0017 Independent Samples t-test on Wine Prices.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 statsmodels.api as sm\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 have collected samples of the wine prices of two fictitious online liquorstores, bestliqs.com and cheapliq.com."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bestliqs_wine_prices = pd.Series(\n",
      "    [9, 5, 6, 11, 8, 5, 7, 13, 12, 13, 9, 8, 10, 6, 11, 9, 7, 12])\n",
      "cheapliq_wine_prices = pd.Series(\n",
      "    [11, 10, 12, 9, 8, 13, 14, 15, 12, 11, 13, 8, 9, 11])\n",
      "\n",
      "data = pd.DataFrame({'bestliqs': bestliqs_wine_prices, \n",
      "                     'cheapliq': cheapliq_wine_prices})\n",
      "data.describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "        bestliqs   cheapliq\n",
        "count  18.000000  14.000000\n",
        "mean    8.944444  11.142857\n",
        "std     2.645134   2.178819\n",
        "min     5.000000   8.000000\n",
        "25%     7.000000   9.250000\n",
        "50%     9.000000  11.000000\n",
        "75%    11.000000  12.750000\n",
        "max    13.000000  15.000000"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sns.violinplot(data.dropna())\n",
      "plt.xlabel('Online Liquor Store')\n",
      "plt.ylabel('Price')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KW6hhNkOPDg5KFNIZMXwgJ04cVx3pL6S0FViyZCG7d2wjqXY17JH5VccRt8to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\nnJmQRkVyiwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbc98320>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Question and hypothesis\n",
      "Well, it looks like cheapliq.com isn't as cheap as they say. However, is the difference statistically significant? We don't want to spend too much on the first batch of wine for our new cellar. Which online liquor store to choose if we want to decide on the lowest mean wine price?\n",
      "\n",
      "|Hypothesis||$\\alpha = .05$|\n",
      "|---:|:---:|---|:---|\n",
      "|$H_0:$|$\\mu_{best} = \\mu_{cheap}$|There is no significant difference in mean wine prices|\n",
      "|$H_a:$|$\\mu_{best} \\neq \\mu_{cheap}$|There is a significant difference in mean wine prices|"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Independent Samples t-test"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# First find out what the mean prices are\n",
      "xbar_best = data.bestliqs.mean()\n",
      "xbar_cheap = data.cheapliq.mean()\n",
      "xbar_best, xbar_cheap"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "(8.9444444444444446, 11.142857142857142)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Then we get the sample standard devation for each liquor store\n",
      "s_best = data.bestliqs.std(ddof=1)\n",
      "s_cheap = data.cheapliq.std(ddof=1)\n",
      "s_best, s_cheap"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "(2.6451336499586904, 2.1788191176076901)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Standard Error of the Mean\n",
      "To calculate the standard error of the mean combined for both independent wine price samples, we need to use the following formula:\n",
      "\n",
      "$$sem=\\sqrt{\\frac{s_{best}^2}{n_{best}}+\\frac{s_{cheap}^2}{n_{cheap}}}$$\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Calculate the standard error of the mean combined\n",
      "n_best = data.bestliqs.count()\n",
      "n_cheap = data.cheapliq.count()\n",
      "sem = math.sqrt(s_best ** 2 / n_best + \n",
      "                s_cheap ** 2 / n_cheap)\n",
      "sem"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "0.8531100847677227"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Now calculate the t-statistic\n",
      "t = (xbar_best - xbar_cheap) / sem\n",
      "t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "-2.5769390582356815"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get the criotical values for a two-tailed test at alpha .05\n",
      "alpha = .05\n",
      "dof = n_best + n_cheap - 2  # for both samples combined\n",
      "t_critical = stats.t.ppf(alpha / 2, dof)  # two sided\n",
      "t_critical"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "-2.0422724563012382"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Hypothesis testing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Test our alternative hypothesis\n",
      "t < t_critical or t > -t_critical"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Another way to test the alternative hypothesis by comparing \n",
      "# the probability of getting this mean with the alpha level.\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": [
        "0.01512946515275131"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p < alpha"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Based on these result, we conclude that the difference in mean wine price is not due to random chance or variation in the samples. Therefor we will reject the null hypothesis. Bestliqs.com is, on average, the better choice for the better wine price. Note there is a 5% chance (1 - alpha) on commiting a type I error in which the null hypothesis is true, but was rejected."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Using scipy.stats or statsmodels"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# A quicker way to get these results is to call scipy stats\n",
      "# ttest_ind on both samples for unequal variances\n",
      "# equal_var False makes it effectively Welch's t-test\n",
      "t_statistic, p = stats.ttest_ind(data.bestliqs, data.cheapliq.dropna(), \n",
      "                                 equal_var=False)\n",
      "t_statistic, p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "(-2.576939058235681, 0.015153519382495312)"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Another alternative is using Statsmodels\n",
      "t_statistic, p, dof = sm.stats.ttest_ind(data.bestliqs, data.cheapliq.dropna(), \n",
      "                   alternative='two-sided', usevar='unequal')\n",
      "t_statistic, p, dof"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "(-2.576939058235681, 0.015153519382495319, 29.870886188503025)"
       ]
      }
     ],
     "prompt_number": 13
    }
   ],
   "metadata": {}
  }
 ]
}