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Lab_8_hypotesis_testing_part_I.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "metadata": { | |
| "colab": { | |
| "name": "Lab_8_hypotesis_testing_part_I.ipynb", | |
| "provenance": [], | |
| "authorship_tag": "ABX9TyNdlh1w91qyB0RTcNKge5+t", | |
| "include_colab_link": true | |
| }, | |
| "kernelspec": { | |
| "name": "python3", | |
| "display_name": "Python 3" | |
| }, | |
| "language_info": { | |
| "name": "python" | |
| } | |
| }, | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/jamm1985/5a466632c28353d682bb0b61aeaf825d/lab_8_hypotesis_testing_part_i.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "PmwPjRsR5DIU" | |
| }, | |
| "source": [ | |
| "Видео лабораторной: https://youtu.be/JogmM2je_Sw\n", | |
| "\n", | |
| "TG: https://t.me/data_science_news" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "tOvcIRZS5JOo" | |
| }, | |
| "source": [ | |
| "\n", | |
| "\n", | |
| "---\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "GTaF6F8SKmhV" | |
| }, | |
| "source": [ | |
| "import numpy as np\n", | |
| "import matplotlib.pylab as plt\n", | |
| "from scipy.stats import norm\n", | |
| "\n", | |
| "plt.rcParams['figure.figsize'] = [12, 8]" | |
| ], | |
| "execution_count": 10, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Qfi9IA8cXPGT" | |
| }, | |
| "source": [ | |
| "## Задача 1 (простой односторонный асимтотический тест)\n", | |
| "\n", | |
| "На автомобильном заводе разрабатывают новую функцию двигателей для более экономного расхода топлива. Допустим, из передыдущих исследований известно, что на 1 литр топлива можно проехать 11 километров в стиле городской езды со стандартным отклонением 4.3. После внедрения нового механизма расхода топлива на 1 литр, в среднем, автомобили стали проезжать 11.3 километров. Нужно ли внедрять новые двигатели в производство или такой результат просто случайно получился? Предположим, что условия для применения центральной предельной теоремы удовлетворяются. Количество измерений равно 30.\n", | |
| " " | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "GVdxsg65YrzU" | |
| }, | |
| "source": [ | |
| "### Формализация задачи\n", | |
| "\n", | |
| "Средний расход топлива, при соблюдении технических условий, согласно CLT подчиняется нормальному распределению:\n", | |
| "\n", | |
| "$$\\frac{1}{n} \\Sigma_{i=1}^N=\\bar{X}_{N} \\sim N(\\mu,\\frac{\\sigma^2}{N})$$\n", | |
| "\n", | |
| "С нормализацией:\n", | |
| "\n", | |
| "$$\\left( \\sqrt{N}\\frac{\\bar{X}_{N}-\\mu}{\\sigma} \\right) \\sim N(0,1)$$\n", | |
| "\n", | |
| "По условию известно, то текущий расход $\\mu_0=11$, расход с новой функцией это $\\mu_A=11.3$.\n", | |
| "\n", | |
| "Для рещения задачи необходимо выполнить **тест** \n", | |
| "\n", | |
| "$$H_0: \\mu_A = \\mu_0\\ \\mathrm{VS}\\ H_A: \\mu_A > \\mu_0$$ \n", | |
| "\n", | |
| "где $H_0$ это нулевая гипотеза (средний расход топлива до внедрения улучшений в двигатель), $H_A$ альтернативная гипотеза.\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "VZm1W_j1fiHo" | |
| }, | |
| "source": [ | |
| "mu_0 = 11\n", | |
| "mu_a = 11.3\n", | |
| "sigma = 4.3\n", | |
| "N=30" | |
| ], | |
| "execution_count": 11, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 500 | |
| }, | |
| "id": "FW_8uUOdK5B-", | |
| "outputId": "4574dc72-2a2e-4c73-bbc4-c2b419ddfafc" | |
| }, | |
| "source": [ | |
| "x = np.linspace(10,12.5,1000)\n", | |
| "plt.plot(x,norm.pdf(x, mu_0, sigma/N), label=r\"$N(\\mu_0,\\frac{\\sigma}{N}$)\")\n", | |
| "plt.plot(x,norm.pdf(x, mu_a, sigma/N), label=r\"$N(\\mu_A,\\frac{\\sigma}{N}$)\")\n", | |
| "plt.vlines(mu_0,-0.02,+0.3, 'blue')\n", | |
| "plt.vlines(mu_a,-0.02,+0.3, 'orange')\n", | |
| "plt.ylabel('PDF', fontsize = 15)\n", | |
| "plt.legend(fontsize=15)" | |
| ], | |
| "execution_count": 12, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<matplotlib.legend.Legend at 0x7f7001f455d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 12 | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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\n", | |
| "text/plain": [ | |
| "<Figure size 864x576 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "wwwwMnfnh9wI" | |
| }, | |
| "source": [ | |
| "\n", | |
| "\n", | |
| "Source: https://www.scribbr.com/statistics/type-i-and-type-ii-errors/" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "UfiJ_HHhkW60" | |
| }, | |
| "source": [ | |
| "\n", | |
| "\n", | |
| "source: https://en.wikipedia.org/wiki/Type_I_and_type_II_errors" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Y7bC5f5Ai1bw" | |
| }, | |
| "source": [ | |
| "### Статистический критерий (test statistics)\n", | |
| "\n", | |
| "Зафиксируем уровень статистической значимости в 95%. Следовательно, ошибка первого рода равна $\\alpha=0.05$. То есть вероятность того, что мы отклоним нулевую гипотезу, при том что она истинна равна 5%.\n", | |
| "\n", | |
| "Или формально: $P(\\mathrm{reject\\ H_o}|\\mathrm{H_o\\ true})=0.05$\n", | |
| "\n", | |
| "Из этого следует:\n", | |
| "\n", | |
| "$$P \\left(\\sqrt{N} \\frac{\\bar{X}_{N_0} - \\mu_0}{\\sigma} \\geq \\sqrt{N} \\frac{\\bf{c} - \\mu_0}{\\sigma} \\right)=P \\left( Z \\geq \\sqrt{N} \\frac{\\bf{c} - \\mu_0}{\\sigma} \\right)=0.05$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "R9QW2ljBgLcc", | |
| "outputId": "10acbc12-d0de-4bb7-aead-179bb952f04c" | |
| }, | |
| "source": [ | |
| "norm.ppf(0.95)" | |
| ], | |
| "execution_count": 13, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "1.6448536269514722" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 13 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "SoU4M6KToAKw" | |
| }, | |
| "source": [ | |
| "5% квантиль стандартного нормального распределения равен $\\approx 1.65$, следовательно:\n", | |
| "\n", | |
| "$$P(Z \\geq q_{5\\%})=0.05 \\implies \\left(\\sqrt{N} \\frac{\\bf{c} - \\mu_0}{\\sigma} \\right)=1.65 \\implies \\bf{c} \\approx 12.3 $$\n", | |
| "\n", | |
| "Формально: критическая обалсть (rejection regeon) $$R\\{(x_1,...,x_n): T(x_1,...,x_n) > c \\}$$ где $x_1,...,x_n$ это набор данных, $T(\\cdot)$ это тест статистика. \n", | |
| "\n", | |
| "Для нашего примера $T(x_1,..,x_n)=\\bar{X}_N$, $c=12.3$, следовательно:\n", | |
| "\n", | |
| "$$R_{\\alpha=5\\%} = (12.3, \\infty)$$ это критическая область (rejection regeon)." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "MbO4hNKKn7kY", | |
| "outputId": "e95f1e03-3a9d-41c6-efa5-247f563c45e7" | |
| }, | |
| "source": [ | |
| "1.65*sigma/np.sqrt(N)+mu_0" | |
| ], | |
| "execution_count": 14, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "12.295363848499719" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 14 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "EMyFM4ybtNi9" | |
| }, | |
| "source": [ | |
| "\n", | |
| "\n", | |
| "Формально, статистический критерий выражен:\n", | |
| "\n", | |
| "$$\\psi_\\alpha=\\mathbb{1}\\left[\\left( \\sqrt{N} \\frac{\\bar{X}_{N_A} - \\mu_0}{\\sigma} \\right) > q_{5\\%}=1.65 \\right] = \\mathbb{1}\\left[\\bar{X}_{N_A} \\geq 12.3 \\right]$$\n", | |
| "\n", | |
| "Таким образом, мы должны отклонить нулевую гипотезу, если $\\bar{X}_{N_A} \\geq 12.3$. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "lzzxKTrBNHEe", | |
| "outputId": "b5563b4f-4700-4aa6-daf6-022aefd52f63" | |
| }, | |
| "source": [ | |
| "np.sqrt(N)*(11.3-mu_0)/sigma" | |
| ], | |
| "execution_count": 15, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "0.3821320168640703" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 15 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "hfFPOYqVR9mb" | |
| }, | |
| "source": [ | |
| "Таким образом:\n", | |
| "\n", | |
| "$$\\sqrt{N}\\frac{\\bar{X}_{N_A} - \\mu_0}{\\sigma} \\approx 0.38 < 1.65$$\n", | |
| "\n", | |
| "$$\\bar{X}_{N_A} = 11.3 < 12.3$$\n", | |
| "\n", | |
| "следовательно, **нулевая гипотеза сохраняется** на уровне занчимости 5%." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "MdFTAlCZttME" | |
| }, | |
| "source": [ | |
| "### $p$-value\n", | |
| "\n", | |
| "**Формально** предположим, что для любого $\\alpha \\in (0,1)$ мы имеем тест статистику порядка $\\alpha$ c критической областью (rejection regeon) $R_\\alpha$, такой что:\n", | |
| "\n", | |
| "$$p\\mathrm{-value}=\\mathrm{inf}\\{ \\alpha: T(X_n) \\in R_\\alpha\\}$$\n", | |
| "\n", | |
| "$p$-value это верятность, что нулевая гипотеза корректна на конкретной реализации, то есть, это такой минимальный уровень занчимости, $\\alpha$, при котором мы можем отклонить нулевую гипотезу. \n", | |
| "\n", | |
| "Для нашего примера:\n", | |
| "\n", | |
| "$$p=P\\left(Z \\geq \\sqrt{N} \\frac{\\bar{X}_{N_A} - \\mu_0}{\\sigma} |\\mathrm{H_0\\ true} \\right)=0.35$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "3r9uvxVRL4__", | |
| "outputId": "11973e66-8b41-445a-a22e-f025c722d0bb" | |
| }, | |
| "source": [ | |
| "1 - norm.cdf(np.sqrt(N)*(11.3-mu_0)/sigma)" | |
| ], | |
| "execution_count": 16, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "0.35118172230334943" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 16 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "aEFtRf9z1okN" | |
| }, | |
| "source": [ | |
| "## Задача 2 (простой двусторонний асимтотический тест)\n", | |
| "\n", | |
| "На мебельной фабрике выбирают поставщика материалов ДСП. Для текущих проектов необходима толщина материала в 5 мм с допустимым стандартным отклонением в 0.01. У поставщика отобрали 30 изделий, котрые в среднем имеют толщину 4.99 мм. Стоит ли выбрать этого поставщика для поставок?" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "jksHP5cJDfER" | |
| }, | |
| "source": [ | |
| "mu_0 = 5.0000\n", | |
| "mu_a = 4.9900\n", | |
| "sigma = 0.01\n", | |
| "N=30" | |
| ], | |
| "execution_count": 17, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "LvJTasu-736Z" | |
| }, | |
| "source": [ | |
| "### Формализация задачи и статистический критерий\n", | |
| "\n", | |
| "Толщина изделия должна составлять 5 мм, следовательно, любое отклонение выше допустимого не может удовлетворять потребности производства. \n", | |
| "\n", | |
| "Зафиксируем уровень значимости $\\alpha=0.05$.\n", | |
| "\n", | |
| "По условию задачи $H_0=\\mu_0=5.0$\n", | |
| "\n", | |
| "Для рещения задачи необходимо выполнить **тест** \n", | |
| "\n", | |
| "$$H_0: \\mu_A = \\mu_0\\ \\mathrm{VS}\\ H_A: \\mu_A \\neq \\mu_0$$ \n", | |
| "\n", | |
| "Из данных известно: $$\\frac{1}{n} \\Sigma_{i=1}^N=\\bar{X}_{N} \\sim N(\\mu,\\frac{\\sigma^2}{n})$$\n", | |
| "\n", | |
| "С нормализацией:\n", | |
| "\n", | |
| "$$\\left( \\sqrt{N}\\frac{\\bar{X}_{N}-\\mu}{\\sigma} \\right) \\sim N(0,1)$$\n", | |
| "\n", | |
| "Таким образом:\n", | |
| "\n", | |
| "$$P(\\mathrm{reject\\ H_o}|\\mathrm{H_o\\ true})= P \\left(\\sqrt{N} \\frac{{c^-} - \\mu_0}{\\sigma} \\geq \\sqrt{N} \\frac{\\bar{X}_{N_0} - \\mu_0}{\\sigma} \\geq \\sqrt{N} \\frac{{c^+} - \\mu_0}{\\sigma} \\right)=P \\left(\\sqrt{N} \\frac{{c^-} - \\mu_0}{\\sigma}\\geq Z \\geq \\sqrt{N} \\frac{{c^+} - \\mu_0}{\\sigma} \\right) = 0.05$$\n", | |
