diff --git a/bootstrap-t.ipynb b/bootstrap-t.ipynb index feee38d..d8baa0d 100644 --- a/bootstrap-t.ipynb +++ b/bootstrap-t.ipynb @@ -17,15 +17,45 @@ "Wyróżniamy 3 wersję testu t:\n", "\n", "1. test t Studenta dla jednej próby\n", - "2. test t Studenta dla prób niezależnych\n", - "3. test t Studenta dla prób zależnych\n", + "2. test t Studenta dla prób niezależnych \n", + "3. test t Studenta dla prób zależnych" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Test Shapiro Wilka\n", "\n", - "Wszystkie rodzaje testów są testami parametrycznymi, a co za tym idzie nasze mierzone zmienne ilościowe powinny mieć rozkład normalny." + "Wszystkie rodzaje testów są testami parametrycznymi, a co za tym idzie nasze mierzone zmienne ilościowe powinny mieć rozkład normalny. \n", + "Dzięki testowi Shapiro Wilka możemy sprawdzić to założenie." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "## Testowanie hipotez metodą bootstrap\n", + "\n", + "**Bootstrap** – metoda szacowania (estymacji) wyników poprzez wielokrotne losowanie ze zwracaniem z próby. Polega ona na utworzeniu nowego rozkładu wyników, na podstawie posiadanych danych, poprzez wielokrotne losowanie wartości z posiadanej próby. Metoda ze zwracaniem polega na tym, że po wylosowaniu danej wartości, “wraca” ona z powrotem do zbioru.\n", + "\n", + "Metoda bootstrapowa znajduje zastosowanie w sytuacji, w której nie znamy rozkładu z populacji z której pochodzi próbka lub w przypadku rozkładów małych lub asymetrycznych. W takim wypadku, dzięki tej metodzie, wyniki testów parametrycznych i analiz opartych o modele liniowe są bardziej precyzyjne. Zazwyczaj losuje się wiele próbek, np. 2000 czy 5000." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# Definicje funkcji" ] }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 134, "metadata": { "pycharm": { "name": "#%%\n" @@ -42,16 +72,16 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 135, "metadata": {}, "outputs": [], "source": [ - "dataset = pd.read_csv('experiment_data.csv')" + "dataset = pd.read_csv('experiment_data.csv') # TODO: del?" ] }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 136, "metadata": {}, "outputs": [], "source": [ @@ -62,7 +92,7 @@ }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 137, "metadata": {}, "outputs": [], "source": [ @@ -74,16 +104,16 @@ " all_stats = len(t_stat_list)\n", " stats_different_count = 0\n", " for t_stat_boot in t_stat_list:\n", - " if alternative is Alternatives.LESS and t_stat_boot < t_stat_sample:\n", + " if alternative is Alternatives.LESS and t_stat_boot > t_stat_sample:\n", " stats_different_count += 1 \n", - " elif alternative is Alternatives.GREATER and t_stat_boot > t_stat_sample:\n", + " elif alternative is Alternatives.GREATER and t_stat_boot < t_stat_sample:\n", " stats_different_count += 1\n", " return stats_different_count / all_stats" ] }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 138, "metadata": { "pycharm": { "name": "#%%\n" @@ -105,7 +135,7 @@ }, { "cell_type": "code", - "execution_count": 73, + "execution_count": 139, "metadata": {}, "outputs": [], "source": [ @@ -123,7 +153,7 @@ }, { "cell_type": "code", - "execution_count": 74, + "execution_count": 140, "metadata": {}, "outputs": [], "source": [ @@ -141,7 +171,7 @@ }, { "cell_type": "code", - "execution_count": 75, + "execution_count": 141, "metadata": {}, "outputs": [], "source": [ @@ -169,7 +199,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 142, "metadata": {}, "outputs": [], "source": [ @@ -197,82 +227,9 @@ " print()" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Test Shapiro Wilka\n", - "\n", - "Wszystkie rodzaje testów są testami parametrycznymi, a co za tym idzie nasze mierzone zmienne ilościowe powinny mieć rozkład normalny." - ] - }, { "cell_type": "code", - "execution_count": 77, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Female height: Dane mają rozkład normalny.\n", - "Male height: Dane mają rozkład normalny.