Rewritten to proper bootstrap
This commit is contained in:
parent
ccd4517925
commit
7abf326bbb
@ -25,7 +25,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 62,
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"execution_count": 313,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -35,6 +35,7 @@
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"source": [
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"import numpy as np\n",
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"import pandas as pd\n",
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"from enum import Enum\n",
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"from math import sqrt\n",
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"from scipy import stats\n",
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"from scipy.stats import sem\n",
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@ -46,7 +47,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"execution_count": 314,
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"metadata": {},
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"outputs": [],
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"source": [
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@ -55,29 +56,39 @@
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"execution_count": 315,
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"metadata": {},
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"outputs": [],
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"source": [
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"def calculate_p(t_stat, df):\n",
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" \"\"\"Funkcja oblicza wartość *p* na podstawie statystyki testowej i stopni swobody\"\"\"\n",
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" return (1.0 - t.cdf(abs(t_stat), df)) * 2.0"
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"class Alternatives(Enum):\n",
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" LESS = 'less'\n",
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" GREATER = 'greater'"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 51,
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"execution_count": 316,
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"metadata": {},
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"outputs": [],
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"source": [
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"def calculate_cv(df, alpha=0.05):\n",
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" \"\"\"Funkcja oblicza wartość krytyczną (critical value)\"\"\"\n",
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" return t.ppf(1.0 - alpha, df)"
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"def calculate_t_difference(t_stat_sample, t_stat_list, alternative):\n",
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" \"\"\"\n",
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" Funkcja oblicza procent statystyk testowych powstałych z prób bootstrapowych, \n",
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" które róznią się od statystyki testowej powstałej ze zbioru według hipotezy alternatywnej.\n",
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" \"\"\"\n",
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" all_stats = len(t_stat_list)\n",
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" stats_different_count = 0\n",
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" for t_stat_boot in t_stat_list:\n",
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" if alternative is Alternatives.LESS and t_stat_boot < t_stat_sample:\n",
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" stats_different_count += 1 \n",
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" elif alternative is Alternatives.GREATER and t_stat_boot > t_stat_sample:\n",
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" stats_different_count += 1\n",
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" return stats_different_count / all_stats"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 53,
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"execution_count": 317,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -85,53 +96,77 @@
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},
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"outputs": [],
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"source": [
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"def t_test(sample_1, sample_2=None, df_fn=df_single, t_stat_fn=t_stat_single, population_mean=None, alpha=0.05):\n",
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"def t_test_1_samp(sample_1, population_mean=None, alternative=Alternatives.LESS):\n",
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" \"\"\"\n",
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" Funkcja przeprowadza test T-studenta dla dwóch zmiennych.\n",
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" liczba kolumn wynosi 1, test jest przeprowadzany dla jednej zmiennej.\n",
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" @param df_fn - funkcja obliczająca stopnie swobody\n",
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" @param t_stat_fn - funkcja obliczająca statystykę T\n",
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" Funkcja przeprowadza test T-studenta dla jednej zmiennej.\n",
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" \"\"\"\n",
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" t_stat_list = get_t_stats(sample_1, sample_2, t_stat_fn, population_mean=population_mean)\n",
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" t_stat_sum = sum(t_stat_list)\n",
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" t_stat_from_sample, _ = ttest_1samp(a=sample_1, popmean=population_mean, alternative=alternative.value)\n",
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" t_stat_list = get_t_stats(sample_1, t_stat_fn=ttest_1samp, alternative=alternative, population_mean=population_mean)\n",
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"\n",
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" data_size = sample_1.shape[0]\n",
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" p = calculate_t_difference(t_stat_from_sample, t_stat_list, alternative)\n",
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"\n",
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" t_stat = t_stat_sum / data_size\n",
