Hypothesis Testing.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5fec4cc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "da686dab",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Date</th>\n",
       "      <th>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>SKU_Category</th>\n",
       "      <th>SKU</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>02/01/2016</td>\n",
       "      <td>2547</td>\n",
       "      <td>1</td>\n",
       "      <td>X52</td>\n",
       "      <td>0EM7L</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>02/01/2016</td>\n",
       "      <td>822</td>\n",
       "      <td>2</td>\n",
       "      <td>2ML</td>\n",
       "      <td>68BRQ</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>02/01/2016</td>\n",
       "      <td>3686</td>\n",
       "      <td>3</td>\n",
       "      <td>0H2</td>\n",
       "      <td>CZUZX</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>02/01/2016</td>\n",
       "      <td>3719</td>\n",
       "      <td>4</td>\n",
       "      <td>0H2</td>\n",
       "      <td>549KK</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>02/01/2016</td>\n",
       "      <td>9200</td>\n",
       "      <td>5</td>\n",
       "      <td>0H2</td>\n",
       "      <td>K8EHH</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.88</td>\n",
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       "    <tr>\n",
       "      <th>131701</th>\n",
       "      <td>131702</td>\n",
       "      <td>04/07/2016</td>\n",
       "      <td>20203</td>\n",
       "      <td>32900</td>\n",
       "      <td>IEV</td>\n",
       "      <td>FO112</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131702</th>\n",
       "      <td>131703</td>\n",
       "      <td>04/07/2016</td>\n",
       "      <td>20203</td>\n",
       "      <td>32900</td>\n",
       "      <td>N8U</td>\n",
       "      <td>I36F2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131703</th>\n",
       "      <td>131704</td>\n",
       "      <td>04/07/2016</td>\n",
       "      <td>20203</td>\n",
       "      <td>32900</td>\n",
       "      <td>U5F</td>\n",
       "      <td>4X8P4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131704</th>\n",
       "      <td>131705</td>\n",
       "      <td>04/07/2016</td>\n",
       "      <td>20203</td>\n",
       "      <td>32900</td>\n",
       "      <td>0H2</td>\n",
       "      <td>ZVTO4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131705</th>\n",
       "      <td>131706</td>\n",
       "      <td>04/07/2016</td>\n",
       "      <td>20203</td>\n",
       "      <td>32900</td>\n",
       "      <td>Q4N</td>\n",
       "      <td>QM9BP</td>\n",
       "      <td>1.0</td>\n",
       "      <td>13.68</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>131706 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        Unnamed: 0        Date  Customer_ID  Transaction_ID SKU_Category  \\\n",
       "0                1  02/01/2016         2547               1          X52   \n",
       "1                2  02/01/2016          822               2          2ML   \n",
       "2                3  02/01/2016         3686               3          0H2   \n",
       "3                4  02/01/2016         3719               4          0H2   \n",
       "4                5  02/01/2016         9200               5          0H2   \n",
       "...            ...         ...          ...             ...          ...   \n",
       "131701      131702  04/07/2016        20203           32900          IEV   \n",
       "131702      131703  04/07/2016        20203           32900          N8U   \n",
       "131703      131704  04/07/2016        20203           32900          U5F   \n",
       "131704      131705  04/07/2016        20203           32900          0H2   \n",
       "131705      131706  04/07/2016        20203           32900          Q4N   \n",
       "\n",
       "          SKU  Quantity  Sales_Amount  \n",
       "0       0EM7L       1.0          3.13  \n",
       "1       68BRQ       1.0          5.46  \n",
       "2       CZUZX       1.0          6.35  \n",
       "3       549KK       1.0          5.59  \n",
       "4       K8EHH       1.0          6.88  \n",
       "...       ...       ...           ...  \n",
       "131701  FO112       3.0          6.46  \n",
       "131702  I36F2       1.0          4.50  \n",
       "131703  4X8P4       1.0          5.19  \n",
       "131704  ZVTO4       1.0          4.57  \n",
       "131705  QM9BP       1.0         13.68  \n",
       "\n",
       "[131706 rows x 8 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=pd.read_csv('scanner_data.csv')\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a4a23a13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 131706 entries, 0 to 131705\n",
      "Data columns (total 8 columns):\n",
      " #   Column          Non-Null Count   Dtype  \n",
      "---  ------          --------------   -----  \n",
      " 0   Unnamed: 0      131706 non-null  int64  \n",
      " 1   Date            131706 non-null  object \n",
      " 2   Customer_ID     131706 non-null  int64  \n",
      " 3   Transaction_ID  131706 non-null  int64  \n",
      " 4   SKU_Category    131706 non-null  object \n",
      " 5   SKU             131706 non-null  object \n",
      " 6   Quantity        131706 non-null  float64\n",
      " 7   Sales_Amount    131706 non-null  float64\n",
      "dtypes: float64(2), int64(3), object(3)\n",
