{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Anscombe's Quartet\n", "\n", "This Script is meant to illustrate the importance of VISUAL INSPECTION of a dataset. The example is taken from a __[paper](http://www.sjsu.edu/faculty/gerstman/StatPrimer/anscombe1973.pdf)__ written by Frank Anscombe in 1973.\n", "\n", "In this problem, you are provided with four datasets sharing the following characteristics:\n", "\n", "- Mean of each x variable: 9.0\n", "- Variance of each x variable: 10.0\n", "- Mean of each y variable: 7.5\n", "- Variance of each y variable: 3.75\n", "- Correlation between each x and y variable: 0.816\n", "- Linear regression line: y = 3 + 0.5x\n", "\n", "The purpose of this example is to show that, despite having similar statistical propeties, data sets can often look very different from one another, hence the importance of plotting the data first.\n", "\n", "### Author: \n", "- Troels C. Petersen (NBI)\n", "- Étienne Bourbeau (NBI)\n", "\n", "### Contact: \n", "petersen@nbi.dk\n", "\n", "### Date: \n", "7th of November 2018\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Your Task\n", "1) First acquaint yourself with the program, and get yourself a \"free\" (hopefully not first!) look at how Python works. Understand that each of the four distributions are being fitted with a linear function (here called \"fit_p1\") and the results plottet. There are comments for most lines in the macro!\n", "\n", "2) Run each step of the notebook sequentially, and then take a close look at each of the four results.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from iminuit import Minuit\n", "from probfit import Chi2Regression #, BinnedChi2, UnbinnedLH, Extended\n", "import sys" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sys.path.append('../../External_Functions')\n", "from ExternalFunctions import nice_string_output, add_text_to_ax # useful functions to print fit results on figure" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We begin by inserting the data into numpy arrays:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "save_plots = True\n", "N_datasets = 4\n", "N_points = 11" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Define data samples\n", "x = np.array([ [ 10.0, 8.0, 13.0, 9.0, 11.0, 14.0, 6.0, 4.0, 12.0, 7.0, 5.0 ] ,\n", " [ 10.0, 8.0, 13.0, 9.0, 11.0, 14.0, 6.0, 4.0, 12.0, 7.0, 5.0 ] ,\n", " [ 10.0, 8.0, 13.0, 9.0, 11.0, 14.0, 6.0, 4.0, 12.0, 7.0, 5.0 ] ,\n", " [ 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 19.0, 8.0, 8.0, 8.0 ] ])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "y = np.array([ [ 8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68 ] ,\n", " [ 9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74 ] ,\n", " [ 7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73 ] ,\n", " [ 6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89 ] ])" ] }, { "cell_type": "markdown", "metadata": { "lines_to_next_cell": 2 }, "source": [ "We then proceed to fit the data with a linear fit defined below:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def linear_fit(x, p0, p1):\n", " return p0 + p1*x" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EDM = 1.995131716247806e-22GOAL EDM = 1e-05\n", " UP = 1.0
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FCN = 13.776290909090903TOTAL NCALL = 33NCALLS = 33
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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(14,10))\n", "ax = ax.flatten() # go from 2d list to 1d list\n", "\n", "for x_i, y_i, ax_i in zip(x, y, ax):\n", " \n", " ax_i.scatter(x_i, y_i, marker='.', color='blue', s=100) # make a scatter plot of the i'th data set as blue dots \n", " ax_i.set_title('Graph') \n", "\n", " chi2_object_lin = Chi2Regression(linear_fit, x_i, y_i) # chi2-regression object\n", " minuit_lin = Minuit(chi2_object_lin, pedantic=False, p0=1., p1=1.) # sets the initial parameters of the fit\n", " minuit_lin.migrad(); # fit the function to the data\n", "\n", " x_fit = np.linspace(0.9*x_i.min(), 1.1*x_i.max()) # Create the x-axis for the plot of the fitted function\n", " y_fit = linear_fit(x_fit, *minuit_lin.args) # the fitted function, where we have unpacked the fitted values\n", " ax_i.plot(x_fit, y_fit, '-r') # plot the fit with a red (\"r\") line (\"-\")\n", " \n", " d = {'p0': [minuit_lin.values['p0'], minuit_lin.errors['p0']],\n", " 'p1': [minuit_lin.values['p1'], minuit_lin.errors['p1']],\n", " }\n", " \n", " text = nice_string_output(d, extra_spacing=2, decimals=3)\n", " add_text_to_ax(0.02, 0.97, text, ax_i, fontsize=14)\n", " \n", " # Alternative \"simple\" way of putting values into the plots:\n", " #string = f\"p0 = {minuit_lin.values['p0']:.3f} +/- {minuit_lin.errors['p0']:.3f}\\n\"\n", " #string += f\"p1 = {minuit_lin.values['p1']:.3f} +/- {minuit_lin.errors['p1']:.3f}\"\n", " #ax_i.text(0.05, 0.95, string, family='monospace', transform=ax_i.transAxes, fontsize=10, verticalalignment='top')\n", " \n", "fig.tight_layout() " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "if save_plots:\n", " fig.savefig('plot_AnscombesQuartet.pdf', dpi=600)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Questions:\n", "1. Which scenario(s) looks most like real data without any mistakes/mismeasurements in it?\n", "\n", "2. Looking closely at each of the four fits, determine which points gives the largest\n", " contribution to the \"mismatch\" (that is chi-square) between the data and the fit,\n", " if any single.\n", "\n", "3. Consider how YOU would treat each of the four datasets and how you would model/fit them!\n", "\n", "\n", "### Advanced questions:\n", "4. How would you with (smarter) statistical techniques detect that something was\n", " not right without looking?\n" ] } ], "metadata": { "executable": "/usr/bin/env python", "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": "3.6.6" }, "main_language": "python" }, "nbformat": 4, "nbformat_minor": 2 }