Hypothesis Testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "86e69257",
   "metadata": {},
   "source": [
    "# Assignment-03-Q1 (Hypothesis Testing)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3efb4b20",
   "metadata": {
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     "end_time": "2021-08-27T15:45:51.752093Z",
     "start_time": "2021-08-27T15:45:51.736070Z"
    }
   },
   "source": [
    "Q1. A F&B manager wants to determine whether there is any significant difference in the diameter of the cutlet between two units. A randomly selected sample of cutlets was collected from both units and measured? Analyze the data and draw inferences at 5% significance level. Please state the assumptions and tests that you carried out to check validity of the assumptions.\n",
    "I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bf8d904c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:11.821976Z",
     "start_time": "2021-08-28T04:30:11.803354Z"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import scipy as sp\n",
    "from scipy import stats\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import chi2_contingency"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c23b4b80",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:12.100788Z",
     "start_time": "2021-08-28T04:30:11.824948Z"
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   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unit A</th>\n",
       "      <th>Unit B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.8090</td>\n",
       "      <td>6.7703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>6.4376</td>\n",
       "      <td>7.5093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6.9157</td>\n",
       "      <td>6.7300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.3012</td>\n",
       "      <td>6.7878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>7.4488</td>\n",
       "      <td>7.1522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7.3871</td>\n",
       "      <td>6.8110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6.8755</td>\n",
       "      <td>7.2212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7.0621</td>\n",
       "      <td>6.6606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>6.6840</td>\n",
       "      <td>7.2402</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>6.8236</td>\n",
       "      <td>7.0503</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unit A  Unit B\n",
       "0  6.8090  6.7703\n",
       "1  6.4376  7.5093\n",
       "2  6.9157  6.7300\n",
       "3  7.3012  6.7878\n",
       "4  7.4488  7.1522\n",
       "5  7.3871  6.8110\n",
       "6  6.8755  7.2212\n",
       "7  7.0621  6.6606\n",
       "8  6.6840  7.2402\n",
       "9  6.8236  7.0503"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the dataset\n",
    "data=pd.read_csv('Cutlets.csv')\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b50fb97f",
   "metadata": {},
   "source": [
    "Assume Null hyposthesis as Ho: μ1 = μ2 (There is no difference in diameters of cutlets between two units) Thus Alternate hypothesis as Ha: μ1 ≠ μ2 (There is significant difference in diameters of cutlets between two units) 2-Sample 2-Tail test applicable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "617e3bc7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:12.131776Z",
     "start_time": "2021-08-28T04:30:12.104728Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     6.8090\n",
       "1     6.4376\n",
       "2     6.9157\n",
       "3     7.3012\n",
       "4     7.4488\n",
       "5     7.3871\n",
       "6     6.8755\n",
       "7     7.0621\n",
       "8     6.6840\n",
       "9     6.8236\n",
       "10    7.3930\n",
       "11    7.5169\n",
       "12    6.9246\n",
       "13    6.9256\n",
       "14    6.5797\n",
       "15    6.8394\n",
       "16    6.5970\n",
       "17    7.2705\n",
       "18    7.2828\n",
       "19    7.3495\n",
       "20    6.9438\n",
       "21    7.1560\n",
       "22    6.5341\n",
       "23    7.2854\n",
       "24    6.9952\n",
       "25    6.8568\n",
       "26    7.2163\n",
       "27    6.6801\n",
       "28    6.9431\n",
       "29    7.0852\n",
       "30    6.7794\n",
       "31    7.2783\n",
       "32    7.1561\n",
       "33    7.3943\n",
       "34    6.9405\n",
       "Name: Unit A, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitA=pd.Series(data.iloc[:,0])\n",
    "unitA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0cac6cba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:12.301026Z",
     "start_time": "2021-08-28T04:30:12.134754Z"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     6.7703\n",
       "1     7.5093\n",
       "2     6.7300\n",
       "3     6.7878\n",
       "4     7.1522\n",
       "5     6.8110\n",
       "6     7.2212\n",
       "7     6.6606\n",
       "8     7.2402\n",
       "9     7.0503\n",
       "10    6.8810\n",
       "11    7.4059\n",
       "12    6.7652\n",
       "13    6.0380\n",
       "14    7.1581\n",
       "15    7.0240\n",
       "16    6.6672\n",
       "17    7.4314\n",
       "18    7.3070\n",
       "19    6.7478\n",
       "20    6.8889\n",
       "21    7.4220\n",
       "22    6.5217\n",
       "23    7.1688\n",
       "24    6.7594\n",
       "25    6.9399\n",
       "26    7.0133\n",
       "27    6.9182\n",
       "28    6.3346\n",
       "29    7.5459\n",
       "30    7.0992\n",
       "31    7.1180\n",