      "memory usage: 8.0+ MB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f362535f",
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   "outputs": [
    {
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       "      <td>0H2</td>\n",
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      "text/plain": [
       "        Unnamed: 0       Date  Customer_ID  Transaction_ID SKU_Category  \\\n",
       "0                1 2016-02-01         2547               1          X52   \n",
       "1                2 2016-02-01          822               2          2ML   \n",
       "2                3 2016-02-01         3686               3          0H2   \n",
       "3                4 2016-02-01         3719               4          0H2   \n",
       "4                5 2016-02-01         9200               5          0H2   \n",
       "...            ...        ...          ...             ...          ...   \n",
       "131701      131702 2016-04-07        20203           32900          IEV   \n",
       "131702      131703 2016-04-07        20203           32900          N8U   \n",
       "131703      131704 2016-04-07        20203           32900          U5F   \n",
       "131704      131705 2016-04-07        20203           32900          0H2   \n",
       "131705      131706 2016-04-07        20203           32900          Q4N   \n",
       "\n",
       "          SKU  Quantity  Sales_Amount  \n",
       "0       0EM7L       1.0          3.13  \n",
       "1       68BRQ       1.0          5.46  \n",
       "2       CZUZX       1.0          6.35  \n",
       "3       549KK       1.0          5.59  \n",
       "4       K8EHH       1.0          6.88  \n",
       "...       ...       ...           ...  \n",
       "131701  FO112       3.0          6.46  \n",
       "131702  I36F2       1.0          4.50  \n",
       "131703  4X8P4       1.0          5.19  \n",
       "131704  ZVTO4       1.0          4.57  \n",
       "131705  QM9BP       1.0         13.68  \n",
       "\n",
       "[131706 rows x 8 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "data['Date']=data['Date'].astype('datetime64[ns]')\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "edd3fe24",
   "metadata": {},
   "outputs": [
    {
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       "      <th>131703</th>\n",
       "      <td>2016-04-07</td>\n",
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       "      <td>U5F</td>\n",
       "      <td>4X8P4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131704</th>\n",
       "      <td>2016-04-07</td>\n",
       "      <td>20203</td>\n",
       "      <td>32900</td>\n",
       "      <td>0H2</td>\n",
       "      <td>ZVTO4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131705</th>\n",
       "      <td>2016-04-07</td>\n",
       "      <td>20203</td>\n",
       "      <td>32900</td>\n",
       "      <td>Q4N</td>\n",
       "      <td>QM9BP</td>\n",
       "      <td>1.0</td>\n",
       "      <td>13.68</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>131706 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Date  Customer_ID  Transaction_ID SKU_Category    SKU  Quantity  \\\n",
       "0      2016-02-01         2547               1          X52  0EM7L       1.0   \n",
       "1      2016-02-01          822               2          2ML  68BRQ       1.0   \n",
       "2      2016-02-01         3686               3          0H2  CZUZX       1.0   \n",
       "3      2016-02-01         3719               4          0H2  549KK       1.0   \n",
       "4      2016-02-01         9200               5          0H2  K8EHH       1.0   \n",
       "...           ...          ...             ...          ...    ...       ...   \n",
       "131701 2016-04-07        20203           32900          IEV  FO112       3.0   \n",
       "131702 2016-04-07        20203           32900          N8U  I36F2       1.0   \n",
       "131703 2016-04-07        20203           32900          U5F  4X8P4       1.0   \n",
       "131704 2016-04-07        20203           32900          0H2  ZVTO4       1.0   \n",
       "131705 2016-04-07        20203           32900          Q4N  QM9BP       1.0   \n",
       "\n",
       "        Sales_Amount  \n",
       "0               3.13  \n",
       "1               5.46  \n",
       "2               6.35  \n",
       "3               5.59  \n",
       "4               6.88  \n",
       "...              ...  \n",
       "131701          6.46  \n",
       "131702          4.50  \n",
       "131703          5.19  \n",
       "131704          4.57  \n",
       "131705         13.68  \n",
       "\n",
       "[131706 rows x 7 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.drop(columns='Unnamed: 0',inplace=True)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "59ad8721",
   "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>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-02</th>\n",
       "      <td>1620617</td>\n",
       "      <td>1896805</td>\n",
       "      <td>482.75</td>\n",
       "      <td>4341.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-03</th>\n",
       "      <td>1616766</td>\n",
       "      <td>3579179</td>\n",
       "      <td>497.00</td>\n",
       "      <td>4436.42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>4846347</td>\n",
       "      <td>6867307</td>\n",
       "      <td>553.00</td>\n",
       "      <td>4637.34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>1820535</td>\n",