| "\n", | |
| "Или\n", | |
| "\n", | |
| "$$P \\left(|Z| \\geq q_{\\frac{\\alpha=5\\%}{2}}\\right)=0.05$$\n", | |
| "\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "IcTB-ZzCV1m0" | |
| }, | |
| "source": [ | |
| "\n", | |
| "\n", | |
| "Source: https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-the-differences-between-one-tailed-and-two-tailed-tests/" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "QuSiAXK_vmib", | |
| "outputId": "64378abb-efa7-4c33-9824-cac51076588a" | |
| }, | |
| "source": [ | |
| "norm.ppf(0.975)" | |
| ], | |
| "execution_count": 18, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "1.959963984540054" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 18 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "4dYK3dnSDQNC", | |
| "outputId": "2f994315-8a45-4965-e7a3-02d0568bb62a" | |
| }, | |
| "source": [ | |
| "1.96*sigma/np.sqrt(N)+mu_0" | |
| ], | |
| "execution_count": 19, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "5.003578454042367" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 19 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "LTgjki-QDsRF", | |
| "outputId": "74498427-9c32-4824-9b2f-eea2cae0ac1a" | |
| }, | |
| "source": [ | |
| "-1.96*sigma/np.sqrt(N)+mu_0" | |
| ], | |
| "execution_count": 20, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "4.996421545957633" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 20 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "4_9oj3-IKn6U" | |
| }, | |
| "source": [ | |
| "\n", | |
| "Следовательно:\n", | |
| "\n", | |
| "$$q_{\\frac{\\alpha=5\\%}{2}} \\approx 1.96 \\implies c^-=4.9964, c^+=5.0036$$\n", | |
| "\n", | |
| "Где $R_{\\frac{\\alpha=5\\%}{2}} \\in (-\\infty, 4.9964) \\cup (5.0036, +\\infty)$ критическая область (rejection regeon)\n", | |
| "\n", | |
| "Статистический критерий:\n", | |
| "\n", | |
| "$$\\psi_\\alpha=\\mathbb{1}\\left[\\left( \\sqrt{N} \\frac{|\\bar{X}_{N_A} - \\mu_0|}{\\sigma} \\right) > q_{\\frac{\\alpha=5\\%}{2}}=1.96 \\right] = \\mathbb{1}\\left[(\\bar{X}_{N_A} \\leq 4.9964) \\vee (\\bar{X}_{N_A} \\geq 5.0036) \\right]$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "mJtw-MOXGw0S", | |
| "outputId": "11e0f408-4489-42fa-d06f-e68ebd159d47" | |
| }, | |
| "source": [ | |
| "np.sqrt(N)*(np.abs(4.99-mu_0))/sigma" | |
| ], | |
| "execution_count": 21, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "5.477225575051545" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 21 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "rBXnkHHNK223", | |
| "outputId": "1a3e084f-74a3-4fe6-cdcf-8b5c7955ed70" | |
| }, | |
| "source": [ | |
| "1 - norm.cdf(np.sqrt(N)*(np.abs(4.99-mu_0))/sigma)" | |
| ], | |
| "execution_count": 22, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "2.1602315269930727e-08" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 22 | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "JYwOYpWeWzN8" | |
| }, | |
| "source": [ | |
| "$$ \\sqrt{N} \\frac{|\\bar{X}_{N_A} - \\mu_0|}{\\sigma} \\approx 5.48 > 1.96 $$\n", | |
| "\n", | |
| "$$\\bar{X}_{N_A} = 4.99 \\in R_N^- $$\n", | |
| "\n", | |
| "$$p=2.16*10^{-8}$$\n", | |
| "\n", | |
| "Следовательно, мы **отвергаем нулевую гипотезу** на уровне значимости 5%." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "FIPDMZeZLLxE" | |
| }, | |
| "source": [ | |
| "" | |
| ], | |
| "execution_count": null, | |
| "outputs": [] | |
| } | |
| ] | |
| } |
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