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" # TODO: dolna i górna opcja dają inne wyniki z jakiegoś powodu (???)\n",
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" t_stat = mean(t_stat_list)\n",
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"\n",
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" if sample_2 is None:\n",
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" df = df_fn(sample_1)\n",
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" else:\n",
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" df = df_fn(sample_1, sample_2)\n",
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" cv = calculate_cv(df, alpha)\n",
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" p = calculate_p(t_stat, df)\n",
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" return t_stat, df, cv, p, t_stat_list"
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" return p, t_stat_list"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 54,
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"execution_count": 318,
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"metadata": {},
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"outputs": [],
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"source": [
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"def get_t_stats(sample_1, sample_2=None, t_stat_fn=t_stat_single, population_mean=None):\n",
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"def t_test_ind(sample_1, sample_2, alternative=Alternatives.LESS):\n",
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" \"\"\"\n",
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" Funkcja przeprowadza test T-studenta dla dwóch zmiennych niezależnych.\n",
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" \"\"\"\n",
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" t_stat_from_sample, _ = ttest_ind(sample_1, sample_2, alternative=alternative.value)\n",
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" t_stat_list = get_t_stats(sample_1, sample_2, alternative=alternative, t_stat_fn=ttest_ind)\n",
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"\n",
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" p = calculate_t_difference(t_stat_from_sample, t_stat_list, alternative)\n",
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"\n",
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" return p, t_stat_list"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 319,
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"metadata": {},
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"outputs": [],
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"source": [
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"def t_test_dep(sample_1, sample_2, alternative=Alternatives.LESS):\n",
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" \"\"\"\n",
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" Funkcja przeprowadza test T-studenta dla dwóch zmiennych zależnych.\n",
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" \"\"\"\n",
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" t_stat_list = get_t_stats(sample_1, sample_2, alternative=alternative, t_stat_fn=ttest_rel)\n",
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" t_stat_from_sample, _ = ttest_rel(sample_1, sample_2, alternative=alternative.value)\n",
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"\n",
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" p = calculate_t_difference(t_stat_from_sample, t_stat_list, alternative)\n",
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"\n",
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" return p, t_stat_list"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 320,
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"metadata": {},
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"outputs": [],
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"source": [
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"def get_t_stats(sample_1, sample_2=None, t_stat_fn=ttest_1samp, alternative=Alternatives.LESS, population_mean=None):\n",
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" \"\"\"Funkcja oblicza listę statystyk testowych dla każdej próbki bootstrapowej wybranej na podstawie danych sample_1 i sample_2\"\"\"\n",
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" t_stat_list = []\n",
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"\n",
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" # One sample test\n",
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" if t_stat_fn==t_stat_single:\n",
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" if t_stat_fn is ttest_1samp and sample_2 is None:\n",
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" if not population_mean:\n",
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" raise Exception(\"population_mean not provided\")\n",
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" for bootstrap in generate_bootstraps(sample_1):\n",
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" stat = t_stat_fn(bootstrap, population_mean)\n",
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" stat, _ = t_stat_fn(bootstrap, population_mean, alternative=alternative.value)\n",
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" t_stat_list.append(stat)\n",
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" return t_stat_list\n",
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"\n",
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" # Two sample test\n",
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" for bootstrap_1, bootstrap_2 in zip(generate_bootstraps(sample_1), generate_bootstraps(sample_2)):\n",
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" stat = t_stat_fn(bootstrap_1, bootstrap_2)\n",
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" for bootstrap_sample in generate_bootstraps(pd.concat((sample_1, sample_2))):\n",
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" bootstrap_1, bootstrap_2 = bootstrap_sample.iloc[: round(len(bootstrap_sample) * 0.5)], bootstrap_sample.iloc[: round(-len(bootstrap_sample) * 0.5)]\n",
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" stat, _ = t_stat_fn(bootstrap_1, bootstrap_2, alternative=alternative.value)\n",
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" t_stat_list.append(stat)\n",
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" return t_stat_list"
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]
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@ -145,34 +180,6 @@
