Case Study #04 - Testing of Hypothesis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "85473de8",
   "metadata": {},
   "source": [
    "Case Study #04 - Testing of Hypothesis by Jayaram K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aba1a975",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing necessary libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "30d09063",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read the data to Python environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1a242cc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('Sales_add.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1ac93ee8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# To check first 5 rows of Data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "aa081609",
   "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>Month</th>\n",
       "      <th>Region</th>\n",
       "      <th>Manager</th>\n",
       "      <th>Sales_before_digital_add(in $)</th>\n",
       "      <th>Sales_After_digital_add(in $)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Month-1</td>\n",
       "      <td>Region - A</td>\n",
       "      <td>Manager - A</td>\n",
       "      <td>132921</td>\n",
       "      <td>270390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Month-2</td>\n",
       "      <td>Region - A</td>\n",
       "      <td>Manager - C</td>\n",
       "      <td>149559</td>\n",
       "      <td>223334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Month-3</td>\n",
       "      <td>Region - B</td>\n",
       "      <td>Manager - A</td>\n",
       "      <td>146278</td>\n",
       "      <td>244243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Month-4</td>\n",
       "      <td>Region - B</td>\n",
       "      <td>Manager - B</td>\n",
       "      <td>152167</td>\n",
       "      <td>231808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Month-5</td>\n",
       "      <td>Region - C</td>\n",
       "      <td>Manager - B</td>\n",
       "      <td>159525</td>\n",
       "      <td>258402</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Month      Region      Manager  Sales_before_digital_add(in $)  \\\n",
       "0  Month-1  Region - A  Manager - A                          132921   \n",
       "1  Month-2  Region - A  Manager - C                          149559   \n",
       "2  Month-3  Region - B  Manager - A                          146278   \n",
       "3  Month-4  Region - B  Manager - B                          152167   \n",
       "4  Month-5  Region - C  Manager - B                          159525   \n",
       "\n",
       "   Sales_After_digital_add(in $)  \n",
       "0                         270390  \n",
       "1                         223334  \n",
       "2                         244243  \n",
       "3                         231808  \n",
       "4                         258402  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "15d38383",
   "metadata": {},
   "outputs": [],
   "source": [
    "# To check any null values present in the Data frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7d66f23e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Month                             0\n",
       "Region                            0\n",
       "Manager                           0\n",
       "Sales_before_digital_add(in $)    0\n",
       "Sales_After_digital_add(in $)     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.isna().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "999a1c2d",
   "metadata": {},
   "source": [
    "- No Null Values present in the data. We can continue with the same Data for calculations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8eb96e32",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "929c9b93",
   "metadata": {},
   "source": [
    "# 1. The company wishes to clarify whether there is any increase in sales after stepping into digital marketing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92625c1c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "fa6d0541",
   "metadata": {},
   "source": [
    "We can use Hypothesis testing to check whether two groups are different from one another. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c2ce2db4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating a new DataFrame with only necessary columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "496459ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "sale_add = data[['Sales_before_digital_add(in $)','Sales_After_digital_add(in $)']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06c0a3bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check the data using a histograms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "f3c6a6c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10,5))   \n",
    "plt.subplot(1,2,1)\n",
    "plt.hist(sale_add['Sales_before_digital_add(in $)']) \n",
    "plt.title('Sales Before digital marketing',fontsize = 16)\n",
    "plt.xlabel('Sales (in $)')\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.hist(sale_add['Sales_After_digital_add(in $)']) \n",
    "plt.title('Sales After digital marketing',fontsize = 16)\n",
    "plt.xlabel('Sales (in $)')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bdedb24",
   "metadata": {},
   "source": [
    "- The data seems to be normally distributed. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "945cdc6e",
   "metadata": {},
   "source": [
    "Step 1. Define Hypothesis: "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "647fc0f5",
   "metadata": {},
   "source": [
    "**Null hypothesis, H<sub>0</sub>:** Sales Before digital marketing >= Sales After digital marketing  \n",
    "**Alternative hypothesis, H<sub>a</sub>:** Sales Before digital marketing < Sales After digital marketing  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bde88aef",
   "metadata": {},
   "source": [
    "Step 2. Set significance level(alpha value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "83828051",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac315eba",
   "metadata": {},
   "source": [
    "- The level of significance in hypothesis testing indicates if a statistical result could have significance if the null hypothesis stands to be true."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2400c016",
   "metadata": {},
   "source": [
    "Step 3. Identify Test Statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "33922ad4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06f634f6",
   "metadata": {},
   "source": [
    "- Here sample size is less than 30. So, we are going to use T-test."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "271ceda9",
   "metadata": {},
   "source": [