\n", - "Weight before: Dane mają rozkład normalny.\n", - "Weight after: Dane mają rozkład normalny.\n" - ] - } - ], - "source": [ - "ALPHA = 0.05\n", - "female_heights = dataset['Female height'].to_numpy()\n", - "shapiro_test = shapiro(female_heights)\n", - "\n", - "if shapiro_test.pvalue > ALPHA:\n", - " print(\"Female height: Dane mają rozkład normalny.\")\n", - "else:\n", - " print(\"Female height: Dane nie mają rozkładu normalnego.\")\n", - "\n", - "male_heights = dataset['Male height'].to_numpy()\n", - "shapiro_test = shapiro(male_heights)\n", - "\n", - "if shapiro_test.pvalue > ALPHA:\n", - " print(\"Male height: Dane mają rozkład normalny.\")\n", - "else:\n", - " print(\"Male height: Dane nie mają rozkładu normalnego.\")\n", - "\n", - "weights_before = dataset['Weight before'].to_numpy()\n", - "shapiro_test = shapiro(weights_before)\n", - "\n", - "if shapiro_test.pvalue > ALPHA:\n", - " print(\"Weight before: Dane mają rozkład normalny.\")\n", - "else:\n", - " print(\"Weight before: Dane nie mają rozkładu normalnego.\")\n", - "\n", - "weights_after = dataset['Weight after'].to_numpy()\n", - "shapiro_test = shapiro(weights_after)\n", - "\n", - "if shapiro_test.pvalue > ALPHA:\n", - " print(\"Weight after: Dane mają rozkład normalny.\")\n", - "else:\n", - " print(\"Weight after: Dane nie mają rozkładu normalnego.\")\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Testowanie hipotez metodą bootstrap\n", - "\n", - "**Bootstrap** – metoda szacowania (estymacji) wyników poprzez wielokrotne losowanie ze zwracaniem z próby. Polega ona na utworzeniu nowego rozkładu wyników, na podstawie posiadanych danych, poprzez wielokrotne losowanie wartości z posiadanej próby. Metoda ze zwracaniem polega na tym, że po wylosowaniu danej wartości, “wraca” ona z powrotem do zbioru.\n", - "\n", - "Metoda bootstrapowa znajduje zastosowanie w sytuacji, w której nie znamy rozkładu z populacji z której pochodzi próbka lub w przypadku rozkładów małych lub asymetrycznych. W takim wypadku, dzięki tej metodzie, wyniki testów parametrycznych i analiz opartych o modele liniowe są bardziej precyzyjne. Zazwyczaj losuje się wiele próbek, np. 2000 czy 5000." - ] - }, - { - "cell_type": "code", - "execution_count": 78, + "execution_count": 143, "metadata": { "pycharm": { "name": "#%%\n" @@ -287,20 +244,9 @@ " yield data.iloc[indices, :]" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Test t studenta dla jednej próby\n", - "\n", - "**Test t Studenta dla jednej próby** wykorzystujemy gdy chcemy porównać średnią “teoretyczną” ze średnią, którą faktycznie możemy zaobserwować w naszej bazie danych. Średnia teoretyczna to średnia pochodząca z innych badań lub po prostu bez większych uzasadnień pochodząca z naszej głowy.\n", - "\n", - "Wyobraźmy sobie, że mamy dane z takimi zmiennymi jak wzrost pewnej grupy ludzi. Dzięki testowi t Studenta dla jednej próby możemy dowiedzieć się np. czy wzrost naszego młodszego brata wynoszący 155cm odbiega znacząco od średniej wzrostu tej grupy. Hipoteza zerowa w takim badaniu wyglądałaby następująco H0: Badana próba została wylosowana z populacji, w której wzrost osób wynosi średnio 155cm. Z kolei hipoteza alternatywna będzie brzmiała H1: Badana próba nie została wylosowana z populacji gdzie średni wzrost wynosi 155cm\n" - ] - }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 144, "metadata": { "collapsed": false, "pycharm": { @@ -321,81 +267,9 @@ " return p, t, ts" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Sprawdzenie czy osoba o wzroście 165cm pasuje do populacji (nie jest odmieńcem)" - ] - }, { "cell_type": "code", - "execution_count": 80, - "metadata": {}, - "outputs": [], - "source": [ - "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])" - ] - }, - { - "cell_type": "code", - "execution_count": 81, - "metadata": { - "collapsed": false, - "pycharm": { - "name": "#%%\n" - } - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Wyniki bootstrapowej wersji testu T-studenta\n", - "\n", - "Hipoteza: średnia jest równa 165\n", - "Hipoteza alternatywna: średnia jest mniejsza\n", - "\n", - "p: 0.72\n", - "Wartość statystyki testowej z próby: [-229.1025971]\n", - "Wartości statystyk z prób boostrapowych:\n", - "[-239.4457368], [-201.5], [-176.97470898], [-256.14449047], [-436.1703468], ... (i 95 pozostałych)\n", - "\n", - "\n", - "\n" - ] - } - ], - "source": [ - "#TODO: poprawić kod aby można było podawać kolumny\n", - "\n", - "p, t, ts = bootstrap_one_sample(dummy, 165)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "TODO: Wniosek" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Test t studenta dla prób niezależnych\n", - "\n", - "**Test t Studenta dla prób niezależnych** jest najczęściej stosowaną metodą statystyczną w celu porównania średnich z dwóch niezależnych od siebie grup. Wykorzystujemy go gdy chcemy porównać dwie grupy pod względem jakiejś zmiennej ilościowej. Na przykład gdy chcemy porównać średni wzrost kobiet i mężczyzn w danej grupie.\n", - "\n", - "Zazwyczaj dwie średnie z różnych od siebie grup będą się różnić. Test t Studenta powie nam jednak czy owe różnice są istotne statystycznie – czy nie są przypadkowe. Hipoteza zerowa takiego testu będzie brzmiała H0: Średni wzrost w grupie mężczyzn jest taki sam jak średni w grupie kobiet. Hipoteza alternatywna z kolei H1: Kobiety będą różnić się od mężczyzn pod wzrostu.\n", - "Jeśli wynik testu t Studenta będzie istotny na poziomie p < 0,05 możemy odrzucić hipotezę zerową na rzecz hipotezy alternatywnej.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 82, + "execution_count": 145, "metadata": { "collapsed": false, "pycharm": { @@ -415,27 +289,9 @@ " return p, t, ts" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "TODO: Wniosek" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Test t studenta dla prób zależnych\n", - "\n", - "W odróżnieniu od testu t – Studenta dla prób niezależnych, gdzie porównujemy dwie grupy, ten rodzaj testu stosujemy gdy poddajemy analizie tą samą pojedynczą grupę, ale dwukrotnie w czasie. Na przykład gdy chcemy porównać średnie wagi grupy osób przed dietą oraz po diecie, aby sprawdzić czy dieta spowodowała istotne zmiany statystyczne.\n", - "\n", - "Hipoteza zerowa takiego testu będzie brzmiała H0: Średnia waga osób po diecie jest taka sama jak przed dietą. Hipoteza alternatywna z kolei H1: Dieta znacząco wpłynęła na średnią wagę danej grupy." - ] - }, { "cell_type": "code", - "execution_count": 83, + "execution_count": 146, "metadata": { "collapsed": false, "pycharm": { @@ -455,32 +311,9 @@ " return p, t, ts" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# TODO: Wyciągnąć wagi przed dietą i po oraz poprawić kod aby można było podawać kolumny\n", - "t_stat, df, cv, p, _ = bootstrap_dependent(dataset, dataset)\n", - "pretty_print_full_stats(t_stat, df, cv, p)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "TODO: Wniosek" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Wykresy" - ] - }, { "cell_type": "code", - "execution_count": 84, + "execution_count": 147, "metadata": { "collapsed": false, "pycharm": { @@ -489,12 +322,14 @@ }, "outputs": [], "source": [ - "def draw_distribution(stats):\n", + "def draw_distribution(stats, comparision_value):\n", " \"\"\"\n", " Funkcja rysuje rozkład statystyki testowej\n", " @param stats: lista statystyk testowych\n", + " @param comparision_value: pierwotna próbka\n", " \"\"\"\n", " plt.hist(stats)\n", + " plt.axvline(comparision_value, color='red')\n", " plt.xlabel('Test statistic value')\n", " plt.ylabel('Frequency')\n", " plt.show()" @@ -502,113 +337,386 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "collapsed": false + }, "source": [ - "## Testy" + "# Wczytanie danych" ] }, { "cell_type": "code", - "execution_count": 85, - "metadata": {}, + "execution_count": 148, + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Statystyki dla jednej