{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simpson's Paradox\n", "\n", "### Authors: \n", "- Christian Michelsen (Niels Bohr Institute)\n", "\n", "### Date: \n", "- 05-11-2018 (latest update)\n", "\n", "***\n", "\n", "The aim of this notebook is to illustrate Simpson's paradox through a simple, quick example.\n", "\n", "For more information on the Simpson's Paradox, see: __[Wikipedia](https://en.wikipedia.org/wiki/Simpson%27s_paradox)__\n", "\n", "This small example is meant to show how aggregating different samples can change the overall statistics completely. In this specific case we will look at how the amount of exercise can change the risk of catching a highly infectioness disease. \n", "\n", "***\n", "\n", "First, we import the modules we want to use:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import seaborn as sns\n", "\n", "sns.set(color_codes=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then load the data located in the csv file `Simpsons_paradox.csv` into a Pandas DataFrame and see what it contains:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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ExerciseAgeProbability
09.72015920-4020.988422
12.49893710-2022.323348
25.52074210-205.875953
38.44135060-8074.790105
410.81393740-6050.120903
58.36277240-6050.933656
65.23243120-4036.104305
711.19211860-8064.977362
813.17465060-8076.653905
98.46382910-204.628246
\n", "
" ], "text/plain": [ " Exercise Age Probability\n", "0 9.720159 20-40 20.988422\n", "1 2.498937 10-20 22.323348\n", "2 5.520742 10-20 5.875953\n", "3 8.441350 60-80 74.790105\n", "4 10.813937 40-60 50.120903\n", "5 8.362772 40-60 50.933656\n", "6 5.232431 20-40 36.104305\n", "7 11.192118 60-80 64.977362\n", "8 13.174650 60-80 76.653905\n", "9 8.463829 10-20 4.628246" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.read_csv(\"Simpsons_paradox.csv\", index_col=0) #index_col=0 to make sure that the first columns is used as the index\n", "df.head(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a very quick, but illustrating, example of how to work with Pandas DataFrames, see the following __[link](https://jalammar.github.io/gentle-visual-intro-to-data-analysis-python-pandas)__.\n", "\n", "***\n", "\n", "To further see any relationships in the data, we plot the hours pr. week of exercise vs. the probability of catching the highly infectious disease. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig1, ax1 = plt.subplots(ncols=1, figsize=(14, 8))\n", "ax1 = sns.scatterplot(x=\"Exercise\", y=\"Probability\", data=df, label=\"Age: All\", ax=ax1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the plot is done using Seaborn and its `scatterplot` function. This works closely together with Pandas DataFrames, where we simply write the strings of the dataframe columns and provide the dataframe via the `data` keyword. \n", "\n", "## Questions: \n", "\n", "- What can you conclude from the following plot? \n", "\n", "***\n", "\n", "- In this example we have more data that we haven't used yet; the age of the patient. How would you include this information in the plot and does this alter your above conclusion? " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "# insert code here\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "- ___Hint___: _look up the `hue` keyword in the `scatterplot` function_\n", "\n", "***\n", "\n", "### Optional question:\n", "\n", "When finished, you can take at the generating function located in `Simpsons_paradox_generate_data.py` and see if it makes sense.\n" ] } ], "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }