drorata/hypothesis-test-t-test.ipynb

## hypothesis-test-t-test.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $t$-Test tested\n",
    "\n",
    "In this post we shall try to run a quick experiment with the intention of convincing ourselves that $t$-test works.\n",
    "We will examine what is the underlaying distribution of many different samples obtained from many different distributions.\n",
    "Furthermore, we will see how the size of the sample influence the reliability of the test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Modules used\n",
    "%matplotlib inline\n",
    "import pylab as plt\n",
    "plt.style.use('ggplot')\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definitions\n",
    "\n",
    "**Hypothesis:** a statement about a population parameter. A population may be the users' traffic and the parameter may be conversion rate.\n",
    "\n",
    "**Objectives:** given sample taken from the population, decide whether the *null-hypothesis* ($H_0$) holds or not.\n",
    "\n",
    "## Example\n",
    "\n",
    "A classical example is to consider the height of a population.\n",
    "The null-hypothesis, $H_0$, in this case would suggest that the mean of the distribution is $H_0$.\n",
    "Ideally, we should measure the height of all members of the population, but this is going to be tricky.\n",
    "Therefore, we take a sample from the population and measure the heights in the sample.\n",
    "The objective of the test is to answer the following question: \n",
    "\n",
    "> *Does the mean of the underlaying distribution equals to $H_0$?*\n",
    "\n",
    "So, next, we compute the mean of the sample.\n",
    "At this point, we should use the statistical test and answer the question."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fixed hypothesis on varying populations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us set some parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dx = 1.\n",
    "means = np.arange(146,200+dx,dx)\n",
    "sizes = [10, 50, 100, 500, 1000]\n",
    "STD=20\n",
    "H0=172"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this experiment we fix $H_0=${{H0}} and we apply the $t$-test on various samples obtained from different normal distributions.\n",
    "For simplicity, we use fixed STD for the distribution and varying means.\n",
    "\n",
    "Next, for each size $n$ and mean $\\mu$, we generate a sample of size $n$ with mean $\\mu$.\n",
    "Recall, the STD is fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.seed(10)\n",
    "samples = pd.DataFrame()\n",
    "for size in sizes:\n",
    "    # For a fixed size, genearte list of samples, one sample for each mean\n",
    "    fixed_size_samples = [pd.Series(np.random.normal(loc=mean, scale=STD, size=size)) for mean in means]\n",
    "    samples[str(size)] = fixed_size_samples\n",
    "samples.index=means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The snippet above generates a matrix where each row has samples with the same mean and each column has samples with the same size.\n",
    "The index of the `DataFrame` is the mean in use and the column name is the size of the sample.\n",
    "Here are the first 3 rows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>10</th>\n",
       "      <th>50</th>\n",
       "      <th>100</th>\n",
       "      <th>500</th>\n",
       "      <th>1000</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>146.0</th>\n",
       "      <td>0    172.631730\n",
       "1    160.305579\n",
       "2    115.09199...</td>\n",
       "      <td>0     146.094211\n",
       "1     148.940679\n",
       "2     136.74...</td>\n",
       "      <td>0     136.876549\n",
       "1     168.284188\n",
       "2     148.19...</td>\n",
       "      <td>0      119.963494\n",
       "1      148.695017\n",
       "2      175...</td>\n",
       "      <td>0      127.606195\n",
       "1      145.544374\n",
       "2      166...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147.0</th>\n",
       "      <td>0    155.660524\n",
       "1    171.060747\n",
       "2    127.69868...</td>\n",
       "      <td>0     158.413869\n",
       "1     136.742496\n",
       "2     152.51...</td>\n",
       "      <td>0     177.846774\n",
       "1     162.064209\n",
       "2     136.09...</td>\n",
       "      <td>0      166.033778\n",
       "1      146.662981\n",
       "2      159...</td>\n",
       "      <td>0      142.859633\n",
       "1      104.352055\n",
