{ "cells": [ { "cell_type": "markdown", "id": "c33197dd", "metadata": {}, "source": [ "# The Wilcoxon Sign-Rank Test\n", "\n", "The Wilcoxon Sign-Rank Test is a rank-based test for the median **difference** in paired samples. It tests whether the median difference between the members of each pair is greater than zero. As such it is often considered to be a non-parametric equivalent for the **paired samples** t-test (which we will meet next week).\n", "\n", "The Wilcoxon Sign-rank test is **not** the same as the Wilcoxon Rank Sum test (Mann Whitney U test) which is for independent samples\n", "\n", "We will us a Python function called `stats.wilcoxon()` from the `scipy.stats` library to run the test" ] }, { "cell_type": "markdown", "id": "b563240d", "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": "93d0feed", "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" ] }, { "cell_type": "markdown", "id": "8b8bd7b3", "metadata": {}, "source": [ "## Example: the Sign-Rank Test\n", "\n", "It has been argued that birth order in families affects how independent individuals are as adults - either that first-born children tend to be more independent than later born children or vice versa.\n", "\n", "In a (fictional!) study, a researcher identified 20 sibling pairs, each comprising a first- and second- born child from a two-child family. The participants were young adults; each participant was interviewed at the age of 21. \n", "\n", "The researcher scored independence for each participant, using a 25 point scale where a higher score means the person is more independent, based on a structured interview.\n", "\n", "Carry out a statistical test for a difference in independence scores between the first- and second-born children.\n", "\n", "Note that this is a paired samples design - each member of one group (the first-borns) has a paired member of the other group (second-borns).\n", "\n", "\n", "### Inspect the data\n", "\n", "The data are provided in a text (.csv) file.\n", "\n", "Let's load the data as a Pandas dataframe, and plot them to get a sense for their distribution (is it normal?) and any outliers\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "da622d51", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " FirstBorn SecondBorn\n", "0 12 10\n", "1 18 12\n", "2 13 15\n", "3 17 13\n", "4 8 9\n", "5 15 12\n", "6 16 13\n", "7 5 8\n", "8 8 10\n", "9 12 8\n", "10 13 8\n", "11 5 9\n", "12 14 8\n", "13 20 10\n", "14 19 14\n", "15 17 11\n", "16 2 7\n", "17 5 7\n", "18 15 13\n", "19 18 12" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# load the data and have a look\n", "birthOrder = pd.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook_2024/main/data/BirthOrderIndependence.csv')\n", "birthOrder" ] }, { "cell_type": "markdown", "id": "5481f8e9", "metadata": {}, "source": [ "### Scatterplot\n", "\n", "In the case of paired data, the most effective way to get a sense of the data is a scatterplot:" ] }, { "cell_type": "code", "execution_count": 4, "id": "ce6a5214", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.scatterplot(data = birthOrder, x=\"FirstBorn\", y=\"SecondBorn\")\n", "plt.xlabel(\"independence: first born\")\n", "plt.ylabel(\"independence: second born\")\n", "\n", "# add the line x=y (ie a line from point(50,50) to (110,110)) for reference \n", "plt.plot([0,20],[0,20],'r--')" ] }, { "cell_type": "markdown", "id": "850462ee", "metadata": {}, "source": [ "Comments:\n", " \n", "" ] }, { "cell_type": "markdown", "id": "1e0d04e2", "metadata": {}, "source": [ "### Check the data distribution\n", "\n", "In the case of paired data, we are interested in the distribution of *differences* within pairs.\n", "\n", "Let's add a column to our dataframe to contain the differences" ] }, { "cell_type": "code", "execution_count": 7, "id": "ce83eb84", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
FirstBornSecondBornDiff
012102
118126
21315-2
317134
489-1
515123
616133
758-3
8810-2
91284
101385
1159-4
121486
13201010
1419145
1517116
1627-5
1757-2
1815132
1918126
\n", "
" ], "text/plain": [ " FirstBorn SecondBorn Diff\n", "0 12 10 2\n", "1 18 12 6\n", "2 13 15 -2\n", "3 17 13 4\n", "4 8 9 -1\n", "5 15 12 3\n", "6 16 13 3\n", "7 5 8 -3\n", "8 8 10 -2\n", "9 12 8 4\n", "10 13 8 5\n", "11 5 9 -4\n", "12 14 8 6\n", "13 20 10 10\n", "14 19 14 5\n", "15 17 11 6\n", "16 2 7 -5\n", "17 5 7 -2\n", "18 15 13 2\n", "19 18 12 6" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "birthOrder['Diff'] = birthOrder.FirstBorn - birthOrder.SecondBorn\n", "birthOrder" ] }, { "cell_type": "markdown", "id": "3953720c", "metadata": {}, "source": [ "Now let's plot the differences to get a sense of whether they are normally distributed." ] }, { "cell_type": "code", "execution_count": 9, "id": "8f5e728d", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.kdeplot(data=birthOrder, x='Diff', color='b', fill=True)\n", "sns.rugplot(data=birthOrder, x='Diff', height=0.1, color='b')\n", "plt.xlabel('Difference 1st-2nd born')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "41d53375", "metadata": {}, "source": [ "The distribution hasa hint of bimodaility, with a hint of bimodality (two peaks)." ] }, { "cell_type": "markdown", "id": "30e5dff0", "metadata": {}, "source": [ "### Hypotheses\n", "\n", "$\\mathcal{H_o}$: the median difference in independence between first- and second-born siblings is is zero\n", "\n", "$\\mathcal{H_a}$: the median difference in independence is not zero\n", " \n", "This is a two-tailed test as the researcher's hypothesis (described above) is not directional.