{ "cells": [ { "cell_type": "code", "execution_count": 265, "id": "17e0a614", "metadata": {}, "outputs": [], "source": [ "from scipy import stats\n", "import numpy as np\n", "import random\n", "from matplotlib import pyplot as plt\n", "\n", "def mystatistics1(*data):\n", " return (np.mean(data[0]) - np.mean(data[1]))\n", "\n", "def mystatistics2(*data):\n", " return abs(np.mean(data[0]) - np.mean(data[1]))" ] }, { "cell_type": "markdown", "id": "62c8520d", "metadata": {}, "source": [ "## Estimating the data from Amazon histogram" ] }, { "cell_type": "code", "execution_count": 211, "id": "10b30420", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([161.91, 46.26, 17.99, 12.85, 17.99])" ] }, "execution_count": 211, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array([.63,.18,.07,.05,.07])*257" ] }, { "cell_type": "code", "execution_count": 212, "id": "aa9eea47", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "257" ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "black = [5]*162 + [4]*46 + [3]*18 + [2]*13 + [1]*18; len(black)" ] }, { "cell_type": "code", "execution_count": 213, "id": "2f9416a8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([62.7 , 18.24, 14.82, 7.98, 11.4 ])" ] }, "execution_count": 213, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array([.55,.16,.13,.07,.1])*114" ] }, { "cell_type": "code", "execution_count": 214, "id": "3510920d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "115" ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "blue = [5]*63 + [4]*18 + [3]*15 + [2]*8 + [1]*11; len(blue)" ] }, { "cell_type": "markdown", "id": "db78cc5c", "metadata": {}, "source": [ "## Running the permutation test with 1- and 2-sided version" ] }, { "cell_type": "code", "execution_count": 233, "id": "da57433e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PermutationTestResult(statistic=0.2577228895279986, pvalue=0.0764, null_distribution=array([-0.03177127, 0.45911013, 0.09409575, ..., -0.00659787,\n", " 0.11926916, -0.22057182]))" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.permutation_test([black, blue], statistic=mystatistics1)" ] }, { "cell_type": "code", "execution_count": 235, "id": "b4d48520", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PermutationTestResult(statistic=0.2577228895279986, pvalue=0.1408, null_distribution=array([0.01857554, 0.1450516 , 0.47169684, ..., 0.08150905, 0.16961597,\n", " 0.08211808]))" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.permutation_test([black, blue], statistic=mystatistics2)" ] }, { "cell_type": "markdown", "id": "ebbd528a", "metadata": {}, "source": [ "## Fake data: what if we 2x the group of customers who bought blue?\n", "\n", "Assuming the same percentages of each mark." ] }, { "cell_type": "code", "execution_count": 218, "id": "c0901cf2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PermutationTestResult(statistic=0.2577228895279986, pvalue=0.0548, null_distribution=array([0.08470648, 0.01879547, 0.20005075, ..., 0.05535442, 0.15885637,\n", " 0.12126544]))" ] }, "execution_count": 218, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.permutation_test([black, blue+blue], statistic=mystatistics2)" ] }, { "cell_type": "markdown", "id": "ca364ec3", "metadata": {}, "source": [ "## Fake data: what if we take random subgroup of customers who bought black?\n", "\n", "Random sample => should have approax. the same average." ] }, { "cell_type": "code", "execution_count": 219, "id": "fab75472", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4.249027237354086, 4.252173913043478)" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "small_black = random.sample(black, k=115)\n", "np.mean(black),np.mean(small_black)" ] }, { "cell_type": "code", "execution_count": 220, "id": "99ae1f72", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PermutationTestResult(statistic=0.26086956521739113, pvalue=0.2962, null_distribution=array([0.12173913, 0.22608696, 0.08695652, ..., 0.15652174, 0.20869565,\n", " 0.36521739]))" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.permutation_test([small_black, blue], statistic=mystatistics2)" ] }, { "cell_type": "code", "execution_count": null, "id": "f7d092e4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f7e42b4c", "metadata": {}, "source": [ "# 11.1 -- Wilcoxon test" ] }, { "cell_type": "code", "execution_count": 55, "id": "7a760279", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=2.0, pvalue=0.375)" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,3,4,-2])" ] }, { "cell_type": "code", "execution_count": 56, "id": "accda3a0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=8.0, pvalue=0.1875)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,3,4,-2], alternative=\"greater\")" ] }, { "cell_type": "code", "execution_count": 57, "id": "a6ff8580", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=8.0, pvalue=0.875)" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,3,4,-2], alternative=\"less\")" ] }, { "cell_type": "code", "execution_count": null, "id": "adc0d2f6", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 145, "id": "0e211bad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=2.0, pvalue=0.046875)" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,-2,3,4,5,6,7])" ] }, { "cell_type": "code", "execution_count": null, "id": "97485257", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 