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"Wszystkie rodzaje testów są testami parametrycznymi, a co za tym idzie nasze mierzone zmienne ilościowe powinny mieć rozkład normalny."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 69,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.9606528878211975\n",
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"2.666284970587185e-10\n",
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"Dane nie mają rozkładu normalnego.\n"
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]
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}
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],
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"source": [
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"# TODO: Test Shapiro Wilka sprawdzający czy nasze dane mają rozkład normalny\n",
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"x = dataset['Height'].to_numpy()\n",
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"shapiro_test = stats.shapiro(x)\n",
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"print(shapiro_test.statistic)\n",
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"print(shapiro_test.pvalue)\n",
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"\n",
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"if shapiro_test.pvalue > shapiro_test.statistic:\n",
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" print(\"Dane mają rozkład normalny.\")\n",
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"else:\n",
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" print(\"Dane nie mają rozkładu normalnego.\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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@ -186,7 +193,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 55,
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"execution_count": 321,
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"metadata": {
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"pycharm": {
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"name": "#%%\n"
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@ -214,7 +221,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 60,
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"execution_count": 322,
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"metadata": {
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"collapsed": false,
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"pycharm": {
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@ -223,44 +230,11 @@
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},
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"outputs": [],
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"source": [
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"def t_stat_single(sample, population_mean):\n",
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" \"\"\"Funkcja oblicza wartość statystyki testowej dla jednej próbki\"\"\"\n",
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" if sample.empty:\n",
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" raise Exception(\"Empty sample\")\n",
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" sample = sample['Height'].values.tolist()\n",
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" sample_size = len(sample)\n",
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" return (mean(sample) - population_mean) / (stdev(sample) / sqrt(sample_size))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 57,
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"metadata": {},
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"outputs": [],
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"source": [
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"def df_single(sample_1):\n",
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" \"\"\"Funkcja oblicza stopnie swobody dla jednej próbki\"\"\"\n",
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" # TODO: I have no clue what to return from here\n",
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" return len(sample_1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 58,
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"metadata": {
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"collapsed": false,
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": [
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"def bootstrap_one_sample(sample, population_mean):\n",
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" return t_test(\n",
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"def bootstrap_one_sample(sample, population_mean, alternative=Alternatives.LESS):\n",
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" return t_test_1_samp(\n",
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" sample_1=sample,\n",
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" df_fn=df_single,\n",
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" t_stat_fn=t_stat_single,\n",
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" population_mean=population_mean\n",
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" population_mean=population_mean,\n",
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" alternative=alternative,\n",
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" )"
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]
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},
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@ -273,7 +247,18 @@
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},
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{
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"cell_type": "code",
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"execution_count": 61,
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"execution_count": 323,
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"metadata": {},
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"outputs": [],
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"source": [
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"dummy = pd.DataFrame([1, 2, 3, 4, 5])\n",
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"dummy2 = pd.DataFrame([4, 5, 6, 7, 8])\n",
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"dummy3 = pd.DataFrame([1, 3 , 3, 4, 6])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 324,
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"metadata": {
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"collapsed": false,
