to reject H0)\n" ] } ], "source": [ "# Shapiro-Wilk Test\n", "from scipy.stats import shapiro\n", "# normality test\n", "stat, p = shapiro(data)\n", "print('Statistics=%.3f, p=%.3f' % (stat, p))\n", "# interpret\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)')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Statistics=0.102, p=0.950\n", "Sample looks Gaussian (fail to reject H0)\n" ] } ], "source": [ "# D'Agostino and Pearson's Test\n", "from scipy.stats import normaltest\n", "# normality test\n", "stat, p = normaltest(data)\n", "print('Statistics=%.3f, p=%.3f' % (stat, p))\n", "# interpret\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)')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.9756130576133728, 0.937462329864502)\n", "(0.9822366833686829, 0.6493431925773621)\n", "(0.9902752041816711, 0.6868489384651184)\n", "(0.9980342984199524, 0.297299861907959)\n" ] } ], "source": [ "# From: https://medium.com/@rrfd/testing-for-normality-applications-with-python-6bf06ed646a9\n", "# Shapiro-Wilk Test\n", "from scipy.stats import shapiro\n", "from scipy.stats import norm\n", "# Create the random variables with mean 5, and sd 3\n", "x_10 = norm.rvs(loc=5, scale=3, size=10)\n", "x_50 = norm.rvs(loc=5, scale=3, size=50)\n", "x_100 = norm.rvs(loc=5, scale=3, size=100)\n", "x_1000 = norm.rvs(loc=5, scale=3, size=1000)\n", "# Print the p values\n", "print(shapiro(x_10))\n", "print(shapiro(x_50))\n", "print(shapiro(x_100))\n", "print(shapiro(x_1000))\n", "# (The test statistic, the p-value) for x_N above\n", "# (0.9122101664543152, 0.2965205907821655) # Null Accepted\n", "# (0.9418673515319824, 0.015981076285243034) # Null Rejected\n", "# (0.9918511509895325, 0.810341477394104) # Null Accepted\n", "# (0.9987027645111084, 0.6903988718986511) Null Accepted" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.9467288255691528, 7.196542352923968e-14)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "from sklearn.datasets.samples_generator import make_blobs\n", "X, y_true = make_blobs(n_samples=300, centers=4,\n", " cluster_std=0.60, random_state=0)\n", "plt.scatter(X[:, 0], X[:, 1], s=50);\n", "from scipy.stats import shapiro\n", "from scipy.stats import norm\n", "stat, p = shapiro(X)\n", "print(shapiro(X))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }