T-Tests_Types.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1-Sample T-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#To compare population mean and sample means if they are same or different\n",
    "\n",
    "#Null Hypothesis says that there is no difference in mean of a population and sample.\n",
    "#Alternate Hypothesis says there is difference in means of a population and sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import ttest_1samp,ttest_ind,norm,ttest_rel\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "ages=[10,20,35,50,28,40,55,18,16,55,30,25,43,18,30,28,14,24,16,17,32,35,26,27,65,18,43,23,21,20,19,70]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "population_mean=np.mean(ages)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.34375"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "population_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample_population=np.random.choice(ages,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([30, 23, 30, 65, 18, 24, 16, 20, 23, 20])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_population"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "26.9"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_mean=np.mean(sample_population)\n",
    "sample_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "one_sample_ttest,pvalue=ttest_1samp(sample_population,population_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.7694263435329401"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_sample_ttest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.46135557443352215"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accept Null Hypothesis.There is Difference in Means \n"
     ]
    }
   ],
   "source": [
    "if pvalue<=0.05:\n",
    "    print('Reject Null Hypothesis.No Difference in Means ')\n",
    "else:\n",
    "    print('Accept Null Hypothesis.There is Difference in Means ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2-Sample T-Test or Independent T-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#NULL Hypotheses      : Means of two groups are Not same\n",
    "#Alternate Hypotheses : Means of two groups are same"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#2 Sample T-test will compare two independent means of two features to validate if both are same or different "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "classA_Ages=np.random.randint(12,high=18,size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([17, 14, 12, 17, 13, 12, 15, 14, 13, 16])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classA_Ages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "classB_Ages=np.random.randint(12,high=18,size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([17, 15, 15, 14, 16, 16, 16, 13, 12, 13])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classB_Ages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "classA_Ages_mean=np.mean(classA_Ages)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "classB_Ages_mean=np.mean(classB_Ages)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.3"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classA_Ages_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14.7"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classB_Ages_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "two_sample_t_test_stats,p_val=ttest_ind(a=classA_Ages,b=classB_Ages,equal_var =False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5061894487315155"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_sample_t_test_stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6189904093635026"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Do Not Reject Null Hypothesis.Means are Not same\n"
     ]
    }
   ],
   "source": [
    "if p_val<=0.05:\n",
    "    print('Reject Null Hypothesis.Means are same')\n",
    "else:\n",
    "    print('Do Not Reject Null Hypothesis.Means are Not same')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Paired T-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#We go for paired t-test when we want to compare different means of same group taken at differnt time interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "weight1=[25,30,28,35,28,34,26,29,30,26,28,32,31,30,45]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "weight2=weight1 +norm.rvs(scale=5,loc=-1.25,size=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[25, 30, 28, 35, 28, 34, 26, 29, 30, 26, 28, 32, 31, 30, 45]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24.52960561, 23.83188231, 21.88564266, 31.57268761, 22.60292559,\n",
       "       31.20880647, 28.1443266 , 33.60569785, 20.80937386, 27.47027227,\n",
       "       31.49986073, 27.67681776, 27.90935884, 28.43787232, 39.15093676])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weight2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Data Frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights_df=pd.DataFrame({'weight1':np.array(weight1),\n",
    "                         'weight2':np.array(weight2),\n",
    "                         'weight_diff':np.array(weight2)-np.array(weight1)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>weight1</th>\n",
       "      <th>weight2</th>\n",
       "      <th>weight_diff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25</td>\n",
       "      <td>24.529606</td>\n",
       "      <td>-0.470394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30</td>\n",
       "      <td>23.831882</td>\n",
       "      <td>-6.168118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>28</td>\n",
       "      <td>21.885643</td>\n",
       "      <td>-6.114357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>35</td>\n",
       "      <td>31.572688</td>\n",
       "      <td>-3.427312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>28</td>\n",
       "      <td>22.602926</td>\n",
       "      <td>-5.397074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>34</td>\n",
       "      <td>31.208806</td>\n",
       "      <td>-2.791194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>26</td>\n",
       "      <td>28.144327</td>\n",
       "      <td>2.144327</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>29</td>\n",
       "      <td>33.605698</td>\n",
       "      <td>4.605698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>30</td>\n",
       "      <td>20.809374</td>\n",
       "      <td>-9.190626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>26</td>\n",
       "      <td>27.470272</td>\n",
       "      <td>1.470272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>28</td>\n",
       "      <td>31.499861</td>\n",
       "      <td>3.499861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>32</td>\n",
       "      <td>27.676818</td>\n",
       "      <td>-4.323182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>31</td>\n",
       "      <td>27.909359</td>\n",
       "      <td>-3.090641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>30</td>\n",
       "      <td>28.437872</td>\n",
       "      <td>-1.562128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>45</td>\n",
       "      <td>39.150937</td>\n",
       "      <td>-5.849063</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    weight1    weight2  weight_diff\n",
       "0        25  24.529606    -0.470394\n",
       "1        30  23.831882    -6.168118\n",
       "2        28  21.885643    -6.114357\n",
       "3        35  31.572688    -3.427312\n",
       "4        28  22.602926    -5.397074\n",
       "5        34  31.208806    -2.791194\n",
       "6        26  28.144327     2.144327\n",
       "7        29  33.605698     4.605698\n",
       "8        30  20.809374    -9.190626\n",
       "9        26  27.470272     1.470272\n",
       "10       28  31.499861     3.499861\n",
       "11       32  27.676818    -4.323182\n",
       "12       31  27.909359    -3.090641\n",
       "13       30  28.437872    -1.562128\n",
       "14       45  39.150937    -5.849063"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weights_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "stats,p_val=ttest_rel(a=weight1,b=weight2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.365145888204346"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03299626791354203"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reject Null Hypothesis.Means are same\n"
     ]
    }
   ],
   "source": [
    "if p_val<=0.05:\n",
    "    print('Reject Null Hypothesis.Means are same')\n",
    "else:\n",
    "    print('Do Not Reject Null Hypothesis.Means are Not same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}