Hypothesis Testing Par Inc. Golf Equipment Manufacturer .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.Import the Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import the libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "import scipy\n",
    "from scipy.stats import ttest_1samp,ttest_ind,mannwhitneyu,levene,shapiro,wilcoxon\n",
    "from statsmodels.stats.power import ttest_power\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.Load the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load the dataset\n",
    "\n",
    "mydata=pd.read_excel('SM4-Golf.xls',sheet_name='Data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.Descriptive Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>Current</th>\n",
       "      <th>New</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>264</td>\n",
       "      <td>277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>261</td>\n",
       "      <td>269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>267</td>\n",
       "      <td>263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>272</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>258</td>\n",
       "      <td>262</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Current  New\n",
       "0      264  277\n",
       "1      261  269\n",
       "2      267  263\n",
       "3      272  266\n",
       "4      258  262"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To show the top 5 rows of dataset\n",
    "\n",
    "mydata.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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>Current</th>\n",
       "      <th>New</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>count</td>\n",
       "      <td>40.000000</td>\n",
       "      <td>40.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>mean</td>\n",
       "      <td>270.275000</td>\n",
       "      <td>267.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>std</td>\n",
       "      <td>8.752985</td>\n",
       "      <td>9.896904</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>min</td>\n",
       "      <td>255.000000</td>\n",
       "      <td>250.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25%</td>\n",
       "      <td>263.000000</td>\n",
       "      <td>262.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50%</td>\n",
       "      <td>270.000000</td>\n",
       "      <td>265.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>75%</td>\n",
       "      <td>275.250000</td>\n",
       "      <td>274.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>max</td>\n",
       "      <td>289.000000</td>\n",
       "      <td>289.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Current         New\n",
       "count   40.000000   40.000000\n",
       "mean   270.275000  267.500000\n",
       "std      8.752985    9.896904\n",
       "min    255.000000  250.000000\n",
       "25%    263.000000  262.000000\n",
       "50%    270.000000  265.000000\n",
       "75%    275.250000  274.500000\n",
       "max    289.000000  289.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To get the basic statistical summary of data\n",
    "\n",
    "mydata.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* It shows that mean and median of the two columns 'Current' and 'New' are very close.\n",
    "\n",
    "* The standard deviations also have no significant change. Hence, data is normally distributed.\n",
    "\n",
    "* There is dip in the performance of Current and New balls driving force as mean, median, min values differ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 40 entries, 0 to 39\n",
      "Data columns (total 2 columns):\n",
      "Current    40 non-null int64\n",
      "New        40 non-null int64\n",
      "dtypes: int64(2)\n",
      "memory usage: 768.0 bytes\n"
     ]
    }
   ],
   "source": [
    "## To show the detailed summary \n",
    "\n",
    "mydata.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* There are 40 values in the dataset. There are 2 columns Current and New .\n",
    "\n",
    "* Both have non-null values.There is no missing values in the dataset.\n",
    "\n",
    "* Both variables are integer types.The memory usage is 720 bytes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1f983b9ba20>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax2 = plt.subplots(2,2, figsize=(10, 8))\n",
    "mydata['Current'].hist(ax=ax2[0][0])\n",
    "mydata['New'].hist(ax=ax2[0][1])\n",
    "sns.boxplot(mydata['Current'],ax=ax2[1][0])\n",
    "sns.boxplot(mydata['New'],ax=ax2[1][1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The histogram of both vaiable 'Current' and 'New' are nearly normally distributed.\n",
    "\n",
    "* 'Current' is little bit left skewed.\n",
    "\n",
    "* 'New' is right skewed.\n",
    "\n",
    "* Boxplot of both variables show that there are no outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1f984ea07f0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax2 = plt.subplots(1, 2)\n",
    "sns.distplot(mydata['Current'],ax=ax2[0])\n",
    "sns.distplot(mydata['New'],ax=ax2[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4.Hypothesis Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The sample size is n=40. As the sample size is greater than 30 we will go for Z test. But the population standard deviation (Sigma) is unknown, Therefore, we have to use T test.\n",
    "\n",
    "* Assume the significance level (Alpha)=0.05.\n",
    "\n",
    "* To compare the driving distances of of the Current and New golf balls, we use Two tailed t test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Formulation of Hypothesis\n",
    "\n",
    "Here we use two tailed independent t test\n",
    "\n",
    "* **Null Hypothesis** \n",
    "\n",
    "$\n",
    "H_{0}:{\\mu_{1}}-{\\mu_{2}}=0\n",
    "$\n",
    "It means there is no significant change in the driving distances of the current and new golf balls.\n",
    "\n",
    "* **Alternate Hypothesis** \n",
    "\n",
    "$\n",
    "H_{a}:{\\mu_{1}}-{\\mu_{2}} {\\not=} 0\n",
    "$\n",