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"pycharm": {
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@ -282,19 +267,18 @@
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"name": "stdout",
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"text": [
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"t: 6.854929920812628, df: 500, cv: 1.6479068539295045, p: 2.1091128843409024e-11\n",
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"\n"
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"p: 0.73\n"
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]
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}
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],
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"source": [
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"#TODO: poprawić kod aby można było podawać kolumny\n",
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"\n",
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"t_stat, df, cv, p, _ = bootstrap_one_sample(dataset, 165)\n",
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"pretty_print_full_stats(t_stat, df, cv, p)"
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"p, _ = bootstrap_one_sample(dummy, 165)\n",
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"print(f'p: {p}')"
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]
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},
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{
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},
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{
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"cell_type": "code",
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"execution_count": 159,
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"execution_count": 325,
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"metadata": {
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"collapsed": false,
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"pycharm": {
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@ -327,44 +311,11 @@
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},
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"outputs": [],
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"source": [
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"def t_stat_ind(sample_1, sample_2):\n",
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" \"\"\"Funkcja oblicza wartość statystyki testowej dla dwóch próbek niezależnych\"\"\"\n",
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" if sample_1.empty or sample_2.empty:\n",
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" raise Exception(\"Empty sample\")\n",
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" sample_1 = sample_1[0].values.tolist()\n",
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" sample_2 = sample_2[0].values.tolist()\n",
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" sed = sqrt(sem(sample_1)**2 + sem(sample_2)**2)\n",
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" return (mean(sample_1) - mean(sample_2)) / sed"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 162,
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"metadata": {},
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"outputs": [],
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"source": [
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"def df_ind(sample_1, sample_2):\n",
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" \"\"\"Funkcja oblicza stopnie swobody dla dwóch próbek niezależnych\"\"\"\n",
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" return len(sample_1) + len(sample_2) - 2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 167,
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"metadata": {
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"collapsed": false,
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"pycharm": {
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"name": "#%%\n"
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}
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},
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"outputs": [],
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"source": [
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"def bootstrap_independent(sample_1, sample_2):\n",
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" return t_test(\n",
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"def bootstrap_independent(sample_1, sample_2, alternative=Alternatives.LESS):\n",
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" return t_test_ind(\n",
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" sample_1=sample_1,\n",
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" sample_2=sample_2,\n",
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" df_fn=df_ind,\n",
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" t_stat_fn=t_stat_ind\n",
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" alternative=alternative,\n",
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" )"
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]
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},
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@ -397,7 +348,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 160,
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"execution_count": 326,
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"metadata": {
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"collapsed": false,
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"pycharm": {
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@ -406,48 +357,11 @@
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},
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"outputs": [],
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"source": [
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"def t_stat_dep(sample_1, sample_2, mu=0):\n",
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" \"\"\"Funkcja oblicza wartość statystyki testowej dla dwóch próbek zależnych\"\"\"\n",
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" if sample_1.empty or sample_2.empty:\n",
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" raise Exception(\"Empty sample\")\n",
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" sample_1 = sample_1[0].values.tolist()\n",
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" sample_2 = sample_2[0].values.tolist()\n",
