0016 Paired Samples t-Test on Women's Shoes.ipynb

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   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import scipy\n",
      "import matplotlib.pyplot as plt\n",
      "import seaborn as sns\n",
      "from scipy import stats\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "# turn of data table rendering\n",
      "pd.set_option('display.notebook_repr_html', False)\n",
      "\n",
      "sns.set_palette(['#00A99D', '#F5CA0C', '#B6129F', '#76620C', '#095C57'])\n",
      "np.version.full_version"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "'1.9.1'"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data\n",
      "We use two samples of the same subjects, in this case a group of 19 randomly selected women walking on high heels in one sample and flat shoes in another. The samples show the number of steps taken in 30 days for each woman in the group."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "high_heels = pd.Series(\n",
      "    [189158.,  192110.,  176194.,  156349.,  161981.,  152096.,\n",
      "     168058.,  156401.,  174939.,  170711.,  170485.,  150565.,\n",
      "     167770.,  157289.,  191459.,  160661.,  190667.,  184006.,  174503.])\n",
      "flat_shoes = pd.Series(\n",
      "    [188777.,  196981.,  190510.,  184603.,  192341.,  197897.,\n",
      "     154040.,  168098.,  192263.,  154085.,  176084.,  189249.,\n",
      "     176291.,  151454.,  198118.,  162959.,  167480.,  159884.,  184386.])\n",
      "\n",
      "data = pd.DataFrame({'high': high_heels, 'flat': flat_shoes})\n",
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "     flat    high\n",
        "0  188777  189158\n",
        "1  196981  192110\n",
        "2  190510  176194\n",
        "3  184603  156349\n",
        "4  192341  161981"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's look at the difference in a side-by-side violin plot\n",
      "sns.violinplot(data)\n",
      "plt.ylabel('Number of steps in 30 days')\n",
      "plt.xlabel('Kind of shoes')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FwD+YWQwYhsH8+b/y8msvUup0kNmhLYWNG8goAeETtpxcUpauIiL9GN16XMA9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\nIsRJGBBCCCFCnIQBIYQQIsT9Pz13/u3ps+gWAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xcf38b00>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Just peeking at the plot shows a higher average step frequency over the period of 30 days for the group of women wearing flat shoes. But is it a statistical significant difference?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# The violin plot above shows the median, quartiles, IQR and \n",
      "# probability density function (kernel density estimation) \n",
      "# for both groups\n",
      "data.describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "                flat           high\n",
        "count      19.000000      19.000000\n",
        "mean   178184.210526  170810.631579\n",
        "std     16113.058647   13748.423232\n",
        "min    151454.000000  150565.000000\n",
        "25%    165219.500000  158975.000000\n",
        "50%    184386.000000  170485.000000\n",
        "75%    191386.500000  180100.000000\n",
        "max    198118.000000  192110.000000"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Hypothesis\n",
      "We want to know if there is a significant difference in the mean steps taken in 30 days for women wearing high heels and the same group wearing flat shoes. While walking on high heels, the women scored a mean average of $\\bar{x}_h=170810.63$. On flat shoes the mean average is $\\bar{x}_f=178184.21$ We choose as our test criterium an alpha level of 5%. So our hypothesis states:\n",
      "\n",
      "|Hypothesis||$\\alpha = .05$|\n",
      "|---:|:---:|---|:---|\n",
      "|$H_0:$|$\\mu_h = \\mu_f$|There is no significant difference in mean steps between groups|\n",
      "|$H_a:$|$\\mu_h \\neq \\mu_f$|There is a significant difference in mean steps between groups|\n",
      "\n",
      "Note that the hypothesis is written to denote the whole population, not just the sample."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Take the difference of each subject\n",
      "data['difference'] = data.high - data.flat\n",
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "     flat    high  difference\n",
        "0  188777  189158         381\n",
        "1  196981  192110       -4871\n",
        "2  190510  176194      -14316\n",
        "3  184603  156349      -28254\n",
        "4  192341  161981      -30360"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Conduct a t-Test for dependent means\n",
      "All steps below are actually the same as for a one sample t-test conducted on a sample of mean differences."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the point estimate (mean difference)\n",
      "point_estimate = data['difference'].mean()\n",
      "point_estimate"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "-7373.5789473684208"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the sample standard deviation of the difference\n",
      "s = data.difference.std()\n",
      "s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "19471.738275755764"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Show the mean difference distribution\n",
      "sns.distplot(data.difference, label='mean difference')\n",
      "plt.legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4vLX2AwBjjAd43xgzy1q7h65DF+/EmmBVVTDWJkkrEPBrfknscObX2Bgk2NROp8fXy1XF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\nXCkoiIiIiCsFBREREXGloCAiIiKuFBR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       "text": [
        "<matplotlib.figure.Figure at 0xcf22278>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the t-statistic with the point estimate\n",
      "n = data.high.count() # the same for both samples\n",
      "se = s / math.sqrt(n) # standard error\n",
      "t = point_estimate / se\n",
      "n, se, t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(19, 4467.1231262680149, -1.6506325746898669)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# So what is the probability of getting this mean difference?\n",
      "dof = n - 1\n",
      "p = stats.t.sf(abs(t), dof) * 2 # two sided\n",
      "p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "0.11615318918022229"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# To test our alternative hypothesis\n",
      "alpha = .05\n",
      "p < alpha / 2 # two sided"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We fail to reject the null. There is no statistical significant difference in the mean differences between steps taken on high heels or flat shoes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# A quicker way to perform a dependent t-test is to call the scipy\n",
      "# function ttest_rel on both samples to get our t-statistic and \n",
      "# p value\n",
      "t_statistic, p = stats.ttest_rel(data.high, data.flat)\n",
      "t_statistic, p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "(-1.6506325746898667, 0.11615318918022235)"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Confidence interval"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate t-critical to use with our confidence interval\n",
      "t_critical = abs(stats.t.ppf(alpha / 2, dof)) # two sided\n",
      "t_critical"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "2.1009220402409601"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the confidence interval\n",
      "margin_of_error = se * t_critical\n",
      "CI_lo = point_estimate - margin_of_error\n",
      "CI_hi = point_estimate + margin_of_error\n",
      "CI_lo, CI_hi"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "(-16758.656379814995, 2011.498485078152)"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We are confident that the true mean difference lies somewhere between -16758 and 2011. This confidence interval crosses 0, so a true mean difference could be 0 (meaning no difference at all)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}