       "      <td>3779664</td>\n",
       "      <td>217.00</td>\n",
       "      <td>1514.17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>5149729</td>\n",
       "      <td>9793228</td>\n",
       "      <td>572.66</td>\n",
       "      <td>4750.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>4947929</td>\n",
       "      <td>20833477</td>\n",
       "      <td>397.00</td>\n",
       "      <td>3720.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>4921693</td>\n",
       "      <td>20697883</td>\n",
       "      <td>421.00</td>\n",
       "      <td>3363.16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>6290006</td>\n",
       "      <td>24803663</td>\n",
       "      <td>614.00</td>\n",
       "      <td>3940.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>6022838</td>\n",
       "      <td>25461912</td>\n",
       "      <td>469.75</td>\n",
       "      <td>4045.15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>2843852</td>\n",
       "      <td>12215471</td>\n",
       "      <td>216.00</td>\n",
       "      <td>1713.20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>363 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Customer_ID  Transaction_ID  Quantity  Sales_Amount\n",
       "Date                                                           \n",
       "2016-01-02      1620617         1896805    482.75       4341.46\n",
       "2016-01-03      1616766         3579179    497.00       4436.42\n",
       "2016-01-04      4846347         6867307    553.00       4637.34\n",
       "2016-01-05      1820535         3779664    217.00       1514.17\n",
       "2016-01-06      5149729         9793228    572.66       4750.01\n",
       "...                 ...             ...       ...           ...\n",
       "2016-12-27      4947929        20833477    397.00       3720.79\n",
       "2016-12-28      4921693        20697883    421.00       3363.16\n",
       "2016-12-29      6290006        24803663    614.00       3940.49\n",
       "2016-12-30      6022838        25461912    469.75       4045.15\n",
       "2016-12-31      2843852        12215471    216.00       1713.20\n",
       "\n",
       "[363 rows x 4 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_daily=data.groupby('Date').sum()\n",
    "data_daily"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bed869d",
   "metadata": {},
   "source": [
    "### 1-Sample Two-Tailed Penjualan Harian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "58e6bdd6",
   "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>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>3.630000e+02</td>\n",
       "      <td>3.630000e+02</td>\n",
       "      <td>363.000000</td>\n",
       "      <td>363.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.494132e+06</td>\n",
       "      <td>1.175180e+07</td>\n",
       "      <td>538.910273</td>\n",
       "      <td>4347.213829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.163295e+06</td>\n",
       "      <td>8.453714e+06</td>\n",
       "      <td>202.031640</td>\n",
       "      <td>1715.470966</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>5.084740e+05</td>\n",
       "      <td>1.730500e+04</td>\n",
       "      <td>107.000000</td>\n",
       "      <td>503.880000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.360648e+06</td>\n",
       "      <td>4.957075e+06</td>\n",
       "      <td>374.665000</td>\n",
       "      <td>2958.190000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.846347e+06</td>\n",
       "      <td>1.059243e+07</td>\n",
       "      <td>563.000000</td>\n",
       "      <td>4683.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.107174e+06</td>\n",
       "      <td>1.668024e+07</td>\n",
       "      <td>690.250000</td>\n",
       "      <td>5565.010000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.618223e+06</td>\n",
       "      <td>3.784991e+07</td>\n",
       "      <td>1211.500000</td>\n",
       "      <td>8650.640000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Customer_ID  Transaction_ID     Quantity  Sales_Amount\n",
       "count  3.630000e+02    3.630000e+02   363.000000    363.000000\n",
       "mean   4.494132e+06    1.175180e+07   538.910273   4347.213829\n",
       "std    2.163295e+06    8.453714e+06   202.031640   1715.470966\n",
       "min    5.084740e+05    1.730500e+04   107.000000    503.880000\n",
       "25%    2.360648e+06    4.957075e+06   374.665000   2958.190000\n",
       "50%    4.846347e+06    1.059243e+07   563.000000   4683.000000\n",
       "75%    6.107174e+06    1.668024e+07   690.250000   5565.010000\n",
       "max    9.618223e+06    3.784991e+07  1211.500000   8650.640000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_daily.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "315ba446",
   "metadata": {},
   "source": [
    "Apakah penjualan di toko tersebut rata-rata pendapatan hariannya sebesar 4347?\n",
    "\n",
    "H0: Rata-rata pendapatan harian sebesar 4347,  $\\mu$ = 4347\n",
    "\n",
    "H1: Rata-rata pendapatan harian bukan sebesar 4347,  $\\mu$ != 4347"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "89b79e56",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-statistic:0.08396742186176558\n",
      "p-value:0.9331287481069328\n"
     ]
    }
   ],
   "source": [
    "pop=np.random.normal(data_daily['Sales_Amount'].mean(),data_daily['Sales_Amount'].std(),10000)\n",
    "\n",
    "t,p=stats.ttest_1samp(data_daily.Sales_Amount,pop.mean())\n",
