{ "cells": [ { "cell_type": "markdown", "id": "49887e83", "metadata": {}, "source": [ "# Tutorial Exercises: non-parametric tests \n", "\n", " \n", "Here are some exercises on comparing groups of data (medians or means) using rank-based non-parametric tests, or permutation tests\n" ] }, { "cell_type": "markdown", "id": "741220b6", "metadata": {}, "source": [ "### Set up Python libraries\n", "\n", "As usual, run the code cell below to import the relevant Python libraries" ] }, { "cell_type": "code", "execution_count": 1, "id": "692abf91", "metadata": { "tags": [] }, "outputs": [], "source": [ "# Set-up Python libraries - you need to run this but you don't need to change it\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats\n", "import pandas as pd\n", "import seaborn as sns\n", "sns.set_theme(style='white')\n", "import statsmodels.api as sm\n", "import statsmodels.formula.api as smf\n", "import warnings \n", "warnings.simplefilter('ignore', category=FutureWarning)" ] }, { "cell_type": "markdown", "id": "91eef546", "metadata": {}, "source": [ "## 1. Whose peaches are heavier?\n", "\n", "\"There\n", "\n", "\n", "Mr Robinson’s juice factory buys peaches from farmers by the tray. Each tray contains 50 peaches. Farmer McDonald claims that this is unfair as his peaches are juicier and therefore weigh more than the peaches of his rival, Mr McGregor. \n", "\n", "Mr Robinson weighs eight trays of Farmer McDonald’s peaches and 8 trays of Mr McGregor’s peaches. \n", "\n", "Investigate whether McDonald's claim is justified by testing for a difference in weight between McDonald and McGregor's peaches using a non-parametric (rank-based) test." ] }, { "cell_type": "markdown", "id": "134615c7", "metadata": {}, "source": [ "a) Load the data into a Pandas dataframe" ] }, { "cell_type": "code", "execution_count": 2, "id": "e524eb4b", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " McGregor MacDonald\n", "0 7.867 8.289\n", "1 7.637 7.972\n", "2 7.652 8.237\n", "3 7.772 7.789\n", "4 7.510 7.345\n", "5 7.743 7.861\n", "6 7.356 7.779\n", "7 7.944 7.974" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "peaches = pd.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook_2024/main/data/peaches.csv')\n", "peaches" ] }, { "cell_type": "markdown", "id": "cf39faa0", "metadata": {}, "source": [ "b) Plot the data and comment. \n", "\n", "A Kernel desity estimate plot (to show the distribution) and rug plot (to show individual data points) would be a good choice here. You should comment on the data distribution " ] }, { "cell_type": "code", "execution_count": 3, "id": "ecb9049b", "metadata": { "tags": [] }, "outputs": [], "source": [ "# your code here to plot the data\n" ] }, { "cell_type": "markdown", "id": "be0c251b", "metadata": {}, "source": [ "c) Conduct an appropriate rank-based non-parametric test of Farmer McDonald's claim\n", "\n", "* State your hypotheses\n", "* State relevant descriptive statistics\n", "* Carry out the test using the built in function from `scipy.stats` with appropriate option choices\n", "* State your conclusions" ] }, { "cell_type": "code", "execution_count": 4, "id": "6d79296d-b266-44d5-ab6b-c8d6de3aa949", "metadata": { "tags": [] }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "id": "a9d9b2b9-c8e0-4d8f-8b07-4188e0ca3fb9", "metadata": { "tags": [] }, "source": [ "d) Conduct a permutation test of the same claim\n", "\n", "* State your hypotheses\n", "* State relevant descriptive statistics\n", "* Carry out the test using the built in function from `scipy.stats` with appropriate option choices\n", "* State your conclusions" ] }, { "cell_type": "code", "execution_count": 5, "id": "5a021668-2dc2-4592-8ffc-3013e123c5c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "id": "bf2702d0", "metadata": {}, "source": [ "## 2. IQ and vitamins\n", "\n", "\"There\n", "\n", "The VitalVit company claim that after taking their VitalVit supplement, IQ is increased. \n", "\n", "They run a trial in which 22 participants complete a baseline IQ test, then take VitalVit for six weeks, then complete another IQ test." ] }, { "cell_type": "markdown", "id": "3ea0f132", "metadata": {}, "source": [ "a) What kind of design is this." ] }, { "cell_type": "markdown", "id": "d0f6401b", "metadata": {}, "source": [ "< your answer here >\n" ] }, { "cell_type": "markdown", "id": "4c839052", "metadata": {}, "source": [ "b) What are the advantages and possible disadvantages of this type of design? Should the company have done something different or additional to rule out confounding factors?" ] }, { "cell_type": "markdown", "id": "2f1b84e7", "metadata": {}, "source": [ "< your answer here >" ] }, { "cell_type": "markdown", "id": "36be5eb5", "metadata": {}, "source": [ "c) Load the data into a Pandas dataframe" ] }, { "cell_type": "code", "execution_count": 6, "id": "864de087", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " ID_code before after\n", "0 688870 82.596 83.437\n", "1 723650 117.200 119.810\n", "2 445960 85.861 83.976\n", "3 708780 125.640 127.680\n", "4 109960 96.751 99.103\n", "5 968530 105.680 106.890\n", "6 164930 142.410 145.550\n", "7 744410 109.650 109.320\n", "8 499380 128.210 125.110\n", "9 290560 84.773 87.249\n", "10 780690 110.470 112.650\n", "11 660820 100.870 99.074\n", "12 758780 94.117 95.951\n", "13 363320 96.952 96.801\n", "14 638840 86.280 87.669\n", "15 483930 89.413 94.379\n", "16 102800 85.283 88.316\n", "17 581620 94.477 96.300\n", "18 754980 90.649 94.158\n", "19 268960 103.190 104.300\n", "20 314040 92.880 94.556\n", "21 324960 97.843 97.969" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vitamin = pd.