       "32    6.6965\n",
       "33    6.5780\n",
       "34    7.3875\n",
       "Name: Unit B, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unitB=pd.Series(data.iloc[:,1])\n",
    "unitB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8b89a323",
   "metadata": {
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     "end_time": "2021-08-28T04:30:12.592790Z",
     "start_time": "2021-08-28T04:30:12.304233Z"
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.7228688704678063, pvalue=0.4722394724599501)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2-sample 2-tail ttest:   stats.ttest_ind(array1,array2)     # ind -> independent samples\n",
    "p_value=stats.ttest_ind(unitA,unitB)\n",
    "p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "20915f19",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:12.730811Z",
     "start_time": "2021-08-28T04:30:12.595813Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4722394724599501"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value[1]     # 2-tail probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "6fbc3e44",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:12.838939Z",
     "start_time": "2021-08-28T04:30:12.736808Z"
    }
   },
   "outputs": [],
   "source": [
    "# compare p_value with α = 0.05 (At 5% significance level)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ced4fb1",
   "metadata": {},
   "source": [
    "Inference: As (p_value=0.4722) > (α = 0.05); Accept Null Hypothesis i.e. μ1 = μ2.\n",
    "Thus, there is no difference in diameters of cutlets between two units\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "860e238b",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6c618a37",
   "metadata": {},
   "source": [
    "# Assignment-03-Q2 (Hypothesis Testing)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b43e8061",
   "metadata": {},
   "source": [
    "Q2. A hospital wants to determine whether there is any difference in the average Turn Around Time (TAT) of reports of the laboratories on their preferred list. They collected a random sample and recorded TAT for reports of 4 laboratories. TAT is defined as sample collected to report dispatch. Analyze the data and determine whether there is any difference in average TAT among the different laboratories at 5% significance level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ff11ce65",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:13.007047Z",
     "start_time": "2021-08-28T04:30:12.843326Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Laboratory 1</th>\n",
       "      <th>Laboratory 2</th>\n",
       "      <th>Laboratory 3</th>\n",
       "      <th>Laboratory 4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>185.35</td>\n",
       "      <td>165.53</td>\n",
       "      <td>176.70</td>\n",
       "      <td>166.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>170.49</td>\n",
       "      <td>185.91</td>\n",
       "      <td>198.45</td>\n",
       "      <td>160.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>192.77</td>\n",
       "      <td>194.92</td>\n",
       "      <td>201.23</td>\n",
       "      <td>185.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>177.33</td>\n",
       "      <td>183.00</td>\n",
       "      <td>199.61</td>\n",
       "      <td>176.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>193.41</td>\n",
       "      <td>169.57</td>\n",
       "      <td>204.63</td>\n",
       "      <td>152.60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>179.45</td>\n",
       "      <td>197.00</td>\n",
       "      <td>181.51</td>\n",
       "      <td>161.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>191.37</td>\n",
       "      <td>166.36</td>\n",
       "      <td>214.21</td>\n",
       "      <td>154.02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>166.81</td>\n",
       "      <td>169.60</td>\n",
       "      <td>183.43</td>\n",
       "      <td>163.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>158.81</td>\n",
       "      <td>175.36</td>\n",
       "      <td>191.60</td>\n",
       "      <td>152.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>165.88</td>\n",
       "      <td>198.68</td>\n",
       "      <td>208.43</td>\n",
       "      <td>161.98</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Laboratory 1  Laboratory 2  Laboratory 3  Laboratory 4\n",
       "0        185.35        165.53        176.70        166.13\n",
       "1        170.49        185.91        198.45        160.79\n",
       "2        192.77        194.92        201.23        185.18\n",
       "3        177.33        183.00        199.61        176.42\n",
       "4        193.41        169.57        204.63        152.60\n",
       "5        179.45        197.00        181.51        161.12\n",
       "6        191.37        166.36        214.21        154.02\n",
       "7        166.81        169.60        183.43        163.25\n",
       "8        158.81        175.36        191.60        152.79\n",
       "9        165.88        198.68        208.43        161.98"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the dataset\n",
    "data=pd.read_csv('LabTAT.csv')\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e148c7fb",
   "metadata": {},
   "source": [
