{ "cells": [ { "cell_type": "markdown", "id": "8501b536", "metadata": {}, "source": [ "# Spearman's Rank Correlation" ] }, { "cell_type": "markdown", "id": "06a3540a", "metadata": {}, "source": [ "## Climate Example\n", "\n", "We will again use the a dataset containing carbon emissions, GDP and population for 164 countries (data from 2018).\n", "\n", "These data came from Our World in Data, a fabulous Oxford-based organization that provides datasets and visualizations addressing global issues.\n", "\n", "\n", "### Set up Python libraries\n", "\n", "As usual, run the code cell below to import the relevant Python libraries" ] }, { "cell_type": "code", "execution_count": 2, "id": "7f1d34e0", "metadata": {}, "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 \n", "import seaborn as sns\n", "sns.set_theme() # use pretty defaults" ] }, { "cell_type": "markdown", "id": "8b500ab6", "metadata": {}, "source": [ "### Load and inspect the data\n", "\n", "Load the data from the file CO2vGDP.csv." ] }, { "cell_type": "code", "execution_count": 3, "id": "0554fc72", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CountryCO2GDPpopulation
0Afghanistan0.22451934.55505436686788
1Albania1.642211104.1660202877019
2Algeria3.824114228.02539041927008
3Angola0.79127771.44189531273538
4Argentina4.082418556.38281044413592
...............
159Venezuela4.160210709.95020029825652
160Vietnam2.34156814.14209094914328
161Yemen0.35032284.88989330790514
162Zambia0.42153534.03369117835898
163Zimbabwe0.82101611.40515115052191
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164 rows × 4 columns

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" ], "text/plain": [ " Country CO2 GDP population\n", "0 Afghanistan 0.2245 1934.555054 36686788\n", "1 Albania 1.6422 11104.166020 2877019\n", "2 Algeria 3.8241 14228.025390 41927008\n", "3 Angola 0.7912 7771.441895 31273538\n", "4 Argentina 4.0824 18556.382810 44413592\n", ".. ... ... ... ...\n", "159 Venezuela 4.1602 10709.950200 29825652\n", "160 Vietnam 2.3415 6814.142090 94914328\n", "161 Yemen 0.3503 2284.889893 30790514\n", "162 Zambia 0.4215 3534.033691 17835898\n", "163 Zimbabwe 0.8210 1611.405151 15052191\n", "\n", "[164 rows x 4 columns]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "CO2vGDP = pandas.read_csv('https://raw.githubusercontent.com/jillxoreilly/StatsCourseBook/main/data/CO2vGDP.csv')\n", "display(CO2vGDP)" ] }, { "cell_type": "markdown", "id": "1cbcecb6", "metadata": {}, "source": [ "\n", "\n", "We noted previously that our climate dataset is not suitable for a 'normal' Pearson's correlation because it has one of the three freatures that violate the assumptions of Pearson's correlation:\n", "\n", "\n", "\n", "In this case the problem was heteroscedasticity\n", "\n", "\n", "### Spearman's Rank Correlation\n", "\n", "We therefore use a rank-based form of correlation called Spearman's rank correlation coefficient $r_s$, which does not rely on the same assumptions as Pearson's correlation.\n", "\n", "$r_s$ can be calculated using the same built-in function pandas.df.corr():" ] }, { "cell_type": "code", "execution_count": 5, "id": "2be910c0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CO2GDPpopulation
CO21.0000000.914369-0.098554
GDP0.9143691.000000-0.122920
population-0.098554-0.1229201.000000