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook_2024/main/data/vitalVit.csv')\n", "vitamin" ] }, { "cell_type": "markdown", "id": "fa85f514", "metadata": {}, "source": [ "d) Plot the data and comment. \n", "A scatterplot would be a good choice as these are paired data. \n", "You could add the line of equality (line x=y) to the graph so we can see whether most people score higer on the IQ test before or after taking VitalVit" ] }, { "cell_type": "code", "execution_count": 7, "id": "1ff48986", "metadata": {}, "outputs": [], "source": [ "# Your code here for a scatter plot." ] }, { "cell_type": "markdown", "id": "8a3f3840", "metadata": {}, "source": [ "e) Conduct a suitable rank-based non-parametric test of VitalVit's claim\n", "\n", "* State your hypotheses\n", "* State relevant descriptive statistics\n", "* Carry out the test using the built in function from `scipy.stats` with appropriate option choices\n", "* State your conclusions" ] }, { "cell_type": "code", "execution_count": 8, "id": "c592df98-dd5c-42e5-9b6a-4910f43f0e31", "metadata": { "tags": [] }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "id": "8e2cd017", "metadata": {}, "source": [ "f) Conduct a suitable permutation test of VitalVit's claim\n", "\n", "* State your hypotheses\n", "* State relevant descriptive statistics\n", "* Carry out the test using the built in function from `scipy.stats` with appropriate option choices\n", "* State your conclusions" ] }, { "cell_type": "code", "execution_count": 9, "id": "3a944291-9de8-4d62-8f75-b005480e3d42", "metadata": { "tags": [] }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "id": "e874c135-6079-408e-8ab6-040a3fcc3db3", "metadata": {}, "source": [ "## 3. Socks\n", "\n", "In the section on permutation testing, we introduced a dataset on sock ownership (number of pairs of socks owned for 14 husband-wife couples. We noticed that when using a permutation test for difference of means, the null distribution of the difference of means was strongly affected by the presences of an outlier: \n", "* in one couple the husband owned about 30 more pairs of socks than the wife\n", "* wheter the difference of means in each permutation was positive or negative depended disproportionately on whether this couple were 'flipped' or not in that particular permutation\n", "\n", "Let's compare the use of the rank-based (Wilcoxon's Sign-Rank test) test with the permutation test for the mean difference.\n", "\n", "**a. Load the data (done for you)**" ] }, { "cell_type": "code", "execution_count": 10, "id": "bc76e3f0-ed73-45cf-bc85-82a81d0be296", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Husband Wife\n", "0 10 12\n", "1 17 13\n", "2 48 20\n", "3 28 25\n", "4 23 18\n", "5 16 14\n", "6 18 13\n", "7 34 26\n", "8 27 22\n", "9 22 14\n", "10 12 10\n", "11 13 17\n", "12 22 21\n", "13 15 16" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "socks = pd.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook_2024/main/data/socks.csv')\n", "socks" ] }, { "cell_type": "markdown", "id": "a906cde9-a9cc-40be-a7a9-301cac7d08c0", "metadata": { "tags": [] }, "source": [ "**b. Plot the data (done for you)**" ] }, { "cell_type": "code", "execution_count": 11, "id": "b8a62d76-9d5f-45ae-b60b-e268bd6b835b", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.barplot(data=socks, color=[0.8,0.8,0.8])\n", "sns.lineplot(data=socks.T, marker='o')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e449fcbc-d629-4069-90a5-21fd32be91d3", "metadata": {}, "source": [ "**c. Carry out a suitable rank-based non-parametric test of the hypothesis that men own more socks than women**" ] }, { "cell_type": "code", "execution_count": 12, "id": "4ceb291d-513a-49f2-953c-deeb780acecf", "metadata": { "tags": [] }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "id": "58c4dcf7-dde9-49f1-95e9-a05082e9cbe2", "metadata": {}, "source": [ "**d. Carry out a suitable permutation test test of the hypothesis that men own more socks than women**" ] }, { "cell_type": "code", "execution_count": 13, "id": "0c8671ef-8cf5-4085-a6d8-ed4e0cb14761", "metadata": { "tags": [] }, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "id": "535f5ead-26d5-4be3-ba2b-3f9e9642d487", "metadata": {}, "source": [ "**e. Compare the two tests.**\n", "\n", "In this case the rank-based test has a (slightly) smaller $p$-value than the permutation test. \n", "\n", "The permutation test preserves thhe following features of the data:\n", "1. In each couple one partner usually has more socks (what we shuffle is *which* partner this is)\n", "2. One couple has an extreme difference in sock-counts (we shuffle whether it is the husband or wife who has more socks)\n", "3. We retain the sample sizes and overall distribution of difference of means\n", "\n", "The rank-based test 'neutralizes' one of these features, which is it and what is the effect?" ] }, { "cell_type": "code", "execution_count": null, "id": "f9a9a976-f7cd-424e-9e6c-5fc874dfdb80", "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": "3.11.7" } }, "nbformat": 4, "nbformat_minor": 5 }