\n", "\n", "We will test at the $\\alpha = 0.05$ significance level" ] }, { "cell_type": "markdown", "id": "0ed79570", "metadata": {}, "source": [ "## Descriptive statistics\n", "\n", "We obtain some relevant descriptive statistics. \n", "\n", "Since we are testing for a difference of medians, we will want the median for each group; it would also be useful to have a measure of spread, and the sample size." ] }, { "cell_type": "code", "execution_count": 19, "id": "11de87b4", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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FirstBornSecondBornDiff
count20.00000020.00000020.000000
mean12.60000010.4500002.150000
std5.3646012.4381834.120232
min2.0000007.000000-5.000000
25%8.0000008.000000-2.000000
50%13.50000010.0000003.000000
75%17.00000012.2500005.250000
max20.00000015.00000010.000000
\n", "
" ], "text/plain": [ " FirstBorn SecondBorn Diff\n", "count 20.000000 20.000000 20.000000\n", "mean 12.600000 10.450000 2.150000\n", "std 5.364601 2.438183 4.120232\n", "min 2.000000 7.000000 -5.000000\n", "25% 8.000000 8.000000 -2.000000\n", "50% 13.500000 10.000000 3.000000\n", "75% 17.000000 12.250000 5.250000\n", "max 20.000000 15.000000 10.000000" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "birthOrder.describe()" ] }, { "cell_type": "markdown", "id": "b7ab9c7d", "metadata": {}, "source": [ "### Carry out the test\n", "\n", "We carry out the test using the function wilcoxon from scipy.stats, here loaded as stats" ] }, { "cell_type": "code", "execution_count": 29, "id": "85858db8", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "WilcoxonResult(statistic=164.0, pvalue=0.0133209228515625)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.wilcoxon(birthOrder.FirstBorn,birthOrder.SecondBorn,alternative='greater')\n", "#help(stats.wilcoxon)" ] }, { "cell_type": "markdown", "id": "3dcd664c", "metadata": {}, "source": [ "The inputs to `stats.wilcoxon()` are:\n", "\n", "* the two samples to be compared (the values of FirstBorn and SecondBorn from our Pandas data frame birthOrder)\n", "* the argument `alternative='greater'`, which tells the computer to run a one tailed test that median of the first input (FirstBorn) is greater than the second (SecondBorn).\n", " \n", "The outputs are a value of the test statistic ($T=164$) and pvalue ($p=0.0133$) - if this is less than our $\\alpha$ value 0.5, there is a significant difference.\n", "\n", "More explanation of how T is calculated below." ] }, { "cell_type": "markdown", "id": "69dcbf20", "metadata": {}, "source": [ "### Draw conclusions\n", "\n", "As the p value of 0.0133 is less than our alpha value of 0.05, the test is significant. \n", "\n", "We can conclude that the median difference in idenpendence is positive, ie the first borns are more independent" ] }, { "cell_type": "markdown", "id": "1a80a337", "metadata": {}, "source": [ "### How the Wilcoxon Sign-Rank test works\n", "\n", "The mechanism of the test but is similar in principle to the ranksum test, except that here we work with ranked *differences*.\n" ] }, { "cell_type": "markdown", "id": "7ea850fa-1f9c-4cea-bee4-7b70ba7360b2", "metadata": {}, "source": [ "### How to do the test (if you were doing it with pencil and paper)\n", "\n", "1. Obtain the difference (in independence score) for each pair\n", "\n", "1. Rank the differences regardless of sign (e.g. a difference of +4 is greater than a difference of -3, which is greater than a difference of +2). Remove pairs with zero difference\n", "\n", "1. Calculate the sum of ranks assigned to pairs with a positive difference (first-born more independent than second-born) - this is $R+$\n", "1. Calculate the sum of ranks assigned to pairs with a negative difference (first-born more independent than second-born) - this is $R-$\n", "\n", "1. The test statistic $T$ is either:\n", " * $R+$ if we expect positive differences to have the larger ranks (in this case, that equates to expecting first-borns to have higher scores)\n", " * $R-$ if we expect negative differences to have the larger ranks (in this case, that equates to expecting second-borns to have higher scores)\n", " * The smaller of $R+$ and $R-$ for a two tailed test (as in the example, we have no a-prior hypothesis about direction of effect)\n", "\n", "1. $T$ is compared with a null distribution (the expected distribubtion of $T$ obtained in samples drawn from a population in which there is no true difference between groups)\n", "\n", "\n", "We will not build code to do this here, although if you are feeling brave you are welcome to have a try yourself, using the between groups rank sum test as a model. \n" ] } ], "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": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 5 }