    "print (\"t-statistic:\" + str(t))\n",
    "print(\"p-value:\" + str(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6bebe9ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1471f1ee0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ci = stats.norm.interval(0.95, pop.mean(), pop.std())\n",
    "plt.hist(pop, bins=100)\n",
    "plt.axvline(pop.mean(), color='yellow', linestyle='dashed', linewidth=2)\n",
    "\n",
    "plt.axvline(ci[0], color='green', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(ci[1], color='green', linestyle='dashed', linewidth=2)\n",
    "\n",
    "plt.axvline(pop.mean()+t*pop.std(), color='black', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(pop.mean()-t*pop.std(), color='black', linestyle='dashed', linewidth=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce3982e4",
   "metadata": {},
   "source": [
    "### Two-Sample Independent Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "eaa2326b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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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>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-02</th>\n",
       "      <td>10928</td>\n",
       "      <td>14721</td>\n",
       "      <td>4.0</td>\n",
       "      <td>16.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>43707</td>\n",
       "      <td>61793</td>\n",
       "      <td>4.0</td>\n",
       "      <td>21.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>34186</td>\n",
       "      <td>42132</td>\n",
       "      <td>2.0</td>\n",
       "      <td>12.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>31413</td>\n",
       "      <td>54546</td>\n",
       "      <td>2.0</td>\n",
       "      <td>18.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-07</th>\n",
       "      <td>63902</td>\n",
       "      <td>130002</td>\n",
       "      <td>5.0</td>\n",
       "      <td>29.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>91678</td>\n",
       "      <td>319714</td>\n",
       "      <td>6.0</td>\n",
       "      <td>30.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>24448</td>\n",
       "      <td>128213</td>\n",
       "      <td>2.0</td>\n",
       "      <td>15.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>78790</td>\n",
       "      <td>321308</td>\n",
       "      <td>5.0</td>\n",
       "      <td>29.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>79393</td>\n",
       "      <td>322361</td>\n",
       "      <td>5.0</td>\n",
       "      <td>31.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>54286</td>\n",
       "      <td>193993</td>\n",
       "      <td>3.0</td>\n",
       "      <td>19.15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>351 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Customer_ID  Transaction_ID  Quantity  Sales_Amount\n",
       "Date                                                           \n",
       "2016-01-02        10928           14721       4.0         16.80\n",
       "2016-01-04        43707           61793       4.0         21.75\n",
       "2016-01-05        34186           42132       2.0         12.23\n",
       "2016-01-06        31413           54546       2.0         18.95\n",
       "2016-01-07        63902          130002       5.0         29.99\n",
       "...                 ...             ...       ...           ...\n",
       "2016-12-27        91678          319714       6.0         30.33\n",
       "2016-12-28        24448          128213       2.0         15.06\n",
       "2016-12-29        78790          321308       5.0         29.85\n",
       "2016-12-30        79393          322361       5.0         31.78\n",
       "2016-12-31        54286          193993       3.0         19.15\n",
       "\n",
       "[351 rows x 4 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_ML=data[data.SKU_Category=='2ML'].groupby('Date').sum()\n",
    "two_ML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "584ead12",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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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>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>351.000000</td>\n",
       "      <td>351.000000</td>\n",
       "      <td>351.000000</td>\n",
       "      <td>351.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>61208.039886</td>\n",
       "      <td>164712.065527</td>\n",
       "      <td>5.125356</td>\n",
       "      <td>31.967949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>44702.010058</td>\n",
       "      <td>134309.651177</td>\n",
       "      <td>3.138919</td>\n",
       "      <td>20.474494</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>131.000000</td>\n",
       "      <td>377.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.920000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>24470.000000</td>\n",
       "      <td>49702.500000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>16.665000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>52768.000000</td>\n",
       "      <td>143872.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>29.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>88164.000000</td>\n",
       "      <td>251554.500000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>42.325000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>298303.000000</td>\n",
       "      <td>631055.000000</td>\n",
