Inferential Statistics/Inferential Statistics - IBM_HR_Analytics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inferential Statistics-IBM HR Analytics Employee Attrition & Performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
      ],
      "text/vnd.plotly.v1+html": [
       "<script type=\"text/javascript\">window.PlotlyConfig = {MathJaxConfig: 'local'};</script><script type=\"text/javascript\">if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}</script><script>requirejs.config({paths: { 'plotly': ['https://cdn.plot.ly/plotly-latest.min']},});if(!window._Plotly) {require(['plotly'],function(plotly) {window._Plotly=plotly;});}</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import libraries\n",
    "import numpy as np\n",
    "from numpy import median\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "from plotly import __version__\n",
    "from plotly import plotly\n",
    "from plotly.offline import download_plotlyjs, init_notebook_mode, plot, iplot\n",
    "import plotly.offline as py\n",
    "py.init_notebook_mode(connected=True)\n",
    "import plotly.graph_objs as go\n",
    "import plotly.tools as tls\n",
    "import plotly.figure_factory as ff\n",
    "\n",
    "# Import and suppress warnings\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read the file\n",
    "df = pd.read_csv('C:/users/eturk/Data_Science/Capstone_Project-IBM_HR_Analytics/data/HR-Employee-Attrition.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reassign response variable\n",
    "df['Attrition'] = df['Attrition'].apply(lambda x: 0 if x == 'No' else 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Drop useless features and rename the dataframe\n",
    "df2 = df.drop(labels = ['Over18','StandardHours','EmployeeCount'], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Moving Response Variable to the last column\n",
    "front = df2['Attrition']\n",
    "df2.drop(labels=['Attrition'], axis=1,inplace=True)\n",
    "df2.insert(31,'Attrition',front)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Changing object types to categories\n",
    "cols = ['BusinessTravel','Department','EducationField','Gender','JobRole','MaritalStatus','OverTime']\n",
    "for col in cols:\n",
    "    df2[col] = df2[col].astype('category')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hypothesis Testing (Examining Attrition in Gender throughout the company)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Selecting appropriate test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "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>Gender</th>\n",
       "      <th>Total Employee</th>\n",
       "      <th>Attrition Number</th>\n",
       "      <th>% of Attrition in the Relevant Group</th>\n",
       "      <th>% of Attrition in the Company</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Female</td>\n",
       "      <td>588</td>\n",
       "      <td>87</td>\n",
       "      <td>14.795918</td>\n",
       "      <td>36.708861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Male</td>\n",
       "      <td>882</td>\n",
       "      <td>150</td>\n",
       "      <td>17.006803</td>\n",
       "      <td>63.291139</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender  Total Employee   Attrition Number  \\\n",
       "0  Female              588                87   \n",
       "1    Male              882               150   \n",
       "\n",
       "   % of Attrition in the Relevant Group  % of Attrition in the Company  \n",
       "0                             14.795918                      36.708861  \n",
       "1                             17.006803                      63.291139  "
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Gender & Attrition Table\n",
    "table_df(x = 'Gender')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Attrition compared to Gender Graph\n",
    "graph_df(x = 'Gender')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the rate of attrition for two groups is compared, a two-proportion z-test is appropriate. Central Limit Theorem (CLT) states that regardless of the population, the distribution of sample averages tends to be normal. This holds for sample sizes greater than or equal to 30. Since the size of the data is big enough and 'female' and 'male' attrition  randomly to the resumes when presented to the employer, CLT could be applied here assuming that samples are respresentative of the population."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. The Null and Alternate Hypotheses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As observed above, it is obvious that male attrition is more than female's attrition but is the difference significant? Here is the important point to define the null and alternative hypothesis: \n",
    "\n",
    "In the context of provided information, the alternative hypothesis assumes that male attrition is pervasive enough to be a factor in attrition throughout the company.\n",
    "\n",
    "Null Hypothesis: There is no difference in the proportion of attrition for male and female employees in the company.\n",
    "\n",
    "$$H_0: \\hat p_{male\\_attrition} - \\hat p_{female\\_attrition} = 0$$\n",
    "\n",
    "Alternative Hypothesis: There is a significant difference in the proportion of attrition for male and female employees in the company.\n",
    "\n",
    "$$H_a: {\\hat p_{male\\_attrition}} - {\\hat p_{female\\_attrition}} \\neq 0$$\n",
    "Significance Level: 95% Confidence:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. The Frequentist Statistical Approach "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Female attrition mean: 0.14795918367346939\n",
      "Male attrition mean: 0.17006802721088435\n",
      "Difference of mean between male and female employees attrition: 0.022108843537414963\n"
     ]
    }
   ],
   "source": [
    "# Assign female and  male into variables\n",
    "female = df2[df2['Gender'] == 'Female']\n",
    "male = df2[df2['Gender'] == 'Male']\n",
    "\n",
    "# Find the mean for female and male employees attrition\n",
    "female_attrition_mean = female['Attrition'].mean()\n",
    "male_attrition_mean = male['Attrition'].mean()\n",
    "print ('Female attrition mean: {}'.format(female_attrition_mean))\n",
    "print ('Male attrition mean: {}'.format(male_attrition_mean))\n",
    "\n",
    "# Find the difference of female and male employees attrition\n",
    "diff_mean = male_attrition_mean - female_attrition_mean\n",
    "print ('Difference of mean between male and female employees attrition: {}'.format(diff_mean))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**z-score**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "z score:1.1292547809155016\n"
     ]
    }
   ],
   "source": [
    "# Compute z-score\n",
    "male_attrition = np.sum(male['Attrition'])\n",
    "female_attrition = np.sum(female['Attrition'])\n",
    "male_ln = len(male)\n",
    "female_ln = len(female)            \n",
    "phat = (male_attrition + female_attrition) / (male_ln + female_ln)\n",
    "z = (diff_mean) / np.sqrt(phat * (1 - phat) * (( 1/ float(male_ln)) + (1/float(female_ln))))\n",
    "print ('z score:{}'.format(z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**p-value**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value:0.2587903704911598\n"
     ]
    }
   ],
   "source": [
    "# Compute p-value\n",
    "p = stats.norm.cdf(-z)*2\n",
    "print ('p-value:{}'.format(p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Margin of error**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Margin of Error: 0.03837338930564671\n"
     ]
    }
   ],
   "source": [
    "# Compute margin of error\n",
    "moe = 1.96 * np.sqrt(phat * (1 - phat) * (( 1/ float(male_ln)) + (1/float(female_ln))))\n",
    "print(\"Margin of Error: {}\".format(moe))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Confidence Interval**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval: [-0.01626455  0.06048223]\n"
     ]
    }
   ],
   "source": [
    "# Compute confidence interval\n",
    "ci = diff_mean + np.array([-1, 1]) * moe\n",
    "print(\"Confidence interval: {}\".format(ci))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conclusion:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The p-value is above the significance level (0.05). So, I fail to reject the null hypothesis. We can conclude that there is no enough evidence to reject the assumption of no difference in the proportion of attrition for male and female employees in the company. "
   ]
  }
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