chi2_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "a1 = [6, 4, 5, 10]\n",
    "a2 = [8, 5, 3, 3]\n",
    "a3 = [5, 4, 8, 4]\n",
    "a4 = [4, 11, 7, 13]\n",
    "a5 = [5, 8, 7, 6]\n",
    "a6 = [7, 3, 5, 9]\n",
    "dice = np.array([a1, a2, a3, a4, a5, a6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "\n",
    "chi2_table = stats.chi2_contingency(dice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "===Chi2 Stat===\n",
      "16.490612061288754\n",
      "\n",
      "\n",
      "===Degrees of Freedom===\n",
      "15\n",
      "\n",
      "\n",
      "===P-Value===\n",
      "0.35021521809742745\n",
      "\n",
      "\n",
      "===Contingency Table===\n",
      "[[ 5.83333333  5.83333333  5.83333333  7.5       ]\n",
      " [ 4.43333333  4.43333333  4.43333333  5.7       ]\n",
      " [ 4.9         4.9         4.9         6.3       ]\n",
      " [ 8.16666667  8.16666667  8.16666667 10.5       ]\n",
      " [ 6.06666667  6.06666667  6.06666667  7.8       ]\n",
      " [ 5.6         5.6         5.6         7.2       ]]\n"
     ]
    }
   ],
   "source": [
    "chi2_stat, p_val, dof, ex = stats.chi2_contingency(dice)\n",
    "print(\"===Chi2 Stat===\")\n",
    "print(chi2_stat)\n",
    "print(\"\\n\")\n",
    "print(\"===Degrees of Freedom===\")\n",
    "print(dof)\n",
    "print(\"\\n\")\n",
    "print(\"===P-Value===\")\n",
    "print(p_val)\n",
    "print(\"\\n\")\n",
    "print(\"===Contingency Table===\")\n",
    "print(ex)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10, 20, 30], [6, 9, 17]]\n"
     ]
    }
   ],
   "source": [
    "# chi-squared test with similar proportions\n",
    "from scipy.stats import chi2_contingency\n",
    "from scipy.stats import chi2\n",
    "\n",
    "# contingency table\n",
    "table = [[10, 20, 30],\n",
    "        [6,  9,  17]]\n",
    "print(table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dof=2\n",
      "Expected: [[10.43478261 18.91304348 30.65217391]\n",
      " [ 5.56521739 10.08695652 16.34782609]]\n"
     ]
    }
   ],
   "source": [
    "stat, p, dof, expected = chi2_contingency(table)\n",
    "print('dof=%d' % dof)\n",
    "print('Expected: {}'.format(expected))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p: 0.873028283380073\n",
      "stat: 0.27157465150403504\n"
     ]
    }
   ],
   "source": [
    "print('p: {}'.format(p))\n",
    "print('stat: {}'.format(stat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# interpret test-statistic\n",
    "prob = 0.95\n",
    "critical = chi2.ppf(prob, dof)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probability=0.950, critical=5.991, stat=0.272 dof=2.000\n"
     ]
    }
   ],
   "source": [
    "print('probability=%.3f, critical=%.3f, stat=%.3f dof=%.3f' % (prob, critical, stat, dof))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent (fail to reject H0) means Categorical Variables are not dependent on each other\n"
     ]
    }
   ],
   "source": [
    "if abs(stat) >= critical:\n",
    "    print('Dependent (reject H0)')\n",
    "else:\n",
    "    print('Independent (fail to reject H0) means Categorical Variables are not dependent on each other')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "significance=0.050, p=0.873\n"
     ]
    }
   ],
   "source": [
    "# interpret p-value\n",
    "alpha = 1.0 - prob\n",
    "print('significance=%.3f, p=%.3f' % (alpha, p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent (fail to reject H0)\n"
     ]
    }
   ],
   "source": [
    "if p <= alpha:\n",
    "    print('Dependent (reject H0)')\n",
    "else:\n",
    "    print('Independent (fail to reject H0)')"
   ]
  },
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   "execution_count": null,
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