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" differences = [x_1 - x_2 for x_1, x_2 in zip(sample_1, sample_2)]\n",
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" sample_size = len(sample_1)\n",
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" return (mean(differences) - mu) / (stdev(differences) / sqrt(sample_size))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 161,
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"metadata": {},
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"outputs": [],
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"source": [
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"def df_dep(sample_1, sample_2):\n",
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" \"\"\"Funkcja oblicza stopnie swobody dla dwóch próbek zależnych\"\"\"\n",
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" l1, l2 = len(sample_1), len(sample_2)\n",
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" if l1 != l2:\n",
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" raise Exception(\"Samples aren't of equal length\")\n",
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" return l1"
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]
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},
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{
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"cell_type": "code",
|
||||
"execution_count": 168,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"pycharm": {
|
||||
"name": "#%%\n"
|
||||
}
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def bootstrap_dependent(sample_1, sample_2):\n",
|
||||
" return t_test(\n",
|
||||
"def bootstrap_dependent(sample_1, sample_2, alternative=Alternatives.LESS):\n",
|
||||
" return t_test_dep(\n",
|
||||
" sample_1=sample_1,\n",
|
||||
" sample_2=sample_2,\n",
|
||||
" df_fn=df_dep,\n",
|
||||
" t_stat_fn=t_stat_dep\n",
|
||||
" alternative=alternative,\n",
|
||||
" )"
|
||||
]
|
||||
},
|
||||
@ -476,7 +390,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 171,
|
||||
"execution_count": 327,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"pycharm": {
|
||||
@ -505,100 +419,45 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 31,
|
||||
"metadata": {
|
||||
"collapsed": false,
|
||||
"pycharm": {
|
||||
"name": "#%%\n"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Statystyka testowa dla jednej próby:\n",
|
||||
"1.414213562373095 - z naszej funkcji\n",
|
||||
"[1.41421356] - z gotowej biblioteki\n",
|
||||
"\n",
|
||||
"Statystyka testowa dla dwóch prób niezależnych:\n",
|
||||
"-3.0 - z naszej funkcji\n",
|
||||
"[-3.] - z gotowej biblioteki\n",
|
||||
"\n",
|
||||
"Statystyka testowa dla dwóch prób zależnych:\n",
|
||||
"-1.6329931618554525 - z naszej funkcji\n",
|
||||
"[-1.63299316] - z gotowej biblioteki\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Testy dla samych statystyk testowych\n",
|
||||
"def pretty_print_stats(t_stat_selfmade, t_stat_lib, suffix):\n",
|
||||
" print(f'Statystyka testowa dla {suffix}:')\n",
|
||||
" print(t_stat_selfmade, '- z naszej funkcji')\n",
|
||||
" print(t_stat_lib, '- z gotowej biblioteki')\n",
|
||||
" print()\n",
|
||||
" \n",
|
||||
"dummy = pd.DataFrame([1, 2, 3, 4, 5])\n",
|
||||
"dummy2 = pd.DataFrame([4, 5, 6, 7, 8])\n",
|
||||
"dummy3 = pd.DataFrame([1, 3 , 3, 4, 6])\n",
|
||||
"\n",
|
||||
"t_stat_selfmade = t_stat_single(dummy, 2)\n",
|
||||
"t_stat_lib, _ = ttest_1samp(dummy, 2)\n",
|
||||
"pretty_print_stats(t_stat_selfmade, t_stat_lib, 'jednej próby')\n",
|
||||
"\n",
|
||||
"t_stat_selfmade = t_stat_ind(dummy, dummy2)\n",
|
||||
"t_stat_lib, _ = ttest_ind(dummy, dummy2)\n",
|
||||
"pretty_print_stats(t_stat_selfmade, t_stat_lib, 'dwóch prób niezależnych')\n",
|
||||
"\n",
|
||||
"t_stat_selfmade = t_stat_dep(dummy, dummy3)\n",
|
||||
"t_stat_lib, _ = ttest_rel(dummy, dummy3)\n",
|
||||
"pretty_print_stats(t_stat_selfmade, t_stat_lib, 'dwóch prób zależnych')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 39,
|
||||
"execution_count": 328,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"name": "stdout",
|
||||
"text": [
|
||||
"<class 'pandas.core.frame.DataFrame'>\n",
|
||||
"Statystyki dla jednej próby:\n",
|
||||
"t: 1.8073147056683616, df: 5, cv: 2.015048372669157, p: 0.13052275003443325\n",
|
||||
"\n",
|
||||
"0.44\n",
|
||||
"Statystyki dla dwóch prób zależnych:\n",
|
||||
"t: 3.0790273716290404, df: 5, cv: 2.015048372669157, p: 0.027500015466573435\n",
|
||||
"\n",
|
||||
"0.0\n",
|
||||
"Statystyki dla dwóch prób niezależnych:\n",
|
||||
"t: 2.8109511013364576, df: 8, cv: 1.8595480375228421, p: 0.02280961069987497\n",
|
||||
"\n"
|
||||
"1.0\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Testy z bootstrappowaniem\n",
|
||||
"\n",
|
||||
"def pretty_print_full_stats(t_stat, df, cv, p):\n",
|
||||
" print(f't: {t_stat}, df: {df}, cv: {cv}, p: {p}\\n')\n",
|
||||
"\n",
|
||||
"print(type(dummy))\n",
|
||||
"\n",
|
||||
"print('Statystyki dla jednej próby:')\n",
|
||||
"t_stat, df, cv, p, _ = bootstrap_one_sample(dummy, 2)\n",
|
||||
"pretty_print_full_stats(t_stat, df, cv, p)\n",
|
||||
"p, _ = bootstrap_one_sample(dummy, 2)\n",
|
||||
"print(f'p {p}')\n",
|
||||
"\n",
|
||||
"print('Statystyki dla dwóch prób zależnych:')\n",
|
||||
"t_stat, df, cv, p, _ = bootstrap_dependent(dummy2, dummy3)\n",
|
||||
"pretty_print_full_stats(t_stat, df, cv, p)\n",
|
||||
"p, _ = bootstrap_dependent(dummy2, dummy3)\n",
|
||||
"print(f'p {p}')\n",
|
||||
"\n",
|
||||
"print('Statystyki dla dwóch prób niezależnych:')\n",
|
||||
"t_stat, df, cv, p, _ = bootstrap_independent(dummy2, dummy3)\n",
|
||||
"pretty_print_full_stats(t_stat, df, cv, p)"
|
||||
"p, _ = bootstrap_independent(dummy2, dummy3)\n",
|
||||
"print(f'p {p}')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
@ -606,9 +465,13 @@
|
||||
"hash": "11938c6bc6919ae2720b4d5011047913343b08a43b18698fd82dedb0d4417594"
|
||||
},
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3.9.1 64-bit",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
"name": "python3",
|
||||
"display_name": "Python 3.8.10 64-bit",
|
||||
"metadata": {
|
||||
"interpreter": {
|
||||
"hash": "767d51c1340bd893661ea55ea3124f6de3c7a262a8b4abca0554b478b1e2ff90"
|
||||
}
|
||||
}
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
@ -620,7 +483,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.1"
|
||||
"version": "3.8.10-final"
|
||||
},
|
||||
"orig_nbformat": 4
|
||||
},
|
||||
|
||||
Loading…
Reference in New Issue
Block a user