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" ], "text/plain": [ " CO2 GDP population\n", "CO2 1.000000 0.914369 -0.098554\n", "GDP 0.914369 1.000000 -0.122920\n", "population -0.098554 -0.122920 1.000000" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CO2vGDP.corr(method='spearman')" ] }, { "cell_type": "markdown", "id": "d49d0f38", "metadata": {}, "source": [ "The 'methods' available are:\n", "\n", "\n", " \n", "The default (the method used if no method is specified) is Pearson - we can see this by comparing the results with method specified as Pearson and no method specified:" ] }, { "cell_type": "code", "execution_count": 6, "id": "c17e0a96", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CO2GDPpopulation
CO21.0000000.795214-0.003745
GDP0.7952141.000000-0.054502
population-0.003745-0.0545021.000000
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" ], "text/plain": [ " CO2 GDP population\n", "CO2 1.000000 0.795214 -0.003745\n", "GDP 0.795214 1.000000 -0.054502\n", "population -0.003745 -0.054502 1.000000" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CO2vGDP.corr(method='pearson')" ] }, { "cell_type": "code", "execution_count": 72, "id": "a658a595", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CO2GDPpopulation
CO21.000000.79512-0.00019
GDP0.795121.00000-0.02783
population-0.00019-0.027831.00000
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" ], "text/plain": [ " CO2 GDP population\n", "CO2 1.00000 0.79512 -0.00019\n", "GDP 0.79512 1.00000 -0.02783\n", "population -0.00019 -0.02783 1.00000" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CO2vGDP.corr()" ] }, { "cell_type": "markdown", "id": "db8d709f", "metadata": {}, "source": [ "### The equation\n", "\n", "Let's check our understanding by calculating Spearman's correlation coefficient oursleves.\n", "\n", "The equation is:\n", " \n", "$$ r_s = 1 - 6 \\sum{\\frac{d^2}{n(n^2 - 1)}} $$\n", "\n", "... where d is the difference in ranks between paired datapoints.\n", "\n", "Let's walk that through.\n", "\n", "First, we create new columns containing the rank of each datapoint - \n", "" ] }, { "cell_type": "code", "execution_count": 7, "id": "a74f0955", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CountryCO2GDPpopulationCO2_rankGDP_rank
39Democratic Republic of Congo0.0331859.381714870873521.04.0
26Central African Republic0.0471623.48889250947952.01.0
21Burundi0.0608651.358887114934763.02.0
27Chad0.06752046.363159156042134.024.0
108Niger0.0830964.660095225770605.05.0
.....................
128Saudi Arabia18.454150304.75000035018132160.0154.0
9Bahrain20.777839498.7656301487346161.0143.0
79Kuwait23.100865520.7382804317190162.0160.0
148Trinidad and Tobago29.122328549.4082001504707163.0128.0
122Qatar38.4397153764.1719002766743164.0164.0
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164 rows × 6 columns

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" ], "text/plain": [ " Country CO2 GDP population \\\n", "39 Democratic Republic of Congo 0.0331 859.381714 87087352 \n", "26 Central African Republic 0.0471 623.488892 5094795 \n", "21 Burundi 0.0608 651.358887 11493476 \n", "27 Chad 0.0675 2046.363159 15604213 \n", "108 Niger 0.0830 964.660095 22577060 \n", ".. ... ... ... ... \n", "128 Saudi Arabia 18.4541 50304.750000 35018132 \n", "9 Bahrain 20.7778 39498.765630 1487346 \n", "79 Kuwait 23.1008 65520.738280 4317190 \n", "148 Trinidad and Tobago 29.1223 28549.408200 1504707 \n", "122 Qatar 38.4397 153764.171900 2766743 \n", "\n", " CO2_rank GDP_rank \n", "39 1.0 4.0 \n", "26 2.0 1.0 \n", "21 3.0 2.0 \n", "27 4.0 24.0 \n", "108 5.0 5.0 \n", ".. ... ... \n", "128 160.0 154.0 \n", "9 161.0 143.0 \n", "79 162.0 160.0 \n", "148 163.0 128.0 \n", "122 164.0 164.0 \n", "\n", "[164 rows x 6 columns]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "CO2vGDP['CO2_rank'] = CO2vGDP['CO2'].rank()\n", "CO2vGDP['GDP_rank'] = CO2vGDP['GDP'].rank()\n", "\n", "# We can see these most clearly if we sort the dataframe before displaying\n", "display(CO2vGDP.sort_values(by='CO2'))" ] }, { "cell_type": "markdown", "id": "c35739d5", "metadata": {}, "source": [ "You can see that countries with low ranks for CO2 do tend to have low ranks for GDP.