49, "id": "d2605aa9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=1.0, pvalue=0.25)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([-1,3,4,2])" ] }, { "cell_type": "code", "execution_count": 50, "id": "a94bb26d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=2.0, pvalue=0.375)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,3,4,-2])" ] }, { "cell_type": "code", "execution_count": 51, "id": "8d5fd4c1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=3.0, pvalue=0.625)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,-3,4,2])" ] }, { "cell_type": "code", "execution_count": 21, "id": "b3de875e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=4.0, pvalue=0.875)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,3,-4,2])" ] }, { "cell_type": "code", "execution_count": 54, "id": "d7f48b7c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=5.0, pvalue=1.0)" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon([1,-3,4,-2])" ] }, { "cell_type": "markdown", "id": "5c992401", "metadata": {}, "source": [ "# 11.1 -- Sign-test" ] }, { "cell_type": "code", "execution_count": 137, "id": "77451b9a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.625" ] }, "execution_count": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binom.cdf(1,4,p=.5)*2" ] }, { "cell_type": "code", "execution_count": null, "id": "3298e60b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 146, "id": "8aae376b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=2, n=4, alternative='two-sided', statistic=0.5, pvalue=1.0)" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(2,4,p=.5, alternative='two-sided')" ] }, { "cell_type": "code", "execution_count": 138, "id": "f594d524", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=3, n=4, alternative='two-sided', statistic=0.75, pvalue=0.625)" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(3,4,p=.5, alternative='two-sided')" ] }, { "cell_type": "code", "execution_count": 42, "id": "a835f980", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=4, n=4, alternative='two-sided', statistic=1.0, pvalue=0.125)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(4,4,p=.5)" ] }, { "cell_type": "code", "execution_count": 32, "id": "6170f0a1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.3125" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "5/16." ] }, { "cell_type": "code", "execution_count": 40, "id": "7f93c69e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=3, n=4, alternative='greater', statistic=0.75, pvalue=0.3125)" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(3,4, alternative='greater')" ] }, { "cell_type": "code", "execution_count": 41, "id": "74160fdf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=4, n=4, alternative='greater', statistic=1.0, pvalue=0.0625)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(4,4, alternative='greater')" ] }, { "cell_type": "code", "execution_count": 140, "id": "adb560aa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0625" ] }, "execution_count": 140, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1/16." ] }, { "cell_type": "code", "execution_count": 139, "id": "2e7327f6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=3, n=4, alternative='less', statistic=0.75, pvalue=0.9375)" ] }, "execution_count": 139, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(3,4, alternative='less')" ] }, { "cell_type": "markdown", "id": "f67a392c", "metadata": {}, "source": [ "# 11.2" ] }, { "cell_type": "code", "execution_count": 160, "id": "8bba8b00", "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 161, "id": "2bb52678", "metadata": {}, "outputs": [], "source": [ "with_sample_problems = np.array([591, 621, 683, 579, 451, 680, 691, 769, 563, 575])\n", "without_sample_problems = np.array([509, 540, 688, 502, 424, 683, 568, 748, 530, 524])" ] }, { "cell_type": "code", "execution_count": 162, "id": "b7d527d3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 82 81 -5 77 27 -3 123 21 33 51]\n" ] } ], "source": [ "print(with_sample_problems-without_sample_problems)" ] }, { "cell_type": "code", "execution_count": 165, "id": "16dddc2e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=52.0, pvalue=0.9970703125)" ] }, "execution_count": 165, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon(with_sample_problems, without_sample_problems, alternative='less')" ] }, { "cell_type": "code", "execution_count": 111, "id": "5ebbe7cd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=52.0, pvalue=0.0048828125)" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon(with_sample_problems-without_sample_problems, alternative='greater')" ] }, { "cell_type": "code", "execution_count": 75, "id": "e1e2f976", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.size(with_sample_problems)" ] }, { "cell_type": "code", "execution_count": 112, "id": "6fede2db", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(620.3, 571.6)" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(with_sample_problems), np.mean(without_sample_problems)" ] }, { "cell_type": "code", "execution_count": null, "id": "59797086", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "86e931dc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 166, "id": "fec2adee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=46.0, pvalue=0.0322265625)" ] }, "execution_count": 166, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon(with_sample_problems, without_sample_problems+20, alternative='greater')" ] }, { "cell_type": "code", "execution_count": 167, "id": "3ee7707b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=46.0, pvalue=0.9755859375)" ] }, "execution_count": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon(with_sample_problems-without_sample_problems-20, alternative='less')" ] }, { "cell_type": "code", "execution_count": 156, "id": "3c3c71f1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=28.0, pvalue=0.5390625)" ] }, "execution_count": 156, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon(with_sample_problems-without_sample_problems-50, alternative='less')" ] }, { "cell_type": "code", "execution_count": null, "id": "54e6c16c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 157, "id": "933b58ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 32, 31, -55, 27, -23, -53, 73, -29, -17, 1])" ] }, "execution_count": 157, "metadata": {}, "output_type": "execute_result" } ], "source": [ "with_sample_problems-without_sample_problems-50" ] }, { "cell_type": "code", "execution_count": 115, "id": "b21c0908", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ True, True, False, True, True, False, True, True, True,\n", " True])" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "with_sample_problems-without_sample_problems>=20" ] }, { "cell_type": "code", "execution_count": 159, "id": "2f29f541", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(with_sample_problems-without_sample_problems>=20)" ] }, { "cell_type": "code", "execution_count": 117, "id": "0326fb08", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=8, n=10, alternative='greater', statistic=0.8, pvalue=0.0546875)" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(8, 10, alternative='greater')" ] }, { "cell_type": "code", "execution_count": 148, "id": "6d14bf50", "metadata": {}, "outputs": [], "source": [ "X = list(with_sample_problems)\n", "Y = list(without_sample_problems+20)" ] }, { "cell_type": "code", "execution_count": 169, "id": "400b917a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[591, 621, 683, 579, 451, 680, 691, 769, 563, 575]" ] }, "execution_count": 169, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X" ] }, { "cell_type": "code", "execution_count": 170, "id": "08869d9c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[529, 560, 708, 522, 444, 703, 588, 768, 550, 544]" ] }, "execution_count": 170, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Y" ] }, { "cell_type": "code", "execution_count": 168, "id": "2b531f7e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PermutationTestResult(statistic=28.699999999999932, pvalue=0.4906, null_distribution=array([ 39.1, 0.7, -5.5, ..., -95.9, -5.3, 38.9]))" ] }, "execution_count": 168, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.permutation_test([X,Y], statistic=mystatistics)" ] }, { "cell_type": "code", "execution_count": 171, "id": "57db5769", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "PermutationTestResult(statistic=28.699999999999932, pvalue=0.0538, null_distribution=array([-14.175, -0.675, 14.825, ..., 18.95 , 0.775, 22.4 ]))" ] }, "execution_count": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.permutation_test([X*8,Y*8], statistic=mystatistics)" ] }, { "cell_type": "markdown", "id": "71ccb593", "metadata": {}, "source": [ "# 11.3/12.3 -- Waiting times" ] }, { "cell_type": "code", "execution_count": 303, "id": "344340e6", "metadata": {}, "outputs": [], "source": [ "times = np.array([17, 15, 20, 20, 32, 28, 12, 26, 25, 25, 35, 24])" ] }, { "cell_type": "code", "execution_count": 304, "id": "75869ab7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([1., 1., 1., 2., 0., 3., 2., 0., 1., 1.]),\n", " array([12. , 14.3, 16.6, 18.9, 21.2, 23.5, 25.8, 28.1, 30.4, 32.7, 35. ]),\n", " )" ] }, "execution_count": 304, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(times)" ] }, { "cell_type": "code", "execution_count": 305, "id": "7af37f8d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 305, "metadata": {}, "output_type": "execute_result" } ], "source": [ "times.size" ] }, { "cell_type": "code", "execution_count": 306, "id": "e642039d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(23.25, 24.5)" ] }, "execution_count": 306, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(times), np.median(times)" ] }, { "cell_type": "code", "execution_count": 299, "id": "8acd4f9e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(3, 7)" ] }, "execution_count": 299, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(times<20), np.sum(times>20)" ] }, { "cell_type": "code", "execution_count": 409, "id": "514bde09", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=7, n=10, alternative='greater', statistic=0.7, pvalue=0.171875)" ] }, "execution_count": 409, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(7,10,.5, alternative='greater')" ] }, { "cell_type": "code", "execution_count": 384, "id": "ebac1b58", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=70, n=100, alternative='greater', statistic=0.7, pvalue=3.925069822796835e-05)" ] }, "execution_count": 384, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(70,100,.5, alternative='greater')" ] }, { "cell_type": "code", "execution_count": null, "id": "e16f6351", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 