próby:\n", - "Wyniki bootstrapowej wersji testu T-studenta\n", - "\n", - "Hipoteza: średnia jest równa 2\n", - "Hipoteza alternatywna: średnia jest mniejsza\n", - "\n", - "p: 0.35\n", - "Wartość statystyki testowej z próby: [1.41421356]\n", - "Wartości statystyk z prób boostrapowych:\n", - "[2.44948974], [3.13785816], [1.72328087], [0.27216553], [1.17669681], ... (i 95 pozostałych)\n", - "\n", - "\n", - "\n" + "0 169.5557\n", + "dtype: float64\n", + "0 175.1417\n", + "dtype: float64\n", + "0 79.6342\n", + "dtype: float64\n", + "0 76.5602\n", + "dtype: float64\n" ] } ], "source": [ - "# Testy z bootstrappowaniem\n", + "dataset = pd.read_csv('experiment_data2.csv')\n", + "heights_female = pd.DataFrame(dataset['Female height'].to_numpy()) # xd\n", + "heights_male = pd.DataFrame(dataset['Male height'].to_numpy())\n", + "weights_before = pd.DataFrame(dataset['Weight before'].to_numpy())\n", + "weights_after = pd.DataFrame(dataset['Weight after'].to_numpy())\n", + "print(np.mean(heights_female))\n", + "print(np.mean(heights_male))\n", + "print(np.mean(weights_before))\n", + "print(np.mean(weights_after))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# Jedna próba\n", "\n", - "print('Statystyki dla jednej próby:')\n", - "p, t, ts = bootstrap_one_sample(dummy, 2)" + "**Test t Studenta dla jednej próby** wykorzystujemy gdy chcemy porównać średnią “teoretyczną” ze średnią, którą faktycznie możemy zaobserwować w naszej bazie danych. Średnia teoretyczna to średnia pochodząca z innych badań lub po prostu bez większych uzasadnień pochodząca z naszej głowy.\n", + "\n", + "Wyobraźmy sobie, że mamy dane z takimi zmiennymi jak wzrost pewnej grupy ludzi. Dzięki testowi t Studenta dla jednej próby możemy dowiedzieć się np. czy wzrost naszego młodszego brata wynoszący 155cm odbiega znacząco od średniej wzrostu tej grupy.\n", + "\n", + "### Hipoteza\n", + "\n", + "*H0: Badana próba została wylosowana z populacji, w której wzrost osób wynosi średnio 155cm.* \n", + "*H1: Badana próba nie została wylosowana z populacji gdzie średni wzrost wynosi 155cm.*\n", + "\n", + "### Sprawdzenie założeń\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "## Test\n" ] }, { "cell_type": "code", - "execution_count": 86, + "execution_count": null, + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "## Wniosek" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# Dwie próby niezależne\n", + "\n", + "**Test t Studenta dla prób niezależnych** jest najczęściej stosowaną metodą statystyczną w celu porównania średnich z dwóch niezależnych od siebie grup. Wykorzystujemy go gdy chcemy porównać dwie grupy pod względem jakiejś zmiennej ilościowej. Na przykład gdy chcemy porównać średni wzrost kobiet i mężczyzn w danej grupie.\n", + "Zazwyczaj dwie średnie z różnych od siebie grup będą się różnić. Test t Studenta powie nam jednak czy owe różnice są istotne statystycznie – czy nie są przypadkowe.\n", + "Jeśli wynik testu t Studenta będzie istotny na poziomie p < 0,05 możemy odrzucić hipotezę zerową na rzecz hipotezy alternatywnej.\n", + "\n", + "## Hipoteza\n", + "\n", + "*H0: Średni wzrost w grupie mężczyzn jest taki sam jak średni w grupie kobiet. Hipoteza alternatywna z kolei* \n", + "*H1: Kobiety będą niższe od mężczyzn pod względem wzrostu.*\n", + "\n", + "## Sprawdzenie założeń\n", + "\n", + "Założenie o rozkładzie normalnym danych - sprawdzane testem Shapiro-Wilka" + ] + }, + { + "cell_type": "code", + "execution_count": 149, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Statystyki dla dwóch prób zależnych:\n", - "Wyniki bootstrapowej wersji testu T-studenta\n", - "\n", - "Hipoteza: średnie są takie same\n", - "Hipoteza alternatywna: średnia jest mniejsza\n", - "\n", - "p: 1.0\n", - "Wartość statystyki testowej z próby: [10.61445555]\n", - "Wartości statystyk z prób boostrapowych:\n", - "[-2.66666667], [-0.14359163], [0.21199958], [0.11470787], [0.76696499], ... (i 95 pozostałych)\n", - "\n", - "\n" + "p = 0.791\n", + "p = 0.7535\n" ] } ], "source": [ - "print('Statystyki dla dwóch prób zależnych:')\n", - "p, t, ts = bootstrap_dependent(dummy2, dummy3)" + "shapiro_test = shapiro(heights_female)\n", + "print(f\"p = {round(shapiro_test.pvalue,4)}\")\n", + "\n", + "shapiro_test = shapiro(heights_male)\n", + "print(f\"p = {round(shapiro_test.pvalue,4)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "Wartości **p** w teście Shapiro-Wilka powyżej **0.05** -> Dane prawdopodobnie mają rozkład normalny" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "## Test" ] }, { "cell_type": "code", - "execution_count": 87, - "metadata": {}, + "execution_count": 150, + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Statystyki dla dwóch prób niezależnych:\n", "Wyniki bootstrapowej wersji testu T-studenta\n", "\n", "Hipoteza: średnie są takie same\n", "Hipoteza alternatywna: średnia jest mniejsza\n", "\n", - "p: 0.95\n", - "Wartość statystyki testowej z próby: [2.4140394]\n", + "p: 0.0\n", + "Wartość statystyki testowej z próby: [8.04931557]\n", "Wartości statystyk z prób boostrapowych:\n", - "[-2.20937908], [0.13187609], [-0.81110711], [-0.94280904], [-0.77151675], ... (i 95 pozostałych)\n", + "[0.36930777], [0.23100612], [-0.6106529], [-0.47586438], [0.86529699], ... (i 95 pozostałych)\n", "\n", "\n" ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "p, t, ts = bootstrap_independent(heights_male, heights_female)\n", + "ts = [x[0] for x in ts]\n", + "draw_distribution(ts, t)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "## Wniosek" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "# Dwie próby zależne\n", + "\n", + "W odróżnieniu od testu dla prób niezależnych, gdzie porównujemy dwie grupy, ten rodzaj testu stosujemy gdy poddajemy analizie tą samą pojedynczą grupę, ale dwukrotnie w czasie.\n", + "\n", + "**Przykład**: Porównane zostały wagi przed dietą i po diecie.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "### Hipoteza\n", + "H0 - Średnia waga nie uległa zmianie po zastosowaniu diety\n", + "H1 - Średnia waga po diecie jest znacząco mniejsza od wagi przed dietą\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "\n", + "### Sprawdzenie założeń\n", + "\n", + "Założenie o rozkładzie normalnym danych - sprawdzane testem Shapiro-Wilka" + ] + }, + { + "cell_type": "code", + "execution_count": 151, + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p = 0.3308\n", + "p = 0.4569\n" + ] } ], "source": [ - "print('Statystyki dla dwóch prób niezależnych:')\n", - "p, t, ts = bootstrap_independent(dummy2, dummy3)" + "shapiro_test = shapiro(weights_before)\n", + "print(f\"p = {round(shapiro_test.pvalue,4)}\")\n", + "\n", + "shapiro_test = shapiro(weights_after)\n", + "print(f\"p = {round(shapiro_test.pvalue,4)}\")" ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "Wartości **p** w teście Shapiro-Wilka powyżej **0.05** -> Dane prawdopodobnie mają rozkład normalny" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "## Test" + ] + }, + { + "cell_type": "code", + "execution_count": 152, + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Wyniki bootstrapowej wersji testu T-studenta\n", + "\n", + "Hipoteza: średnie są takie same\n", + "Hipoteza alternatywna: średnia jest mniejsza\n", + "\n", + "p: 0.0\n", + "Wartość statystyki testowej z próby: [48.30834167]\n", + "Wartości statystyk z prób boostrapowych:\n", + "[0.35583403], [0.29159863], [-1.32145739], [0.13260175], [0.79403136], ... (i 95 pozostałych)\n", + "\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "p, t, ts = bootstrap_dependent(weights_before, weights_after)\n", + "ts = [x[0] for x in ts]\n", + "draw_distribution(ts, t)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "## Wniosek\n", + "\n", + "???" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "pycharm": { + "name": "#%%\n" + } + }, + "outputs": [], + "source": [] } ], "metadata": { "interpreter": { - "hash": "11938c6bc6919ae2720b4d5011047913343b08a43b18698fd82dedb0d4417594" + "hash": "1b132c2ed43285dcf39f6d01712959169a14a721cf314fe69015adab49bb1fd1" }, "kernelspec": { "display_name": "Python 3.8.10 64-bit", - "metadata": { - "interpreter": { - "hash": "767d51c1340bd893661ea55ea3124f6de3c7a262a8b4abca0554b478b1e2ff90" - } - }, + "language": "python", "name": "python3" }, "language_info": { @@ -621,7 +729,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.1" + "version": "3.8.10" } }, "nbformat": 4, diff --git a/experiment_data.csv b/experiment_data.csv index 7803fa8..edafebc 100644 --- a/experiment_data.csv +++ b/experiment_data.csv @@ -1,501 +1,501 @@ Weight before,Weight after,Male height,Female height -94.65,72.55,183.83,152.88 -85.63,119.64,157.09,138.14 -69.57,70.82,205.51,148.7 -59.23,62.22,178.77,176.52 -23.04,54.95,229.87,178.44 -41.96,65.77,178.56,170.29 -87.69,92.12,160.97,153.77 -23.6,67.21,123.92,165.65 -96.17,90.22,211.43,127.89 -32.02,68.08,164.72,207.55 -81.52,91.67,143.74,211.9 -49.49,74.99,142.57,117.28 -111.48,55.91,151.0,169.03 -103.29,64.59,124.73,162.07 -98.41,26.29,141.13,167.59 -55.69,112.81,210.93,154.73 -112.75,69.14,201.46,161.04 -61.9,78.48,123.8,165.84 -93.98,82.49,198.95,194.27 -30.32,79.6,205.72,176.77 -156.03,64.66,117.88,189.42 -91.66,60.93,178.56,173.03 -117.4,93.89,182.25,201.73 -111.3,86.4,143.76,146.82 -86.77,75.96,188.33,129.09 -85.01,69.71,192.77,216.31 -104.5,83.53,202.45,153.81 -74.93,88.73,216.67,152.48 -99.37,87.49,124.29,235.76 -61.75,70.46,165.1,264.41 -115.92,96.84,181.12,137.0 -108.17,11.55,186.18,184.3 -49.2,59.04,147.0,160.46 -97.34,96.89,159.61,116.04 -73.58,92.43,164.62,181.83 -72.23,67.53,160.2,167.6 -83.59,80.67,192.59,116.54 -62.15,87.32,173.94,189.97 -36.26,58.22,142.88,132.67 -19.95,63.46,171.54,139.81 -70.74,78.1,162.96,160.41 -98.38,81.38,171.19,202.46 -91.52,81.0,164.23,159.94 -74.19,61.25,171.05,118.92 -137.72,58.91,107.04,179.47 -49.5,28.77,152.9,180.96 -47.34,45.41,149.18,190.02 -115.34,62.53,165.38,140.1 -78.36,56.97,203.64,115.99 -98.46,107.7,160.68,181.58 -69.09,52.86,195.86,158.86 -110.1,86.81,217.24,143.66 -123.86,70.78,186.32,215.42 -55.12,58.74,194.3,134.13 -49.89,47.91,145.38,177.99 -106.64,43.91,172.47,186.02 -85.46,46.44,148.18,185.01 -25.17,69.09,191.67,202.62 -28.02,87.02,191.78,154.73 -50.77,107.23,169.7,157.06 -138.09,73.89,187.89,150.17 -68.63,52.33,183.53,200.46 -84.62,59.52,194.7,214.83 -96.16,49.11,194.41,158.56 -45.93,82.24,164.98,184.56 -29.67,52.86,203.88,149.16 -47.87,64.31,156.14,192.99 -76.39,110.4,225.16,189.92 -39.98,106.05,160.64,177.23 -142.65,110.76,154.78,158.12 -96.86,50.24,180.52,133.44 -78.83,79.85,168.82,176.48 -113.3,57.59,173.87,167.99 -31.69,72.82,153.51,110.87 -55.17,63.31,211.79,157.61 -44.93,79.61,175.93,149.69 -43.14,85.89,151.81,148.43 -93.38,68.36,144.09,163.6 -48.7,54.16,158.07,182.09 -61.53,74.41,156.91,135.67 -74.05,80.26,209.89,131.86 -85.51,35.54,206.7,145.54 -91.0,69.8,133.49,152.83 -35.36,54.92,183.47,133.77 -121.18,46.15,171.83,110.94 -101.35,65.64,163.5,117.8 -79.73,52.2,151.04,157.01 -23.66,92.72,158.51,138.15 -64.22,54.38,205.66,167.15 -107.4,81.52,154.5,95.18 -96.72,56.94,135.18,184.62 -85.99,50.18,122.59,182.75 -45.28,62.87,144.46,185.89 -138.5,95.61,198.09,171.96 -41.45,21.63,163.69,148.39 -102.4,54.34,148.89,180.09 -104.72,43.78,265.3,156.7 -72.09,69.03,183.14,187.05 -50.4,42.18,175.05,164.88 -120.62,54.17,154.41,178.49 -38.29,43.24,201.76,198.75 -80.31,77.61,149.42,184.43 -82.47,47.92,137.16,113.75 -98.56,54.95,191.85,124.03 -87.94,58.79,221.58,237.36 -111.64,94.53,156.43,135.98 -70.08,27.21,188.38,168.95 -98.04,52.76,183.95,108.7 -108.62,70.97,129.47,162.51 -111.56,74.11,208.25,172.3 -33.67,57.14,158.93,163.95 -116.8,51.81,198.46,145.81 -32.81,113.06,138.0,185.72 -109.34,66.28,193.16,227.87 -79.85,54.09,223.18,223.23 -85.46,84.13,150.92,152.63 -42.21,64.99,132.55,174.55 -115.17,73.57,117.04,159.8 -69.13,54.01,205.76,183.42 -122.07,74.15,264.82,220.11 -88.69,93.31,226.92,167.15 -60.27,78.85,204.8,173.5 -64.37,84.35,176.15,188.42 -42.37,85.01,182.16,198.59 -87.66,67.29,200.14,180.11 -76.06,53.62,215.4,170.26 -90.57,44.03,195.25,136.25 -68.14,59.62,164.71,158.55 --8.27,27.76,166.16,136.38 -70.47,73.79,179.63,159.16 -78.27,83.31,137.37,199.6 -59.81,82.09,185.67,142.9 -80.15,21.22,156.33,181.12 -86.36,69.79,214.68,160.89 -95.53,31.13,204.75,225.02 -85.14,9.18,136.72,144.57 -33.93,84.25,203.41,165.84 -75.97,39.26,154.72,185.17 -78.27,72.09,183.76,121.51 -83.09,59.44,184.55,196.62 -87.42,51.15,143.97,189.23 -125.23,87.01,195.56,172.42 -90.51,41.17,164.88,178.18 -100.62,87.54,201.14,171.68 -135.51,39.81,151.2,144.29 -76.21,40.76,142.47,164.84 -74.54,74.04,196.62,181.55 -53.19,48.49,202.38,163.4 -112.9,59.8,179.93,187.19 -86.12,34.71,171.61,218.13 -66.51,81.36,146.52,180.46 -21.65,54.2,179.6,166.95 -105.42,70.45,117.99,116.53 -103.42,75.08,176.68,181.34 -51.64,31.05,128.22,164.97 -94.84,81.96,197.04,161.79 -81.91,17.75,131.41,183.32 -25.0,59.55,143.04,196.48 -136.62,77.55,193.42,161.08 -84.46,71.99,101.03,204.59 -70.68,40.27,206.15,220.28 -54.32,60.05,173.17,231.2 -69.24,86.26,188.4,124.53 -101.03,76.85,153.04,137.45 -61.52,67.79,158.76,175.11 -56.67,65.42,169.92,159.84 -53.2,55.16,178.49,203.75 -69.25,77.88,172.41,165.22 -89.44,76.74,187.69,185.82 -47.08,70.9,128.14,149.73 --13.68,24.24,148.92,170.59 -103.55,65.61,162.05,187.61 -115.09,78.17,203.79,146.5 -84.27,68.02,192.74,161.12 -57.12,62.46,162.49,197.09 -25.38,83.6,137.11,157.64 -74.31,32.65,199.69,218.68 -66.43,47.58,194.65,142.31 -29.52,48.81,187.6,162.94 -123.91,78.35,193.67,127.23 -51.69,75.99,182.79,148.92 -80.18,50.4,198.58,180.85 -29.16,29.51,138.5,176.56 -46.62,117.95,177.98,135.42 -73.38,49.4,178.07,206.36 -117.83,71.84,203.65,168.0 -68.32,62.42,108.46,89.48 -78.7,57.59,244.7,124.97 -129.92,85.56,138.85,226.28 -114.31,79.86,140.04,150.13 -68.11,66.17,200.8,195.43 -52.93,35.43,110.69,178.04 -82.85,85.68,197.02,168.19 -87.14,106.65,186.91,140.93 -77.3,61.62,115.76,146.85 -63.42,58.25,180.27,138.26 -82.41,49.68,178.18,184.65 -103.54,84.75,180.2,167.91 -21.74,97.03,164.9,190.87 -101.94,57.31,176.96,172.74 -88.44,59.72,179.12,159.69 -35.55,93.31,214.91,208.81 -85.66,71.22,225.85,156.0 -141.36,97.2,169.87,225.0 -32.94,78.83,220.69,94.34 -69.1,93.12,165.98,172.54 -88.8,41.16,192.25,146.19 -105.95,34.46,188.58,123.67 -34.27,60.11,108.86,162.88 -89.81,102.12,125.52,127.65 -86.16,74.57,212.8,134.5 -53.31,53.63,233.09,153.7 -71.57,56.3,176.33,128.3 -91.53,90.91,182.78,133.49 -82.26,79.08,186.01,137.45 -52.1,72.07,152.47,170.02 -90.53,61.33,157.9,112.19 -80.71,76.0,170.22,154.63 -49.07,82.92,200.98,143.46 -66.94,30.04,207.39,182.36 -82.27,93.11,106.19,109.69 -127.99,71.66,200.8,129.26 -90.29,85.72,154.64,198.88 -109.93,61.7,234.7,151.44 -118.73,40.61,179.66,146.42 -37.85,50.43,197.24,141.72 -98.18,44.06,138.62,206.41 -112.01,68.9,105.0,113.15 -74.11,82.8,236.61,159.74 -106.06,45.23,219.94,93.88 -75.9,53.71,145.16,175.7 -61.16,71.42,195.57,158.18 --8.21,75.93,218.73,189.77 -26.69,56.12,149.95,113.68 -49.27,85.4,148.02,152.48 -67.45,70.72,191.63,162.27 -146.44,88.61,192.36,191.22 -73.22,93.69,159.68,144.29 -109.08,57.24,149.44,147.19 -45.67,75.85,179.69,183.54 -74.87,23.13,179.73,144.12 -88.79,93.4,127.88,169.94 -76.2,83.3,154.92,131.54 -117.76,33.41,170.86,159.23 -109.2,96.83,201.83,140.89 -134.41,69.6,175.71,182.42 -94.0,63.08,164.48,140.34 -42.22,54.73,131.04,119.63 -100.19,95.72,182.26,92.12 -87.07,86.94,176.16,157.7 -74.42,53.68,112.02,184.6 -48.62,74.39,186.42,154.43 -77.56,114.4,179.18,202.67 -107.69,70.7,205.89,119.1 -116.74,41.22,194.54,205.53 -108.7,87.37,173.64,137.61 -43.51,48.04,188.14,148.88 -91.05,36.16,128.28,163.35 -105.45,100.13,154.59,200.21 -28.75,92.38,199.46,173.99 -3.84,87.52,214.68,173.86 -82.73,69.6,150.49,133.88 -82.16,83.38,188.91,224.37 -103.73,72.48,163.6,105.24 -85.42,51.22,197.73,172.8 -39.52,31.14,187.43,179.55 -69.29,28.87,178.42,181.24 -76.03,72.3,193.07,100.1 -61.4,49.22,219.87,197.95 -37.63,40.78,202.86,162.63 -116.44,92.89,185.03,168.5 -127.24,56.83,158.81,120.74 -88.22,49.09,176.43,128.63 -74.7,45.3,149.79,121.13 -105.13,52.42,206.78,171.46 -50.88,42.18,158.49,168.31 -57.57,39.96,134.7,186.15 -117.2,56.82,194.48,95.82 -123.39,39.76,137.32,141.63 -70.86,66.46,171.97,210.65 -78.93,83.49,151.41,152.87 -98.56,80.65,164.09,133.94 -103.36,107.37,168.06,153.16 -81.02,66.76,201.01,169.66 -96.82,69.83,174.9,156.9 -42.08,42.57,175.42,194.12 -98.3,72.91,114.73,140.45 -33.64,77.41,180.53,165.45 --16.95,46.83,217.1,179.87 -155.65,50.7,159.4,169.86 -80.0,62.74,131.03,92.7 -61.4,69.28,165.86,136.81 -81.04,104.21,163.56,107.43 -143.0,48.29,149.6,141.45 -83.12,63.77,237.16,183.4 -113.95,45.42,191.17,202.44 -60.73,37.96,147.77,197.13 -88.97,26.07,210.83,176.79 -141.53,47.33,147.74,174.51 -71.05,83.51,216.77,171.2 -65.78,35.03,186.61,155.44 -4.33,60.2,151.32,187.29 -18.59,56.38,169.17,195.07 -62.5,98.76,172.34,122.93 -111.32,64.94,223.98,210.53 -121.35,56.94,176.26,194.41 -85.35,37.66,169.96,147.08 -112.56,59.13,200.75,189.97 -35.1,85.6,209.02,183.22 -74.46,69.51,181.55,193.22 -96.77,43.19,137.98,208.2 -101.36,41.06,132.92,176.47 -33.45,46.65,217.14,196.79 -53.16,72.75,220.5,148.69 -68.38,82.31,134.12,191.0 -81.73,68.68,165.16,101.85 -86.6,85.74,138.57,131.16 -86.6,26.5,99.16,157.4 -89.05,59.47,200.93,134.89 -76.83,67.01,116.38,179.42 -89.79,102.48,144.01,139.59 -65.69,93.41,204.85,171.5 -68.7,68.64,187.96,132.49 -101.33,97.64,153.37,133.0 -92.73,37.29,200.57,191.9 -62.45,73.23,132.23,156.07 -126.05,66.6,195.58,202.88 -112.63,63.67,201.33,51.0 -91.25,62.78,210.98,174.13 -75.72,61.52,184.99,175.64 -83.1,52.14,164.56,145.95 -33.19,59.39,203.96,118.63 -63.63,66.53,194.93,197.12 -57.45,83.41,128.45,158.19 -79.44,50.74,155.31,154.97 -71.68,52.4,176.17,120.47 -80.77,80.03,176.92,150.7 -80.74,63.66,154.64,151.47 -83.78,60.96,185.6,122.15 -138.78,60.1,154.22,168.13 -133.86,52.95,167.02,170.62 -115.67,52.68,190.79,125.01 -96.09,29.9,164.35,132.9 -26.87,36.53,192.26,184.13 -121.47,84.89,152.07,171.21 -161.82,68.84,146.24,163.71 -48.15,54.24,219.64,162.76 -108.97,96.45,174.31,223.53 -96.4,55.62,131.01,211.7 -128.5,83.31,180.48,131.42 -82.89,70.19,173.48,213.8 -104.02,45.72,162.74,188.34 -102.32,54.35,169.13,114.84 -58.21,77.93,160.45,159.73 -88.74,105.64,173.76,155.44 -83.38,45.04,225.41,194.8 -36.28,98.14,207.55,199.12 -83.63,64.44,180.34,131.73 -66.82,62.22,194.99,112.11 -25.46,57.69,191.24,170.45 -82.61,64.52,189.33,132.55 -105.0,67.71,159.09,204.29 -103.21,49.93,184.75,137.92 -66.96,74.57,169.13,135.1 -137.27,91.95,202.16,149.96 -89.7,67.58,185.14,178.38 -100.19,97.56,199.48,145.22 -72.82,45.82,166.46,153.66 -59.32,16.33,185.01,164.3 -88.96,62.48,165.69,241.23 -22.19,53.53,166.79,116.86 -99.57,59.58,190.34,169.22 -78.55,55.42,179.49,101.99 -59.03,47.56,177.14,167.59 -82.56,56.91,208.89,143.21 -50.52,70.4,201.78,92.68 -79.76,31.03,139.47,166.61 -21.9,104.8,158.97,183.48 -83.37,70.98,185.76,178.4 -92.42,53.55,182.74,176.02 -85.89,69.48,176.34,179.77 -63.64,68.38,172.51,185.99 -53.9,72.1,214.67,184.5 -148.48,64.7,212.89,144.96 -9.46,46.41,208.85,132.45 -72.72,53.05,183.2,202.31 -138.98,91.7,122.19,180.43 -119.41,18.03,176.3,133.31 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+man_heights = np.random.normal(175, 10, 500) +woman_heights = np.array([x-randint(1, 10) for x in man_heights]) + +weights_before = np.random.normal(80, 10, 500) +weights_after = np.array([x-randint(1, 5) for x in weights_before]) + +man_heights = np.round(man_heights, 2) +woman_heights = np.round(woman_heights, 2) +weights_before = np.round(weights_before, 2) +weights_after = np.round(weights_after, 2) + +dataset = pd.read_csv('experiment_data.csv') + +dataset['Weight before'] = weights_before +dataset['Weight after'] = weights_after + +dataset['Male height'] = man_heights +dataset['Female height'] = woman_heights + +dataset.to_csv("experiment_data2.csv", encoding="utf-8", index=False)