    "It means there is a significant change in the driving distances of the current and new golf balls."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Levene Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=0.2553238291765741, pvalue=0.6147759523331309)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "levene(mydata['Current'],mydata['New'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "p_value indicate null hypothesis should not be rejected.The null hypothesis of levene test is that the variances are equal.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shapiro Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9707046747207642, 0.378787100315094)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(mydata['Current'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9678263664245605, 0.3064655363559723)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(mydata['New'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The p value greater than 0.5 hence,the normality assumptions for each variable are fulfilled successfully."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Two tailed Two sample independent t-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-statistics= 1.3283615935245678 p_value= 0.18793228491854663\n"
     ]
    }
   ],
   "source": [
    "t_statistics,p_value=ttest_ind(mydata['Current'],mydata['New'])\n",
    "print('t-statistics=',t_statistics,'p_value=',p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Here the p_value is 0.1879 which is greater than the 0.05.Therefore, we failed to reject the Null Hypothesis.\n",
    "\n",
    "* It means there is no significant change in the driving distances of the current and new golf balls.\n",
    "\n",
    "* Hence, the new balls might not be preffered by the management rather than the old ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Current mean= 270.275\n",
      "New mean= 267.5\n"
     ]
    }
   ],
   "source": [
    "print('Current mean=',mydata['Current'].mean())\n",
    "print('New mean=',mydata['New'].mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**One Sample t-test for Current**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The t-statistic is 195.290\n",
      "The p_value is 6.087391701390452e-60\n"
     ]
    }
   ],
   "source": [
    "t_statistics,p_value=ttest_1samp(mydata['Current'],0)\n",
    "print('The t-statistic is %.3f'% t_statistics)\n",
    "print('The p_value is', p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 95% confidence interval for Current balls driving distance mean is 267.47661585316285 to 273.0733841468371\n"
     ]
    }
   ],
   "source": [
    "tstat=-2.022\n",
    "mu=mydata['Current'].mean()\n",
    "s=mydata['Current'].std()\n",
    "n=mydata['Current'].count()\n",
    "xbar1=tstat*(s/np.sqrt(n))+mu\n",
    "tstat=2.022\n",
    "mu=mydata['Current'].mean()\n",
    "s=mydata['Current'].std()\n",
    "n=mydata['Current'].count()\n",
    "xbar2=tstat*(s/np.sqrt(n))+mu\n",
    "\n",
    "print(\"The 95% confidence interval for Current balls driving distance mean is \" ,xbar1, \" to \", xbar2, sep=\"\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**One Sample t-test for New**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 95% confidence interval for NEw balls driving distance mean is 264.3358975753231 to 270.6641024246769\n"
     ]
    }
   ],
   "source": [
    "tstat=-2.022\n",
    "mu=mydata['New'].mean()\n",
    "s=mydata['New'].std()\n",
    "n=mydata['New'].count()\n",
    "xbar1=tstat*(s/np.sqrt(n))+mu\n",
    "tstat=2.022\n",
    "mu=mydata['New'].mean()\n",
    "s=mydata['New'].std()\n",
    "n=mydata['New'].count()\n",
    "xbar2=tstat*(s/np.sqrt(n))+mu\n",
    "print(\"The 95% confidence interval for NEw balls driving distance mean is \" ,xbar1, \" to \", xbar2, sep=\"\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "170.9442133673136 1.0890371893600406e-57\n"
     ]
    }
   ],
   "source": [
    "t_statistics,p_value=ttest_1samp(mydata['New'],0)\n",
    "print(t_statistics,p_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_statistics,p_value=ttest_1samp(mydata['New']-mydata['Current'],0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.2769699827911767 0.20916361823147053\n"
     ]
    }
   ],
   "source": [
    "print(t_statistics,p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5.Pooled Standard Deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Std Deviation of Current golf and New golf sample size\n",
    "\n",
    "std_current = np.std(mydata['Current'])\n",
    "std_new = np.std(mydata['New'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Pooled Standard Deviation is: 9.225\n"
     ]
    }
   ],
   "source": [
    "# Calculating Pooled Standard Deviation\n",
    "pooled_std = math.sqrt(((std_current*std_current)+(std_new*std_new))/(2))\n",
    "print (\"The Pooled Standard Deviation is: %.3f\" %pooled_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. Power of the Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating a function\n",
    "def sample_power_difftest(d,s,power=0.8,sig=0.05):\n",
    "    z = scipy.stats.norm.isf([sig/2])\n",
    "    zp = -1 * scipy.stats.norm.isf([power])\n",
    "    n = (2*(s**2)) * ((zp+z)**2) / (d**2)\n",
    "    return int(round(n[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Mean of Current golf and New golf sample size\n",
    "mean_current=np.mean(mydata['Current'])\n",
    "mean_new=np.mean(mydata['New'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.7749999999999773\n"
     ]
    }
   ],
   "source": [
    "d = mean_current - mean_new\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total Number of Observations:  51\n"
     ]
    }
   ],
   "source": [
    "n=sample_power_difftest(d,pooled_std,power=0.8,sig=0.5)\n",
    "print(\"total Number of Observations: \", n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* It gives the ideal sample size of the two data variables.\n",
    "* We can find the optimal number of observations required for a dataset.\n",
    "* We require the number of oberservations 51 to get a power of 80%. The number of observation we have is 40 which is not sufficient to obtain the power of 80%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7.Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The new golf ball will not be introduced to the market.\n",
    "\n",
    "* There is no significance difference in driving distance of the Current and New golf balls.\n",
    "\n",
    "* It is better to conduct test with larger sample size to improve the accuracy of the test results.\n",
    "\n",
    "* It is also good to interpret other characteristics of the golf balls like size, shape etc."
   ]
  }
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