GolfBall_Coating_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.stats import levene,shapiro,ttest_1samp,wilcoxon,mannwhitneyu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ds = pd.read_excel(\"SM4-Golf.xls\")"
   ]
  },
  {
   "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: 720.0 bytes\n"
     ]
    }
   ],
   "source": [
    "ds.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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",
       "      <th>0</th>\n",
       "      <td>264</td>\n",
       "      <td>277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>261</td>\n",
       "      <td>269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>267</td>\n",
       "      <td>263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>272</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>258</td>\n",
       "      <td>262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>283</td>\n",
       "      <td>251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>258</td>\n",
       "      <td>262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>266</td>\n",
       "      <td>289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>259</td>\n",
       "      <td>286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>270</td>\n",
       "      <td>264</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\n",
       "5      283  251\n",
       "6      258  262\n",
       "7      266  289\n",
       "8      259  286\n",
       "9      270  264"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(40, 2)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "current = ds['Current']\n",
    "new = ds['New']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean - Current 270.275\n",
      "Mean - New 267.5\n",
      "STD - Current 8.752984838884597\n",
      "STD - New 9.896904462947894\n",
      "Varience - Current 76.61474358974361\n",
      "Varience - New 97.94871794871794\n"
     ]
    }
   ],
   "source": [
    "print(\"Mean - Current\",current.mean())\n",
    "print(\"Mean - New\",new.mean())\n",
    "print(\"STD - Current\",current.std())\n",
    "print(\"STD - New\",new.std())\n",
    "print(\"Varience - Current\",current.var())\n",
    "print(\"Varience - New\",new.var())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### H0 : Mu0 - Mu1 = 0\n",
    "#### H1 : Mu0 - Mu1 != 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import ttest_ind\n",
    "t_Statistic, P_Value = ttest_ind(current,new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test _S tatistic, P_Value are  1.3283615935245678 0.18793228491854663\n"
     ]
    }
   ],
   "source": [
    "print(\"Test _S tatistic, P_Value are \",t_Statistic,P_Value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### as PValus is > 0.05, we accept null Hpothesis."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "for Parametric data, we shall use mannwhitneyu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_Statistic_man and P_Value_man are  668.0 0.10265192122893124\n"
     ]
    }
   ],
   "source": [
    "t_Statistic_man,P_Value_man = mannwhitneyu(current, new)\n",
    "print(\"t_Statistic_man and P_Value_man are \", t_Statistic_man,P_Value_man)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### as the PValue is > 0.05, we accept H0."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "To check the varience of the distribution, use Levene test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LeveneResult(statistic=0.2553238291765741, pvalue=0.6147759523331309)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "levene(current,new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### again as the P_Value is greater than 0.05, We accept the HO for Levene test. i.e., Varience are equal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### To analyse if the data is normally distributed or not, perform Shepiro test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9678263664245605, 0.3064655363559723)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9707046747207642, 0.378787100315094)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shapiro(current)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In both cases , we fail to reject null hypothesis saying data is normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3008146650775173\n"
     ]
    }
   ],
   "source": [
    "delta = (np.mean(current)-np.mean(new))/np.sqrt(((39*np.var(current))+(39*np.var(new)))/(40+40-2))\n",
    "print(delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.456522110415285\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.stats.power import ttest_power\n",
    "print(ttest_power(0.30,nobs=40,alpha=0.05,alternative = \"two-sided\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### 45% chance are there to reject the null hypothesis or H0 being false."
   ]
  }
 ],
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