       "      <td>19.000000</td>\n",
       "      <td>141.750000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Customer_ID  Transaction_ID    Quantity  Sales_Amount\n",
       "count     351.000000      351.000000  351.000000    351.000000\n",
       "mean    61208.039886   164712.065527    5.125356     31.967949\n",
       "std     44702.010058   134309.651177    3.138919     20.474494\n",
       "min       131.000000      377.000000    1.000000      2.920000\n",
       "25%     24470.000000    49702.500000    3.000000     16.665000\n",
       "50%     52768.000000   143872.000000    5.000000     29.600000\n",
       "75%     88164.000000   251554.500000    7.000000     42.325000\n",
       "max    298303.000000   631055.000000   19.000000    141.750000"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "two_ML.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "1cd75d22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-03</th>\n",
       "      <td>16595</td>\n",
       "      <td>39624</td>\n",
       "      <td>4.0</td>\n",
       "      <td>25.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>69936</td>\n",
       "      <td>77245</td>\n",
       "      <td>5.0</td>\n",
       "      <td>19.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>10126</td>\n",
       "      <td>21091</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>54874</td>\n",
       "      <td>109377</td>\n",
       "      <td>4.0</td>\n",
       "      <td>44.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-07</th>\n",
       "      <td>73925</td>\n",
       "      <td>194943</td>\n",
       "      <td>6.0</td>\n",
       "      <td>47.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-26</th>\n",
       "      <td>40255</td>\n",
       "      <td>255096</td>\n",
       "      <td>4.0</td>\n",
       "      <td>24.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>75767</td>\n",
       "      <td>319438</td>\n",
       "      <td>5.0</td>\n",
       "      <td>40.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>77275</td>\n",
       "      <td>320385</td>\n",
       "      <td>5.0</td>\n",
       "      <td>59.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>78312</td>\n",
       "      <td>321282</td>\n",
       "      <td>5.0</td>\n",
       "      <td>28.49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>71580</td>\n",
       "      <td>322222</td>\n",
       "      <td>5.0</td>\n",
       "      <td>37.53</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>356 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Customer_ID  Transaction_ID  Quantity  Sales_Amount\n",
       "Date                                                           \n",
       "2016-01-03        16595           39624       4.0         25.29\n",
       "2016-01-04        69936           77245       5.0         19.04\n",
       "2016-01-05        10126           21091       1.0          4.74\n",
       "2016-01-06        54874          109377       4.0         44.65\n",
       "2016-01-07        73925          194943       6.0         47.31\n",
       "...                 ...             ...       ...           ...\n",
       "2016-12-26        40255          255096       4.0         24.24\n",
       "2016-12-27        75767          319438       5.0         40.13\n",
       "2016-12-28        77275          320385       5.0         59.07\n",
       "2016-12-29        78312          321282       5.0         28.49\n",
       "2016-12-30        71580          322222       5.0         37.53\n",
       "\n",
       "[356 rows x 4 columns]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X52=data[data.SKU_Category=='X52'].groupby('Date').sum()\n",
    "X52"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "ae2643df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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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>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>356.000000</td>\n",
       "      <td>356.000000</td>\n",
       "      <td>356.000000</td>\n",
       "      <td>356.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>62037.896067</td>\n",
       "      <td>165334.025281</td>\n",
       "      <td>5.390449</td>\n",
       "      <td>35.868174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>39395.571383</td>\n",
       "      <td>130435.928580</td>\n",
       "      <td>2.677358</td>\n",
       "      <td>20.521357</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>647.000000</td>\n",
       "      <td>388.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.220000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>31096.750000</td>\n",
       "      <td>61153.250000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>21.572500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>58725.500000</td>\n",
       "      <td>138887.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>33.215000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>86198.750000</td>\n",
       "      <td>241051.000000</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>47.330000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>236870.000000</td>\n",
       "      <td>949205.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>117.930000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Customer_ID  Transaction_ID    Quantity  Sales_Amount\n",
       "count     356.000000      356.000000  356.000000    356.000000\n",
       "mean    62037.896067   165334.025281    5.390449     35.868174\n",
       "std     39395.571383   130435.928580    2.677358     20.521357\n",
       "min       647.000000      388.000000    1.000000      3.220000\n",
       "25%     31096.750000    61153.250000    3.000000     21.572500\n",
       "50%     58725.500000   138887.000000    5.000000     33.215000\n",
       "75%     86198.750000   241051.000000    7.000000     47.330000\n",
       "max    236870.000000   949205.000000   15.000000    117.930000"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X52.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b19f44f4",
   "metadata": {},
   "source": [
    "Apakah performa penjualan 2ML dan X52 sama?\n",
    "\n",
    "H0: $\\mu$ Sales Amount 2ML = $\\mu$ Sales Amount X52\n",
    "\n",
    "H1: $\\mu$ Sales Amount 2ML != $\\mu$ Sales Amount X52"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "24b6c913",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-statistic:-2.5295592043233146\n",
      "p-value:0.01163738042113982\n"
     ]
    }
   ],
   "source": [
    "t,p=stats.ttest_ind(two_ML['Sales_Amount'],X52['Sales_Amount'])\n",
    "print (\"t-statistic:\" + str(t))\n",
    "print(\"p-value:\" + str(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "52339a6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x110b9c6d0>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pop=np.random.normal(two_ML['Sales_Amount'].mean(), two_ML['Sales_Amount'].std(), 2000)\n",
    "ci = stats.norm.interval(0.95, pop.mean(), pop.std())\n",
    "plt.hist(pop, bins=100)\n",
    "plt.axvline(pop.mean(), color='yellow', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(ci[0], color='green', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(ci[1], color='green', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(pop.mean()+t*pop.std(), color='black', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(pop.mean()-t*pop.std(), color='black', linestyle='dashed', linewidth=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89ea7ef0",
   "metadata": {},
   "source": [
    "### Two-Sample Dependent/Relative Test / Paired Test\n",
    "\n",
    "H0: Penjualan 2ML bulan Januari = Februari\n",
    "\n",
    "H1: Penjualan 2ML bulan Januari != Februari"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "41654ed4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t-statistic:-1.5449013720698253\n",
      "p-value:0.13445609147460122\n"
     ]
    }
   ],
   "source": [
    "t,p=stats.ttest_rel(two_ML.loc['2016-01']['Sales_Amount'],two_ML.loc['2016-02']['Sales_Amount'][:-1])\n",
    "print (\"t-statistic:\" + str(t))\n",
    "print(\"p-value:\" + str(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "4c1a64ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x1477919d0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pop=np.random.normal(two_ML.loc['2016-01']['Sales_Amount'].mean(), two_ML.loc['2016-01']['Sales_Amount'].std(), 2000)\n",
    "ci = stats.norm.interval(0.95, pop.mean(), pop.std())\n",
    "plt.hist(pop, bins=100)\n",
    "plt.axvline(pop.mean(), color='yellow', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(ci[0], color='green', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(ci[1], color='green', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(pop.mean()+t*pop.std(), color='black', linestyle='dashed', linewidth=2)\n",
    "plt.axvline(pop.mean()-t*pop.std(), color='black', linestyle='dashed', linewidth=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6cae63e",
   "metadata": {},
   "source": [
    "## ANOVA TEST - multiple groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "c0caaff2",
   "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>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-02</th>\n",
       "      <td>15595</td>\n",
       "      <td>29567</td>\n",
       "      <td>6.0</td>\n",
       "      <td>63.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-03</th>\n",
       "      <td>26106</td>\n",
       "      <td>69228</td>\n",
       "      <td>8.0</td>\n",
       "      <td>64.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>100407</td>\n",
       "      <td>123479</td>\n",
       "      <td>8.0</td>\n",
       "      <td>93.11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>88215</td>\n",
       "      <td>189966</td>\n",
       "      <td>13.0</td>\n",
       "      <td>101.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>67259</td>\n",
       "      <td>163541</td>\n",
       "      <td>8.0</td>\n",
       "      <td>73.95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>156595</td>\n",
       "      <td>639131</td>\n",
       "      <td>13.0</td>\n",
       "      <td>94.70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>47195</td>\n",
       "      <td>192373</td>\n",
       "      <td>3.0</td>\n",
       "      <td>41.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>109989</td>\n",
       "      <td>578535</td>\n",
       "      <td>11.0</td>\n",
       "      <td>110.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>82486</td>\n",
       "      <td>322139</td>\n",
       "      <td>5.0</td>\n",
       "      <td>63.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>57623</td>\n",
       "      <td>258559</td>\n",
       "      <td>4.0</td>\n",
       "      <td>52.42</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>362 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Customer_ID  Transaction_ID  Quantity  Sales_Amount\n",
       "Date                                                           \n",
       "2016-01-02        15595           29567       6.0         63.84\n",
       "2016-01-03        26106           69228       8.0         64.29\n",
       "2016-01-04       100407          123479       8.0         93.11\n",
       "2016-01-05        88215          189966      13.0        101.29\n",
       "2016-01-06        67259          163541       8.0         73.95\n",
       "...                 ...             ...       ...           ...\n",
       "2016-12-27       156595          639131      13.0         94.70\n",
       "2016-12-28        47195          192373       3.0         41.05\n",
       "2016-12-29       109989          578535      11.0        110.73\n",
       "2016-12-30        82486          322139       5.0         63.03\n",
       "2016-12-31        57623          258559       4.0         52.42\n",
       "\n",
       "[362 rows x 4 columns]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q4N=data[data.SKU_Category=='Q4N'].groupby('Date').sum()\n",
    "Q4N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "df0492fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    2858.000000\n",
       "mean       11.171568\n",
       "std         7.592091\n",
       "min         0.020000\n",
       "25%         6.240000\n",
       "50%         9.310000\n",
       "75%        13.740000\n",
       "max        64.260000\n",
       "Name: Sales_Amount, dtype: float64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q4N.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "222142d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-02</th>\n",
       "      <td>156838</td>\n",
       "      <td>181924</td>\n",
       "      <td>40.0</td>\n",
       "      <td>172.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-03</th>\n",
       "      <td>105385</td>\n",
       "      <td>227788</td>\n",
       "      <td>29.0</td>\n",
       "      <td>97.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>423813</td>\n",
       "      <td>525348</td>\n",
       "      <td>35.0</td>\n",
       "      <td>142.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>196313</td>\n",
       "      <td>422186</td>\n",
       "      <td>21.0</td>\n",
       "      <td>90.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>265905</td>\n",
       "      <td>436455</td>\n",
       "      <td>17.0</td>\n",
       "      <td>70.18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>397984</td>\n",
       "      <td>1660883</td>\n",
       "      <td>30.0</td>\n",
       "      <td>142.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>425231</td>\n",
       "      <td>1858379</td>\n",
       "      <td>33.0</td>\n",
       "      <td>117.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>470264</td>\n",
       "      <td>2056550</td>\n",
       "      <td>34.0</td>\n",
       "      <td>127.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>697151</td>\n",
       "      <td>3029184</td>\n",
       "      <td>52.0</td>\n",
       "      <td>213.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>328368</td>\n",
       "      <td>1357231</td>\n",
       "      <td>22.0</td>\n",
       "      <td>84.02</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>363 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Customer_ID  Transaction_ID  Quantity  Sales_Amount\n",
       "Date                                                           \n",
       "2016-01-02       156838          181924      40.0        172.46\n",
       "2016-01-03       105385          227788      29.0         97.40\n",
       "2016-01-04       423813          525348      35.0        142.57\n",
       "2016-01-05       196313          422186      21.0         90.48\n",
       "2016-01-06       265905          436455      17.0         70.18\n",
       "...                 ...             ...       ...           ...\n",
       "2016-12-27       397984         1660883      30.0        142.79\n",
       "2016-12-28       425231         1858379      33.0        117.81\n",
       "2016-12-29       470264         2056550      34.0        127.67\n",
       "2016-12-30       697151         3029184      52.0        213.30\n",
       "2016-12-31       328368         1357231      22.0         84.02\n",
       "\n",
       "[363 rows x 4 columns]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N8U=data[data.SKU_Category=='N8U'].groupby('Date').sum()\n",
    "N8U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "018c509d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "        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>Customer_ID</th>\n",
       "      <th>Transaction_ID</th>\n",
       "      <th>Quantity</th>\n",
       "      <th>Sales_Amount</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-02</th>\n",
       "      <td>65290</td>\n",
       "      <td>59093</td>\n",
       "      <td>16.0</td>\n",
       "      <td>52.51</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-03</th>\n",
       "      <td>58130</td>\n",
       "      <td>128839</td>\n",
       "      <td>25.0</td>\n",
       "      <td>68.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>193834</td>\n",
       "      <td>293191</td>\n",
       "      <td>38.0</td>\n",
       "      <td>146.81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>683</td>\n",
       "      <td>21107</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>234784</td>\n",
       "      <td>436224</td>\n",
       "      <td>25.0</td>\n",
       "      <td>117.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-27</th>\n",
       "      <td>130730</td>\n",
       "      <td>575321</td>\n",
       "      <td>14.0</td>\n",
       "      <td>52.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-28</th>\n",
       "      <td>71139</td>\n",
       "      <td>320489</td>\n",
       "      <td>7.0</td>\n",
       "      <td>31.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-29</th>\n",
       "      <td>177265</td>\n",
       "      <td>706304</td>\n",
       "      <td>20.0</td>\n",
       "      <td>57.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-30</th>\n",
       "      <td>153998</td>\n",
       "      <td>644452</td>\n",
       "      <td>14.0</td>\n",
       "      <td>72.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>77745</td>\n",
       "      <td>258516</td>\n",
       "      <td>7.0</td>\n",
       "      <td>183.90</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>352 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Customer_ID  Transaction_ID  Quantity  Sales_Amount\n",
       "Date                                                           \n",
       "2016-01-02        65290           59093      16.0         52.51\n",
       "2016-01-03        58130          128839      25.0         68.81\n",
       "2016-01-04       193834          293191      38.0        146.81\n",
       "2016-01-05          683           21107       2.0          5.00\n",
       "2016-01-06       234784          436224      25.0        117.97\n",
       "...                 ...             ...       ...           ...\n",
       "2016-12-27       130730          575321      14.0         52.90\n",
       "2016-12-28        71139          320489       7.0         31.80\n",
       "2016-12-29       177265          706304      20.0         57.63\n",
       "2016-12-30       153998          644452      14.0         72.48\n",
       "2016-12-31        77745          258516       7.0        183.90\n",
       "\n",
       "[352 rows x 4 columns]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U5F=data[data.SKU_Category=='U5F'].groupby('Date').sum()\n",
    "U5F"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "408ad3ce",
   "metadata": {},
   "source": [
    "Apakah performa penjualan Q4N, X52, U5F, N8U, dan 2ML sama?\n",
    "\n",
    "H0: rata-rata omzet harian kelima kategori produk sama\n",
    "\n",
    "H1: rata-rata omzet harian kelima kategori produk berbeda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "55f68ff6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p-value for significance is:  1.023131613520799e-49\n",
      "reject null hypothesis\n"
     ]
    }
   ],
   "source": [
    "F,p=stats.f_oneway(Q4N.Sales_Amount, U5F.Sales_Amount, N8U.Sales_Amount)\n",
    "\n",
    "print(\"p-value for significance is: \", p)\n",
    "if p<0.05:\n",
    "    print(\"reject null hypothesis\")\n",
    "else:\n",
    "    print(\"accept null hypothesis\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebd4b5f5",
   "metadata": {},
   "source": [
    "## Chi-Squared test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "026c6937",
   "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>Like Shopping?</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Male</td>\n",
       "      <td>Yes</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender Like Shopping?\n",
       "0    Male             No\n",
       "1  Female            Yes\n",
       "2    Male            Yes\n",
       "3  Female            Yes\n",
       "4  Female            Yes\n",
       "5    Male            Yes\n",
       "6    Male             No\n",
       "7  Female             No\n",
       "8  Female             No"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chi_df=pd.read_csv('https://raw.githubusercontent.com/yug95/MachineLearning/master/Hypothesis%20testing/chi-test.csv')\n",
    "chi_df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58a903cf",
   "metadata": {},
   "source": [
    "𝐻0: Tidak ada kaitan hobi belanja dengan jenis kelamin\n",
    "\n",
    "𝐻𝑎: Ada kaitan hobi belanja dengan jenis kelamin\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "3403dafc",
   "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>Like Shopping?</th>\n",
       "      <th>No</th>\n",
       "      <th>Yes</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gender</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Female</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Like Shopping?  No  Yes\n",
       "Gender                 \n",
       "Female           2    3\n",
       "Male             2    2"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "contingency_table=pd.crosstab(chi_df[\"Gender\"],chi_df[\"Like Shopping?\"])\n",
    "contingency_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "92874961",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "stat=0.141, p=0.708\n",
      "Probably independent\n"
     ]
    }
   ],
   "source": [
    "stat, p, dof, expected = stats.chi2_contingency(contingency_table)\n",
    "print('stat=%.3f, p=%.3f' % (stat, p))\n",
    "if p > 0.05:\n",
    "    print('Probably independent')\n",
    "else:\n",
    "    print('Probably dependent')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "58d2a433",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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