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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Practical 7: Hypothesis Testing\n",
      "===============================\n",
      "\n",
      "**Question 1.** I have two sets of trilobite fossils from different localities. I think they are from the same species but want some quantitative confirmation \u2013 on the basis of their mean length:width ratio (triloshape1.csv, triloshape2.csv) is there evidence that they are different?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "\n",
      "# Read in data\n",
      "import numpy as np\n",
      "\n",
      "# Read in the records.\n",
      "record1 = np.recfromcsv(\"../data/triloshape1.csv\") \n",
      "record2 = np.recfromcsv(\"../data/triloshape2.csv\") \n",
      "\n",
      "print record1.dtype.names\n",
      "print record2.dtype.names"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n",
        "('082',)\n",
        "('116',)\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Well that's annoying! We were given a csv file with no header so recfromcsv has read the first line of data as the header. This underscores the importantance of always inspecting your data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Read in the records - take II.\n",
      "record1 = np.recfromtxt(\"../data/triloshape1.csv\") \n",
      "record2 = np.recfromtxt(\"../data/triloshape2.csv\") \n",
      "\n",
      "triloshape1 = np.array(record1, dtype=float)\n",
      "triloshape2 = np.array(record2, dtype=float)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot distribution - triloshape1\n",
      "n, bins, patches = pylab.hist(triloshape1, 10, normed=1)\n",
      "\n",
      "# Add a 'best fit' line\n",
      "sigma = np.std(triloshape1)\n",
      "mu = np.mean(triloshape1)\n",
      "\n",
      "y = pylab.normpdf(bins, mu, sigma)\n",
      "l = pylab.plot(bins, y, 'r--', linewidth=1)\n",
      "\n",
      "pylab.xlabel(\"Samples\")\n",
      "pylab.ylabel(\"Mean length:width ratio\")\n",
      "\n",
      "pylab.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OhaE8qDCEbj8NGcK3X/B7xamnwltvRZd6W97vpamURFcSZrYWcABwJNAd+DMw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\nJ6DVoLcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bd82f90>"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot distribution - triloshape2\n",
      "n, bins, patches = pylab.hist(triloshape2, 10, normed=1)\n",
      "\n",
      "# Add a 'best fit' line\n",
      "sigma = np.std(triloshape2)\n",
      "mu = np.mean(triloshape2)\n",
      "\n",
      "y = pylab.normpdf(bins, mu, sigma)\n",
      "l = pylab.plot(bins, y, 'r--', linewidth=1)\n",
      "\n",
      "pylab.xlabel(\"Samples\")\n",
      "pylab.ylabel(\"Mean length:width ratio\")\n",
      "\n",
      "pylab.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OVlEuCrkjfs7p9GMmZ/AzZrFe1oHMrOg91uQsTmNjXuZqvssZ/JRzOSHrWBXl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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bb4d050>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The plots don't look convincing. However, it is always better to use a quantative test.\n",
      "# Use the D\u2019Agostino & Pearson test to test the null hypothesis that a samples come from\n",
      "# a normal distribution.\n",
      "from scipy import stats\n",
      "\n",
      "k2_1, p_1 = stats.normaltest(triloshape1)\n",
      "k2_2, p_2 = stats.normaltest(triloshape2)\n",
      "\n",
      "print \"p-values = \", p_1, p_2\n",
      "if p_1 <= 0.05 or p_2 <= 0.05:\n",
      "    print \"Reject\",\n",
      "else:\n",
      "    print \"Accept\",\n",
      "print \"the hypothesis that the sample comes from a normal distribution.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p-values =  0.525341968156 0.543279451684\n",
        "Accept the hypothesis that the sample comes from a normal distribution.\n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we are confident that the two distributions come from a normal distribution we are confident that we should use the *T-test* to compare these datasets. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t, p = stats.ttest_ind(triloshape1, triloshape2)\n",
      "\n",
      "print \"T-test - (t, p) = %g, %g\"%(t, p)\n",
      "if p<=0.05:\n",
      "    print \"Reject\",\n",
      "else:\n",
      "    print \"Accept\"\n",
      "print \"the hypothesis that the populations are the same.\"\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "T-test - (t, p) = -2.09157, 0.0380368\n",
