12.6.1.Z-test와 T-test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 필요한 패키지 설치\n",
    "\n",
    "from scipy.stats import shapiro\n",
    "from statsmodels.stats.weightstats import ztest as ztest\n",
    "import scipy.stats\n",
    "from scipy import stats\n",
    "from scipy.stats import ttest_ind\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams['figure.dpi'] = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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>TypeA_before</th>\n",
       "      <th>TypeA_after</th>\n",
       "      <th>TypeB_before</th>\n",
       "      <th>TypeB_after</th>\n",
       "      <th>TypeC_before</th>\n",
       "      <th>TypeC_after</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>277</td>\n",
       "      <td>264</td>\n",
       "      <td>265</td>\n",
       "      <td>268</td>\n",
       "      <td>267</td>\n",
       "      <td>268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>269</td>\n",
       "      <td>261</td>\n",
       "      <td>264</td>\n",
       "      <td>267</td>\n",
       "      <td>264</td>\n",
       "      <td>269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>263</td>\n",
       "      <td>267</td>\n",
       "      <td>269</td>\n",
       "      <td>272</td>\n",
       "      <td>283</td>\n",
       "      <td>283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>266</td>\n",
       "      <td>272</td>\n",
       "      <td>274</td>\n",
       "      <td>277</td>\n",
       "      <td>287</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>262</td>\n",
       "      <td>258</td>\n",
       "      <td>261</td>\n",
       "      <td>264</td>\n",
       "      <td>275</td>\n",
       "      <td>266</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   TypeA_before  TypeA_after  TypeB_before  TypeB_after  TypeC_before  \\\n",
       "0           277          264           265          268           267   \n",
       "1           269          261           264          267           264   \n",
       "2           263          267           269          272           283   \n",
       "3           266          272           274          277           287   \n",
       "4           262          258           261          264           275   \n",
       "\n",
       "   TypeC_after  \n",
       "0          268  \n",
       "1          269  \n",
       "2          283  \n",
       "3          266  \n",
       "4          266  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 데이터 불러오기\n",
    "# https://www.kaggle.com/datasets/sewonghwang/golf-ball-testing\n",
    "df = pd.read_csv(\"datasets/Golf_test.csv\")\n",
    "\n",
    "# 데이터 샘플 확인\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>TypeA_before</th>\n",
       "      <th>TypeA_after</th>\n",
       "      <th>TypeB_before</th>\n",
       "      <th>TypeB_after</th>\n",
       "      <th>TypeC_before</th>\n",
       "      <th>TypeC_after</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>268.460000</td>\n",
       "      <td>270.720000</td>\n",
       "      <td>273.600000</td>\n",
       "      <td>276.100000</td>\n",
       "      <td>270.360000</td>\n",
       "      <td>271.040000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>9.817124</td>\n",
       "      <td>8.487782</td>\n",
       "      <td>8.566665</td>\n",
       "      <td>8.493094</td>\n",
       "      <td>8.385507</td>\n",
       "      <td>9.437139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>250.000000</td>\n",
       "      <td>255.000000</td>\n",
       "      <td>258.000000</td>\n",
       "      <td>261.000000</td>\n",
       "      <td>255.000000</td>\n",
       "      <td>253.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>262.000000</td>\n",
       "      <td>264.000000</td>\n",
       "      <td>266.250000</td>\n",
       "      <td>269.000000</td>\n",
       "      <td>263.250000</td>\n",
       "      <td>265.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>266.000000</td>\n",
       "      <td>271.000000</td>\n",
       "      <td>273.500000</td>\n",
       "      <td>276.500000</td>\n",
       "      <td>268.500000</td>\n",
       "      <td>268.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>275.750000</td>\n",
       "      <td>275.000000</td>\n",
       "      <td>278.000000</td>\n",
       "      <td>280.000000</td>\n",
       "      <td>275.750000</td>\n",
       "      <td>277.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>289.000000</td>\n",
