{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "import scipy.stats" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "t_dist = scipy.stats.t\n", "norm_dist = scipy.stats.norm" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "x_values = np.linspace(-4, 4, 100)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $t$ distribution at different degrees of freedom:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "t_prob_3 = t_dist.pdf(x_values, 3)\n", "t_prob_10 = t_dist.pdf(x_values, 10)\n", "t_prob_40 = t_dist.pdf(x_values, 40)\n", "z_prob = norm_dist.pdf(x_values)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.figure(figsize=(10, 8))\n", "plt.plot(x_values, t_prob_3, 'r:', label='t df=3')\n", "plt.plot(x_values, t_prob_10, 'g:', label='t df=10')\n", "plt.plot(x_values, t_prob_40, 'b:', label='t df=40')\n", "plt.plot(x_values, z_prob, 'k', label='z')\n", "plt.xlabel('$z$ or $t$ value')\n", "plt.ylabel('probability')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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LigJ/f2hm54zOcuLMGbjnnhxiYwNZv349za8sDCdSSHp+OpbGnIlImXP27Fl2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MXf3xVXV1eWLHFlzhxXdLoWuLi48P77LkyZ4kKXLi44OzsTHe3M2LFOdOrkTA9VD2Jj/0bfvvDo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\nk0QAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is the *probability density function* (PDF) - the probability of observing a $z$ or $t$ value.\n", "\n", "The *cumulative density function* (CDF) is the area under the curve of the PDF up until a particular value, and is the probability of observing a $z$ or $t$ value less than or equal to the value on the x axis:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "t_cdf_10 = t_dist.cdf(x_values, 10)\n", "plt.figure(figsize=(10, 8))\n", "plt.plot(x_values, t_cdf_10, 'b', label='t cdf df=10')\n", "plt.plot(x_values, t_prob_10, 'k', label='t pdf df=10')\n", "plt.xlabel('$z$ or $t$ value')\n", "plt.ylabel('probability')\n", "plt.legend()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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1YDVq1OD06dOcP3+emJgYli1bRuvWrZMc88orr7Bz507i4+O5d+8e4eHhVKhQ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\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CDF maps $z$ or $t$ value to a probability. That is, it is a function $f$ such that $p = f(t)$ returns the propability of observing (say) $t$ value greater than or equal to $t$. Here is the probability of observing a t value of 2 or less in a t distribution with 10 degrees of freedom:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "p = t_dist.cdf(2, 10)\n", "p" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "0.96330598261462974" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if we want to go in the opposite direction? I mean, we want a function $g$ such that $t = g(p)$ - where $p$ is a probability and $t$ is the $t$ value?\n", "\n", "In this case our function $g$ is the inverse of $f$ - that is $g(f(t)) = t$. In `scipy` the inverse of the CDF is the *percent point function* or `ppf` (see: http://www.itl.nist.gov/div898/handbook/eda/section3/eda362.htm).\n", "\n", "The $t$ value corresponding to $p$ above should be 2:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "t_dist.ppf(p, 10)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "1.9999999999960625" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It isn't exactly 2, because of [floating point error](http://matthew-brett.github.io/pydagogue/floating_error.html#floating-error), but as you can see, it is very close." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ``ppf`` (inverse cumulative density function) allows us to find a $t$ threshold for a probility of - say - 0.05:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "t_for_05 = t_dist.ppf(0.95, 10)\n", "t_for_05" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "1.8124611228107335" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for completeness, `scipy` also has the *survival function* which is just $1 - cdf(t)$:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "p_sf = t_dist.sf(2, 10)\n", "p_sf" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "0.036694017385370196" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "1 - t_dist.cdf(2, 10)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "0.036694017385370259" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "`scipy` also has the inverse of the survival function, `isf`:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "t_dist.isf(p_sf, 10)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "1.9999999999960638" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "`scipy` has these functions for lots of distributions, including the normal distribution.\n", "\n", "So - what is the probability of observing a $z$ value (from the normal distribution) of 0.9 or lower?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "norm_dist.cdf(0.9)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "0.81593987465324047" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What $z$ value gives me a probability of 0.95 of seeing this $z$ value or less?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "norm_dist.ppf(0.95)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 16, "text": [ "1.6448536269514722" ] } ], "prompt_number": 16 } ], "metadata": {} } ] }