\n", "\n", "Let's plot the data, and the ranked data, on scatterplots. You can see that the ranked data do not have the same heteroscedasticity issue as the data themselves." ] }, { "cell_type": "code", "execution_count": 8, "id": "e117b99f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.subplot(1,2,1)\n", "sns.scatterplot(data=CO2vGDP, x='CO2', y='GDP')\n", "\n", "plt.subplot(1,2,2)\n", "sns.scatterplot(data=CO2vGDP, x='CO2_rank', y='GDP_rank')\n", "\n", "plt.subplots_adjust(wspace = 0.5) # shift the plots sideways so they don't overlap" ] }, { "cell_type": "markdown", "id": "c80e5a6c", "metadata": {}, "source": [ "To continue the process of applying the equation, we make a new column containing the difference of ranks:" ] }, { "cell_type": "code", "execution_count": 10, "id": "a9b41d09", "metadata": {}, "outputs": [], "source": [ "CO2vGDP['d'] = CO2vGDP['CO2_rank']-CO2vGDP['GDP_rank']" ] }, { "cell_type": "markdown", "id": "d1ce5ae7", "metadata": {}, "source": [ "... and apply the formula:" ] }, { "cell_type": "code", "execution_count": 11, "id": "fc41f855", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "r = 0.9143688871356087\n" ] } ], "source": [ "n = len(CO2vGDP)\n", "\n", "r_s = 1 - 6*sum(CO2vGDP['d']**2)/(n*(n**2 - 1))\n", "print('r = ' + str(r_s))" ] }, { "cell_type": "markdown", "id": "d45ec756", "metadata": {}, "source": [ "Ta-daa! This should match the value from the built in function.\n", "\n", "### Spearman = Pearson on Ranks\n", "\n", "The equation for Spearman's $r_s$ looks pretty weird, doesn't it? What is that 6 doing there?!\n", "\n", "I can't tell you the derivation (although I believe I did once know it), but I can tell you a fun thing.\n", "\n", "Spearman's $r_s$ is exactly the same value as Pearson's $r$ claculated on the ranks.\n", "\n", "Let's try it!" ] }, { "cell_type": "code", "execution_count": 86, "id": "e5c44c59", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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165 rows × 2 columns

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" ], "text/plain": [ " CO2_rank GDP_rank\n", "0 16.0 22.0\n", "1 58.0 73.0\n", "2 94.0 93.0\n", "3 41.0 59.0\n", "4 99.0 105.0\n", ".. ... ...\n", "160 77.0 55.0\n", "161 106.0 96.0\n", "162 24.0 26.0\n", "163 29.0 36.0\n", "164 44.0 14.0\n", "\n", "[165 rows x 2 columns]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# make a new dataframe with only ranks\n", "CO2vGDP_ranks = CO2vGDP[['CO2_rank','GDP_rank']]\n", "display(CO2vGDP_ranks)" ] }, { "cell_type": "code", "execution_count": 88, "id": "4407a87e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CO2_rankGDP_rank
CO2_rank1.0000000.913841
GDP_rank0.9138411.000000
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" ], "text/plain": [ " CO2_rank GDP_rank\n", "CO2_rank 1.000000 0.913841\n", "GDP_rank 0.913841 1.000000" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Calculate **Pearson's** correlation on the ranks\n", "CO2vGDP_ranks.corr(method='pearson')" ] }, { "cell_type": "markdown", "id": "7a3f2736", "metadata": {}, "source": [ "Yep, the correlation is 0.9138 - the exact same value as $r_s$" ] }, { "cell_type": "code", "execution_count": null, "id": "9ffc4b8b", "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }