Bootstrap-t-student/bootstrap-t.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "Bootstrapowa wersja testu t.\n",
    "Implementacja powinna obejmować test dla jednej próby, dla dwóch prób niezależnych oraz dla dwóch prób zależnych.\n",
    "W każdej sytuacji oczekiwanym wejście jest zbiór danych w odpowiednim formacie, a wyjściem p-wartość oraz ostateczna decyzja.\n",
    "Dodatkowo powinien być rysowany odpowiedni rozkład statystyki testowej."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Zbiór danych          - ???\n",
    "Hipoteza zerowa       - ???\n",
    "Hipoteza alternatywna - ???\n",
    "\n",
    "Dla każdego z 3 testów inne\n",
    "https://www.jmp.com/en_ch/statistics-knowledge-portal/t-test.html"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from math import sqrt\n",
    "from scipy.stats import sem\n",
    "from scipy.stats import t\n",
    "import matplotlib.pyplot as plt\n",
    "from statistics import mean, stdev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def generate_bootstraps(data, n_bootstraps=100):\n",
    "    data_size = data.shape[0]\n",
    "    for _ in range(n_bootstraps):\n",
    "        indices =  np.random.choice(len(data), size=data_size)\n",
    "        yield data.iloc[indices, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "outputs": [],
   "source": [
    "def get_t_stat(data1, data2):\n",
    "    mean1 = np.mean(data1)\n",
    "    mean2 = np.mean(data2)\n",
    "    sem1 = sem(data1)\n",
    "    sem2 = sem(data2)\n",
    "\n",
    "    sed = sqrt(sem1**2.0 + sem2**2.0)\n",
    "    # To jest wzór chyba tylko dla jednego przypadku\n",
    "    return (mean1 - mean2) / sed"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [
    "def  t_stat_single(sample, population_mean):\n",
    "    \"\"\"Funkcja oblicza wartość statystyki testowej dla jednej próbki\"\"\"\n",
    "    sample_mean = mean(sample)\n",
    "    sample_std = stdev(sample)\n",
    "    sample_size = len(sample)\n",
    "    return (sample_mean - population_mean) / (sample_std / sqrt(sample_size))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [
    "def t_stat_indept():\n",
    "    pass"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [
    "def t_stat_dep():\n",
    "    pass"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def independent_t_test(data, columns, alpha=0.05):\n",
    "    t_stat_sum = 0\n",
    "    for sample in generate_bootstraps(data):\n",
    "        t_stat_sum += get_t_stat(sample[columns[0]], sample[columns[1]])\n",
    "\n",
    "    data_size = data.shape[0]\n",
    "    t_stat = t_stat_sum / data_size\n",
    "    df = 2 * data_size - 2\n",
    "    cv = t.ppf(1.0 - alpha, df)\n",
    "    p = (1.0 - t.cdf(abs(t_stat), df)) * 2.0\n",
    "    return t_stat, df, cv, p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "outputs": [],
   "source": [
    "def make_decision(data, columns, alpha=0.05):\n",
    "    t_stat, df, cv, p = independent_t_test(data, columns, alpha)\n",
    "    print(f't: {t_stat}, df: {df}, cv: {cv}, p: {p}\\n')\n",
    "    if abs(t_stat) <= cv:\n",
    "\t    print('Accept null hypothesis that the means are equal.')\n",
    "    else:\n",
    "        print('Reject the null hypothesis that the means are equal.')\n",
    "    if p > alpha:\n",
    "        print('Accept null hypothesis that the means are equal.')\n",
    "    else:\n",
    "\t    print('Reject the null hypothesis that the means are equal.')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [
    {
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_distribution():\n",
    "    \"\"\"Funkcja rysuje rozkład statystyki testowej\"\"\"\n",
    "    dummy = np.random.normal(170, 10, 500)\n",
    "    plt.hist(dummy)\n",
    "    plt.show()\n",
    "    pass\n",
    "draw_distribution()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t: 6.940510630195086, df: 998, cv: 1.6463818766348755, p: 7.02371494298859e-12\n",
      "\n",
      "Reject the null hypothesis that the means are equal.\n",
      "Reject the null hypothesis that the means are equal.\n"
     ]
    }
   ],
   "source": [
    "dataset = pd.read_csv('experiment_data.csv')\n",
    "make_decision(dataset, ['Weight', 'Age'])"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ],
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