       "2      127...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148.0</th>\n",
       "      <td>0    108.445434\n",
       "1    113.132554\n",
       "2    153.32140...</td>\n",
       "      <td>0     150.522897\n",
       "1     160.511639\n",
       "2     147.46...</td>\n",
       "      <td>0     128.513003\n",
       "1     118.104262\n",
       "2     142.10...</td>\n",
       "      <td>0      159.761616\n",
       "1      159.145997\n",
       "2      113...</td>\n",
       "      <td>0      152.074143\n",
       "1      150.470116\n",
       "2      160...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                      10  \\\n",
       "146.0  0    172.631730\n",
       "1    160.305579\n",
       "2    115.09199...   \n",
       "147.0  0    155.660524\n",
       "1    171.060747\n",
       "2    127.69868...   \n",
       "148.0  0    108.445434\n",
       "1    113.132554\n",
       "2    153.32140...   \n",
       "\n",
       "                                                      50  \\\n",
       "146.0  0     146.094211\n",
       "1     148.940679\n",
       "2     136.74...   \n",
       "147.0  0     158.413869\n",
       "1     136.742496\n",
       "2     152.51...   \n",
       "148.0  0     150.522897\n",
       "1     160.511639\n",
       "2     147.46...   \n",
       "\n",
       "                                                     100  \\\n",
       "146.0  0     136.876549\n",
       "1     168.284188\n",
       "2     148.19...   \n",
       "147.0  0     177.846774\n",
       "1     162.064209\n",
       "2     136.09...   \n",
       "148.0  0     128.513003\n",
       "1     118.104262\n",
       "2     142.10...   \n",
       "\n",
       "                                                     500  \\\n",
       "146.0  0      119.963494\n",
       "1      148.695017\n",
       "2      175...   \n",
       "147.0  0      166.033778\n",
       "1      146.662981\n",
       "2      159...   \n",
       "148.0  0      159.761616\n",
       "1      159.145997\n",
       "2      113...   \n",
       "\n",
       "                                                    1000  \n",
       "146.0  0      127.606195\n",
       "1      145.544374\n",
       "2      166...  \n",
       "147.0  0      142.859633\n",
       "1      104.352055\n",
       "2      127...  \n",
       "148.0  0      152.074143\n",
       "1      150.470116\n",
       "2      160...  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples.loc[:148] # Note that the index is the mean used!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following is the histogram of the sample that has $500$ samples with mean $\\mu = 163$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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0OQAAwALG3y748MMPNX36dK1fv14HDx6Uw+HQjTfeqJ/+9KeSpKamJjmdTmVmZvrvExMT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103551940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples['500'].loc[163].hist();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One may guess, based on the visual observation, that the sample was obtained from a normal distribution with mean between $150$ and $170$.\n",
    "Which is indeed the case, the mean was $163$.\n",
    "But, how can be test it rigorously?\n",
    "\n",
    "The answer is $t$-test.\n",
    "We will iterate over all the samples, and run a $t$-test against the fixed $H_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>10</th>\n",
       "      <th>50</th>\n",
       "      <th>100</th>\n",
       "      <th>500</th>\n",
       "      <th>1000</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>146.0</th>\n",
       "      <td>0.000794</td>\n",
       "      <td>6.893325e-12</td>\n",
       "      <td>5.382195e-22</td>\n",
       "      <td>5.135664e-103</td>\n",
       "      <td>6.562808e-221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147.0</th>\n",
       "      <td>0.006270</td>\n",
       "      <td>1.246921e-08</td>\n",
       "      <td>4.854901e-21</td>\n",
       "      <td>3.431649e-98</td>\n",
       "      <td>5.551791e-198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148.0</th>\n",
       "      <td>0.091243</td>\n",
       "      <td>9.588379e-15</td>\n",
       "      <td>6.716187e-23</td>\n",
       "      <td>7.625131e-98</td>\n",
       "      <td>6.041672e-186</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             10            50           100            500           1000\n",