       "      <td>289.000000</td>\n",
       "      <td>292.000000</td>\n",
       "      <td>295.000000</td>\n",
       "      <td>289.000000</td>\n",
       "      <td>291.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       TypeA_before  TypeA_after  TypeB_before  TypeB_after  TypeC_before  \\\n",
       "count     50.000000    50.000000     50.000000    50.000000     50.000000   \n",
       "mean     268.460000   270.720000    273.600000   276.100000    270.360000   \n",
       "std        9.817124     8.487782      8.566665     8.493094      8.385507   \n",
       "min      250.000000   255.000000    258.000000   261.000000    255.000000   \n",
       "25%      262.000000   264.000000    266.250000   269.000000    263.250000   \n",
       "50%      266.000000   271.000000    273.500000   276.500000    268.500000   \n",
       "75%      275.750000   275.000000    278.000000   280.000000    275.750000   \n",
       "max      289.000000   289.000000    292.000000   295.000000    289.000000   \n",
       "\n",
       "       TypeC_after  \n",
       "count    50.000000  \n",
       "mean    271.040000  \n",
       "std       9.437139  \n",
       "min     253.000000  \n",
       "25%     265.000000  \n",
       "50%     268.000000  \n",
       "75%     277.750000  \n",
       "max     291.000000  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 골프공 타입 별 통계값 확인\n",
    "\n",
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3600x1800 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 그룹 별 박스 플롯 시각화\n",
    "\n",
    "df2 =  pd.melt(df)\n",
    "plt.figure(figsize=(12,6))\n",
    "sns.boxplot(x='variable', y='value', data=df2)\n",
    "plt.title('Golf ball test')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ShapiroResult(statistic=0.965537965297699, pvalue=0.15155252814292908)\n",
      "ShapiroResult(statistic=0.9728281497955322, pvalue=0.3005155026912689)\n",
      "ShapiroResult(statistic=0.9730034470558167, pvalue=0.30533552169799805)\n",
      "ShapiroResult(statistic=0.9693009257316589, pvalue=0.2167525738477707)\n",
      "ShapiroResult(statistic=0.9595518112182617, pvalue=0.08513051271438599)\n",
      "ShapiroResult(statistic=0.9469832181930542, pvalue=0.02568192593753338)\n"
     ]
    }
   ],
   "source": [
    "# 데이터 정규성 검정\n",
    "\n",
    "print(shapiro(df['TypeA_before']))\n",
    "print(shapiro(df['TypeA_after']))\n",
    "print(shapiro(df['TypeB_before']))\n",
    "print(shapiro(df['TypeB_after']))\n",
    "print(shapiro(df['TypeC_before']))\n",
    "print(shapiro(df['TypeC_after']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BartlettResult(statistic=2.232358764161634, pvalue=0.8161484218330712)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 데이터 등분산성 검정\n",
    "stats.bartlett(df['TypeA_before'],df['TypeA_after'],\n",
    "               df['TypeB_before'],df['TypeB_after'],\n",
    "               df['TypeC_before'],df['TypeC_after'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.2313987682249838, 0.21817375744980994)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Z-test (TypeA_Before와 TypeA_After)\n",
    "ztest(df['TypeA_before'], x2=df['TypeA_after'], value=0, alternative='two-sided')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-2.789495974658115, 0.005279015267745852)\n",
      "(-2.789495974658115, 0.002639507633872926)\n",
      "(-2.789495974658115, 0.9973604923661271)\n"
     ]
    }
   ],
   "source": [
    "# Z-test (TypeA_Before와 TypeB_before)\n",
    "\n",
    "# 양측검정\n",
    "print(ztest(df['TypeA_before'], x2=df['TypeB_before'], value=0, alternative='two-sided'))\n",
    "\n",
    "# 단측검정(왼꼬리검정)\n",
    "print(ztest(df['TypeA_before'], x2=df['TypeB_before'], value=0, alternative='smaller'))\n",
    "\n",
    "# 단측검정(오른꼬리검정)\n",
    "print(ztest(df['TypeA_before'], x2=df['TypeB_before'], value=0, alternative='larger'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_relResult(statistic=-1.221439914972903, pvalue=0.22776376448687602)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 대응표본 t검정 수행\n",
    "scipy.stats.ttest_rel(df['TypeA_before'],df['TypeA_after'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-2.789495974658115, pvalue=0.0063642243501398285)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 독립표본 t검정 수행\n",
    "ttest_ind(df['TypeA_before'],df['TypeB_before'], equal_var=False)"
   ]
  }
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