        "Reject the hypothesis that the populations are the same.\n"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Question 2**. I have measured mica percentages in samples of igneous rocks from two different localities (micapercent1.csv, micapercent2.csv). The mean mica percentage is lower in the second locality and I have a geological theory that may explain this, but I first need to rule out the possibility that the lower mica content is just due to chance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Read in data\n",
      "import numpy as np\n",
      "\n",
      "# Read in the records.\n",
      "record1 = np.recfromcsv(\"../data/micapercent1.csv\") \n",
      "record2 = np.recfromcsv(\"../data/micapercent2.csv\") \n",
      "\n",
      "print record1.dtype.names\n",
      "print record2.dtype.names"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('89',)\n",
        "('62',)\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As in the first question we were given a csv file with no header so recfromcsv has read the first line of data as the header. Always check your data!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Read in the records - take II.\n",
      "record1 = np.recfromtxt(\"../data/micapercent1.csv\") \n",
      "record2 = np.recfromtxt(\"../data/micapercent2.csv\") \n",
      "\n",
      "micapercent1 = np.array(record1, dtype=float)\n",
      "micapercent2 = np.array(record2, dtype=float)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot distribution - micapercent1\n",
      "n, bins, patches = pylab.hist(micapercent1, 10, normed=1)\n",
      "\n",
      "# Add a 'best fit' line\n",
      "sigma = np.std(micapercent1)\n",
      "mu = np.mean(micapercent1)\n",
      "\n",
      "y = pylab.normpdf(bins, mu, sigma)\n",
      "l = pylab.plot(bins, y, 'r--', linewidth=1)\n",
      "\n",
      "pylab.xlabel(\"Samples\")\n",
      "pylab.ylabel(\"Mean length:width ratio\")\n",
      "\n",
      "pylab.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LGssO0ILGsgO0orHsAC1oLDvAcityj2IQMDsi5kTEYuBG4MBmyxwAXAsQEROA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\nzCeaoqU/DPAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10be56690>"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Plot distribution - micapercent2\n",
      "n, bins, patches = pylab.hist(micapercent2, 10, normed=1)\n",
      "\n",
      "# Add a 'best fit' line\n",
      "sigma = np.std(micapercent2)\n",
      "mu = np.mean(micapercent2)\n",
      "\n",
      "y = pylab.normpdf(bins, mu, sigma)\n",
      "l = pylab.plot(bins, y, 'r--', linewidth=1)\n",
      "\n",
      "pylab.xlabel(\"Samples\")\n",
      "pylab.ylabel(\"Mean length:width ratio\")\n",
      "\n",
      "pylab.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VFEQkRepKqjFaXTVXCDlCyABh5AghA4SRI4QMEOTgs5SpsbHtbUREUqLCEJJ3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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bd423d0>"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Looking at the first of these two plots it would appear unlikely that the sample comes\n",
      "# from a normal distribution. However, it is always better to use a quantative test.\n",
      "# Use the D\u2019Agostino & Pearson test to test the null hypothesis that a samples come from\n",
      "# a normal distribution.\n",
      "from scipy import stats\n",
      "\n",
      "k2_1, p_1 = stats.normaltest(micapercent1)\n",
      "k2_2, p_2 = stats.normaltest(micapercent2)\n",
      "\n",
      "print \"p-values = \", p_1, p_2\n",
      "if p_1 <= 0.05 or p_2 <= 0.05:\n",
      "    print \"Reject\",\n",
      "else:\n",
      "    print \"Accept\",\n",
      "print \"the hypothesis that the sample comes from a normal distribution.\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p-values =  3.19642639296e-05 0.364148255391\n",
        "Reject the hypothesis that the sample comes from a normal distribution.\n"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u, p = stats.mannwhitneyu(micapercent1, micapercent2)\n",
      "\n",
      "# This is a one-tailed test. We want to consider both tails therefore we multiply the p value by 2.\n",
      "p = p*2\n",
      "\n",
      "print \"Mann-Whitney rank test two-tailed p-value = \", p, \" and u value = \", u\n",
      "if p<=0.05:\n",
      "    print \"Reject\",\n",
      "else:\n",
      "    print \"Accept\"\n",
      "print \"the hypothesis that the populations are the same.\"\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Mann-Whitney rank test two-tailed p-value =  0.0439660870304  and u value =  512.5\n",
        "Reject the hypothesis that the populations are the same.\n"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Therefore, the differences in the two samples really is significant and not by chance."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}