       "146.0  0.000794  6.893325e-12  5.382195e-22  5.135664e-103  6.562808e-221\n",
       "147.0  0.006270  1.246921e-08  4.854901e-21   3.431649e-98  5.551791e-198\n",
       "148.0  0.091243  9.588379e-15  6.716187e-23   7.625131e-98  6.041672e-186"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_vals = samples.applymap(lambda x: stats.ttest_1samp(x, H0)[1])\n",
    "p_vals.loc[:148]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above table, each cell contains the $p$-value of the $t$-test of the corresponding sample against the fixed null-hypothesis $H_0 =$ {{H0}}.\n",
    "\n",
    "**Reminder: What is the $p$-values?**\n",
    "\n",
    "The $p$-value is the probability of observing the result under the assumption of $H_0$.\n",
    "Recall, that a well accepted threshold for null-hypothesis rejection is $\\alpha = 0.05$.\n",
    "In other words, if the $p$-value is smaller than $\\alpha$, we reject the null-hypothesis.\n",
    "In the next step we mark with $1$ (i.e. accepted) the cases where the $p$-value was greater than $\\alpha$ and with $0$ otherwise (i.e. rejected).\n",
    "\n",
    "More intuitively, if the label is $0$, we can claim that mean of the distribution from which the sample was taken is *not* $0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>10</th>\n",
       "      <th>50</th>\n",
       "      <th>100</th>\n",
       "      <th>500</th>\n",
       "      <th>1000</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>146.0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147.0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148.0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       10  50  100  500  1000\n",
       "146.0   0   0    0    0     0\n",
       "147.0   0   0    0    0     0\n",
       "148.0   1   0    0    0     0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accepted = p_vals.applymap(lambda p_val: 0 if p_val < 0.05 else 1)\n",
    "accepted.loc[:148]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now plot a \"heat-map\" of the $0-1$ matrix above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9+rSx0feWW27Rhg0bdO+990bVdHV1KRQKGcerVq1SKBTSoUOHjBfZFRYWym63T+JsAQDA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\nkgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11023fa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "heatmap = ax.pcolormesh(accepted)\n",
    "\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(6, 21)\n",
    "\n",
    "plt.ylim(0,len(accepted.index))\n",
    "ax.xaxis.tick_top()\n",
    "ax.set_yticks(np.arange(len(accepted.index)) + 0.5, minor=False)\n",
    "ax.set_yticklabels(accepted.index, minor=False)\n",
    "ax.set_xticks(np.arange(len(accepted.columns)) + 0.5, minor=False)\n",
    "ax.set_xticklabels(accepted.columns, minor=False)\n",
    "plt.ylabel('Means')\n",
    "plt.xlabel('Sample size')\n",
    "ax.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above graph, every red cell corresponds to a $t$-test of a sample with given size obtained from a normal distribution with given mean.\n",
    "\n",
    "* RED: means that the null-hypothesis cannot be rejected. That is, the obtained sample is likely to be obtained given the null-hypothesis.\n",
    "* BLUE: means that the null-hypothesis has to be rejected. That is, it is very unlikely that we witness the sample assuming $H_0$ holds.\n",
    "\n",
    "We see, that the bigger the sample is, the more accurate the test is. \n",
    "Still, starting from a sample size of 50, we already manage to reject about $2/3$ of the samples.\n",
    "It gets much better the denser the sample is.\n",
    "\n",
    "In general, the smaller the sample, the more likely it is to accept the null-hypothesis even when it is wrong; see sample size of 10 and mean 148.\n",
    "However, the bigger the sample, the more precises the test is; i.e. we correctly identify whether the underlying distribution has a mean equals to $H_0$ or not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Links\n",
    "\n",
    "- [What a p value tells you about statistical data](http://www.dummies.com/education/math/statistics/what-a-p-value-tells-you-about-statistical-data/)\n",
    "- [SciPy Stats](https://docs.scipy.org/doc/scipy-0.18.1/reference/tutorial/stats.html)\n",
    "- [t-Test SciPy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_1samp.html#scipy.stats.ttest_1samp)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}