    "Anova ftest statistics: Analysis of varaince between more than 2 samples or columns. Assume Null Hypothesis Ho as No Varaince: All samples TAT population means are same. Thus Alternate Hypothesis Ha as It has Variance: Atleast one sample TAT population mean is different"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6f3306a2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:13.162893Z",
     "start_time": "2021-08-28T04:30:13.009044Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=118.70421654401437, pvalue=2.1156708949992414e-57)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Anova ftest statistics: stats.f_oneway(column-1,column-2,column-3,column-4)\n",
    "p_value=stats.f_oneway(data.iloc[:,0],data.iloc[:,1],data.iloc[:,2],data.iloc[:,3])\n",
    "p_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c625379c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:13.272236Z",
     "start_time": "2021-08-28T04:30:13.166849Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1156708949992414e-57"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_value[1]  # compare it with α = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaf4de7d",
   "metadata": {},
   "source": [
    "Inference: As (p-value=0) < (α = 0.05); Reject Null Hypothesis i.e. Atleast one sample TAT population mean is different Thus there is variance or difference in average Turn Around Time (TAT) of reports of the laboratories on their preferred list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c821762",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "b0c634c5",
   "metadata": {},
   "source": [
    "# Assignment-03-Q3 (Hypothesis Testing)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be66d347",
   "metadata": {},
   "source": [
    "Sales of products in four different regions is tabulated for males and females. Find if male-female buyer rations are similar across regions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e502be48",
   "metadata": {},
   "source": [
    "Assume Null Hypothesis as Ho: Independence of categorical variables (male-female buyer rations are similar across regions (does not vary and are not related) Thus Alternate Hypothesis as Ha: Dependence of categorical variables (male-female buyer rations are NOT similar across regions (does vary and somewhat/significantly related)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e36c500b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:13.461913Z",
     "start_time": "2021-08-28T04:30:13.276215Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Observed Values</th>\n",
       "      <th>East</th>\n",
       "      <th>West</th>\n",
       "      <th>North</th>\n",
       "      <th>South</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Males</td>\n",
       "      <td>50</td>\n",
       "      <td>142</td>\n",
       "      <td>131</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Females</td>\n",
       "      <td>435</td>\n",
       "      <td>1523</td>\n",
       "      <td>1356</td>\n",
       "      <td>750</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Observed Values  East  West  North  South\n",
       "0           Males    50   142    131     70\n",
       "1         Females   435  1523   1356    750"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the dataset\n",
    "data=pd.read_csv('BuyerRatio.csv')\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e39d3c82",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:13.555012Z",
     "start_time": "2021-08-28T04:30:13.464912Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  50,  142,  131,   70],\n",
       "       [ 435, 1523, 1356,  750]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make dimensional array\n",
    "obs=np.array([[50,142,131,70],[435,1523,1356,750]])\n",
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7ecccdfe",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:13.679672Z",
     "start_time": "2021-08-28T04:30:13.559008Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.595945538661058,\n",
       " 0.6603094907091882,\n",
       " 3,\n",
       " array([[  42.76531299,  146.81287862,  131.11756787,   72.30424052],\n",
       "        [ 442.23468701, 1518.18712138, 1355.88243213,  747.69575948]]))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Chi2 contengency independence test\n",
    "chi2_contingency(obs) # o/p is (Chi2 stats value, p_value, df, expected obsvations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c29ded5a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:13.820094Z",
     "start_time": "2021-08-28T04:30:13.684648Z"
    }
   },
   "outputs": [],
   "source": [
    "# Compare p_value with α = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daff9c99",
   "metadata": {},
   "source": [
    "Inference: As (p-value = 0.6603) > (α = 0.05); Accept the Null Hypothesis i.e. Independence of categorical variables Thus, male-female buyer rations are similar across regions and are not related"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a36a6827",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "65386ca7",
   "metadata": {},
   "source": [
    "# Assignment-03-Q4 (Hypothesis Testing)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c8f7dca",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-27T16:14:13.611736Z",
     "start_time": "2021-08-27T16:14:13.594725Z"
    }
   },
   "source": [
    "Q4. TeleCall uses 4 centers around the globe to process customer order forms. They audit a certain % of the customer order forms. Any error in order form renders it defective and has to be reworked before processing. The manager wants to check whether the defective % varies by centre. Please analyze the data at 5% significance level and help the manager draw appropriate inferences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "91b25eab",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:14.021968Z",