    "Step 4.  Determine P-Value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4d1bc535",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = sale_add['Sales_before_digital_add(in $)']\n",
    "b = sale_add['Sales_After_digital_add(in $)']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "41635cc3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use scipy.stats.ttest_rel() function which Calculate the t-test on Two Related variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "81ee3208",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-Value is: 3.168333502287889e-11\n"
     ]
    }
   ],
   "source": [
    "t_score,p_value = stats.ttest_rel(b,a,alternative='greater') \n",
    "print('P-Value is:',p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2fd2a24",
   "metadata": {},
   "source": [
    "Step 5. Comparing P-Value and Significance level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "b670daf1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reject null hypothesis, that means, There is a increase in Sales after digital add\n"
     ]
    }
   ],
   "source": [
    "if p_value <= alpha:\n",
    "    print('Reject null hypothesis, that means, There is a increase in Sales after digital add')\n",
    "else:\n",
    "    print('Accept null hypothesis, that means, There is no increase in Sales after digital add')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2eecc9a",
   "metadata": {},
   "source": [
    "- So, with the help of Hypothesis testing, we assume that there is a significant effect on the Sales after implementing digital advertisement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "02f90cd7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "8f213a11",
   "metadata": {},
   "source": [
    "# 2. The company needs to check whether there is any dependency between the features “Region” and “Manager”."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d98fff5e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "b887e225",
   "metadata": {},
   "source": [
    "We can use Hypothesis testing to determine whether two variables are likely to be related or not(any dependency)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4f02acf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Check the columns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "18871654",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Region:\n",
      " ['Region - A' 'Region - B' 'Region - C']\n",
      "\n",
      "Manager:\n",
      " ['Manager - A' 'Manager - C' 'Manager - B']\n"
     ]
    }
   ],
   "source": [
    "print('Region:\\n',data[\"Region\"].unique())\n",
    "print('\\nManager:\\n',data[\"Manager\"].unique())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb294f50",
   "metadata": {},
   "source": [
    "- We see that features “Region” and “Manager” are two categorical variables, so we can use the Chi-square test of independence to check the independence of variables.  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9829149",
   "metadata": {},
   "source": [
    "Step 1. Define Hypothesis:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caef7fe7",
   "metadata": {},
   "source": [
    "**Null hypothesis, H<sub>0</sub>:** There is no relationship between the features Region and Manager(or Independent)  \n",
    "**Alternative hypothesis, H<sub>a</sub>:** There is a relationship between the features Region and Manager(or Dependent)  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "182f15d4",
   "metadata": {},
   "source": [
    "Step 2. Set significance level(alpha value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "b5109de4",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = .05"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bfc20c7",
   "metadata": {},
   "source": [
    "Step 3. Create a contigency table from the categorical data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "a9d357e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Contingency Table :\n",
      " Manager     Manager - A  Manager - B  Manager - C\n",
      "Region                                           \n",
      "Region - A            4            3            3\n",
      "Region - B            4            1            2\n",
      "Region - C            1            3            1\n"
     ]
    }
   ],
   "source": [
    "contingency_table=pd.crosstab(data[\"Region\"],data[\"Manager\"])\n",
    "print('Contingency Table :\\n',contingency_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "3e09baa5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Take the values from the contingency table and define it as our observed data for calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "88b1b83d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observed Values :\n",
      " [[4 3 3]\n",
      " [4 1 2]\n",
      " [1 3 1]]\n"
     ]
    }
   ],
   "source": [
    "Observed_Values = contingency_table.values \n",
    "print(\"Observed Values :\\n\",Observed_Values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6b8760a",
   "metadata": {},
   "source": [
    "Step 4. Determine P-Value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bf76831e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use scipy.stats.chi2_contingency() function which computes Chi-square test of independence of variables in a contingency table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "8ba96af0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P-Value is 0.5493991051158094\n"
     ]
    }
   ],
   "source": [
    "stat, p, dof, expected = chi2_contingency(Observed_Values)\n",
    "print(\"P-Value is\",p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdd4e648",
   "metadata": {},
   "source": [
    "Step 5. Comparing P-Value and Significance level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "856913e7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Independent :H0 holds true, There is no relationship between the features “Region” and “Manager”)\n"
     ]
    }
   ],
   "source": [
    "if p <= alpha:\n",
    "    print('Dependent :Reject H0, There is a relationship between the features “Region” and “Manager”')\n",
    "else:\n",
    "    print('Independent :H0 holds true, There is no relationship between the features “Region” and “Manager”)')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35498914",
   "metadata": {},
   "source": [
    "- So, with the help of Chi-square test of independence, we assume that there is no dependency between Region and Manager."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ca643ebe",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "1bc0d022",
   "metadata": {},
   "source": [
    "Thank You."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c9c527f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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