382, "id": "e17fdd8b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=42.5, pvalue=0.0625234400655502)" ] }, "execution_count": 382, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon(times-20, alternative='greater')" ] }, { "cell_type": "code", "execution_count": null, "id": "e3c1ba76", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f41da979", "metadata": {}, "source": [ "# Wilcoxon fails terribly for Exp distribution\n", "\n", "H_0: We have data from Exp(3) distribution. \n", "\n", "We generate our own data, thus this really is true. We will sample the type-I error." ] }, { "cell_type": "code", "execution_count": 388, "id": "64e9fe8d", "metadata": {}, "outputs": [], "source": [ "expdata = stats.expon.rvs(scale=3, size=100)" ] }, { "cell_type": "code", "execution_count": 386, "id": "c88a2b36", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([41., 24., 13., 11., 3., 3., 3., 0., 0., 2.]),\n", " array([ 0.06338363, 1.42545899, 2.78753436, 4.14960972, 5.51168508,\n", " 6.87376045, 8.23583581, 9.59791117, 10.95998654, 12.3220619 ,\n", " 13.68413726]),\n", " )" ] }, "execution_count": 386, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(expdata)" ] }, { "cell_type": "code", "execution_count": 370, "id": "8203cd2f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([28., 25., 19., 12., 7., 4., 2., 1., 1., 1.]),\n", " array([ 0.04347253, 1.3051205 , 2.56676847, 3.82841643, 5.0900644 ,\n", " 6.35171236, 7.61336033, 8.8750083 , 10.13665626, 11.39830423,\n", " 12.65995219]),\n", " )" ] }, "execution_count": 370, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(expdata)" ] }, { "cell_type": "code", "execution_count": 389, "id": "c0bf632a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2.1125229336199345, 2.818046296052764)" ] }, "execution_count": 389, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.median(expdata), np.mean(expdata)" ] }, { "cell_type": "code", "execution_count": 387, "id": "e2f10ae6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2.0794415416798357, 3.0)" ] }, "execution_count": 387, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.expon.median(scale=3), stats.expon.mean(scale=3)" ] }, { "cell_type": "code", "execution_count": 396, "id": "ab81cf0b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.3055421446183436" ] }, "execution_count": 396, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expdata = stats.expon.rvs(scale=3, size=100)\n", "stats.wilcoxon(expdata-2.079).pvalue" ] }, { "cell_type": "code", "execution_count": 400, "id": "cc279213", "metadata": {}, "outputs": [], "source": [ "L = np.array([stats.wilcoxon(stats.expon.rvs(scale=3, size=100)-2.079).pvalue for _ in range(100)])" ] }, { "cell_type": "code", "execution_count": 410, "id": "32ac61b4", "metadata": {}, "outputs": [], "source": [ "def signtest(L):\n", " neg = np.sum(L<0)\n", " pos = np.sum(L>0)\n", " return stats.binomtest(pos,neg+pos,.5)" ] }, { "cell_type": "code", "execution_count": 415, "id": "8b35eacd", "metadata": {}, "outputs": [], "source": [ "L2 = np.array([signtest(stats.expon.rvs(scale=3, size=100)-2.079).pvalue for _ in range(100)])" ] }, { "cell_type": "code", "execution_count": 416, "id": "bdc598f5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([ 7., 8., 9., 11., 11., 0., 12., 14., 0., 28.]),\n", " array([0.0352002 , 0.13168018, 0.22816016, 0.32464014, 0.42112012,\n", " 0.5176001 , 0.61408008, 0.71056006, 0.80704004, 0.90352002,\n", " 1. ]),\n", " )" ] }, "execution_count": 416, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(L2)" ] }, { "cell_type": "code", "execution_count": 417, "id": "0271eaea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.02" ] }, "execution_count": 417, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(L2<.05)" ] }, { "cell_type": "code", "execution_count": null, "id": "65931098", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "1f3d3bf4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "81ec3c06", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "efe602fc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "505bb7d9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "04a89f0c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 255, "id": "5e282930", "metadata": {}, "outputs": [], "source": [ "a = np.array([531, 621, 663, 579, 451, 660, 591, 719, 543, 575])\n", "b = np.array([509, 540, 688, 502, 424, 683, 568, 748, 530, 524])" ] }, { "cell_type": "code", "execution_count": 176, "id": "7cff466d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(593.3, 571.6)" ] }, "execution_count": 176, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.mean(), b.mean()" ] }, { "cell_type": "code", "execution_count": 179, "id": "be6e2d8d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 179, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(a-b>=50)" ] }, { "cell_type": "code", "execution_count": 180, "id": "e058e847", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "BinomTestResult(k=3, n=10, alternative='less', statistic=0.3, pvalue=0.171875)" ] }, "execution_count": 180, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.binomtest(3,10,.5,alternative='less')" ] }, { "cell_type": "code", "execution_count": null, "id": "c96eb038", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.6" } }, "nbformat": 4, "nbformat_minor": 5 }