     "start_time": "2021-08-28T04:30:13.824089Z"
    }
   },
   "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>Phillippines</th>\n",
       "      <th>Indonesia</th>\n",
       "      <th>Malta</th>\n",
       "      <th>India</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>295</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>296</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>297</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>298</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299</th>\n",
       "      <td>Error Free</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Defective</td>\n",
       "      <td>Error Free</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>300 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Phillippines   Indonesia       Malta       India\n",
       "0     Error Free  Error Free   Defective  Error Free\n",
       "1     Error Free  Error Free  Error Free   Defective\n",
       "2     Error Free   Defective   Defective  Error Free\n",
       "3     Error Free  Error Free  Error Free  Error Free\n",
       "4     Error Free  Error Free   Defective  Error Free\n",
       "..           ...         ...         ...         ...\n",
       "295   Error Free  Error Free  Error Free  Error Free\n",
       "296   Error Free  Error Free  Error Free  Error Free\n",
       "297   Error Free  Error Free   Defective  Error Free\n",
       "298   Error Free  Error Free  Error Free  Error Free\n",
       "299   Error Free   Defective   Defective  Error Free\n",
       "\n",
       "[300 rows x 4 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=pd.read_csv('Costomer+OrderForm.csv')\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "47dc3613",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:14.225342Z",
     "start_time": "2021-08-28T04:30:14.025967Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    271\n",
       "Defective      29\n",
       "Name: Phillippines, dtype: int64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Phillippines.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "205dcd62",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:14.381720Z",
     "start_time": "2021-08-28T04:30:14.228341Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    267\n",
       "Defective      33\n",
       "Name: Indonesia, dtype: int64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Indonesia.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "36885632",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:14.535389Z",
     "start_time": "2021-08-28T04:30:14.404760Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    269\n",
       "Defective      31\n",
       "Name: Malta, dtype: int64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Malta.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8ef77a2b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:14.737668Z",
     "start_time": "2021-08-28T04:30:14.542390Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Error Free    280\n",
       "Defective      20\n",
       "Name: India, dtype: int64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.India.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2a8656c4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:14.910188Z",
     "start_time": "2021-08-28T04:30:14.749657Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[271, 267, 269, 280],\n",
       "       [ 29,  33,  31,  20]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make a contingency table\n",
    "obs=np.array([[271,267,269,280],[29,33,31,20]])\n",
    "obs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12225954",
   "metadata": {},
   "source": [
    "Assume Null Hypothesis as Ho: Independence of categorical variables (customer order forms defective % does not varies by centre) Thus, Alternative hypothesis as Ha Dependence of categorical variables (customer order forms defective % varies by centre)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "dc1cbcbf",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:15.095395Z",
     "start_time": "2021-08-28T04:30:14.913167Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.858960685820355,\n",
       " 0.2771020991233135,\n",
       " 3,\n",
       " array([[271.75, 271.75, 271.75, 271.75],\n",
       "        [ 28.25,  28.25,  28.25,  28.25]]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Chi2 contengency independence test\n",
    "chi2_contingency(obs) # o/p is (Chi2 stats value, p_value, df, expected obsvations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "8ca8b7be",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-28T04:30:15.310524Z",
     "start_time": "2021-08-28T04:30:15.098397Z"
    }
   },
   "outputs": [],
   "source": [
    "# Compare p_value with α = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a48c55d2",
   "metadata": {},
   "source": [
    "Inference: As (p_value = 0.2771) > (α = 0.05); Accept Null Hypthesis i.e. Independence of categorical variables Thus, customer order forms defective % does not varies by centre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2daa6bfa",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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