applied_statistics

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{
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 "cells": [
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  {
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   "cell_type": "code",
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   "execution_count": 2,
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   "metadata": {
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    "tags": []
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   },
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   "outputs": [],
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   "source": [
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    "import numpy\n",
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    "import math\n",
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    "\n",
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    "from scipy.stats import norm, gamma, kstest\n",
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    "\n",
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    "from statsmodels.stats.proportion import proportion_confint\n",
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    "from matplotlib import pyplot\n",
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    "\n",
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    "from tqdm import tqdm\n",
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    "\n",
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    "from collections import namedtuple\n",
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    "\n",
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    "numpy.random.seed(42)"
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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": 3,
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   "metadata": {
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    "tags": []
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   },
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   "outputs": [],
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   "source": [
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    "def inverse_plot_colorscheme():\n",
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    "    import cycler\n",
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    "    def invert(color_to_convert): \n",
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    "        table = str.maketrans('0123456789abcdef', 'fedcba9876543210')\n",
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    "        return '#' + color_to_convert[1:].lower().translate(table).upper()\n",
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    "    update_dict = {}\n",
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    "    for key, value in pyplot.rcParams.items():\n",
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    "        if value == 'black':\n",
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    "            update_dict[key] = 'white'\n",
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    "        elif value == 'white':\n",
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    "            update_dict[key] = 'black'\n",
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    "    \n",
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    "    old_cycle = pyplot.rcParams['axes.prop_cycle']\n",
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    "    new_cycle = []\n",
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    "    for value in old_cycle:\n",
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    "        new_cycle.append({\n",
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    "            'color': invert(value['color'])\n",
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    "        })\n",
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    "    pyplot.rcParams.update(update_dict)\n",
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    "    pyplot.rcParams['axes.prop_cycle'] = cycler.Cycler(new_cycle)\n",
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    "    lec = pyplot.rcParams['legend.edgecolor']\n",
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    "    lec = str(1 - float(lec))\n",
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    "    pyplot.rcParams['legend.edgecolor'] = lec"
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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": 4,
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   "metadata": {
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    "tags": []
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   },
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   "outputs": [],
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   "source": [
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    "inverse_plot_colorscheme()"
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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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    "tags": []
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   },
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   "source": [
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    "# Критерии однородности и критерий Колмогорова-Смирнова"
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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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   "source": [
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    "## Критерии однородности"
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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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   "source": [
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    "> **Задача**\n",
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    ">\n",
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    "> Первая выборка — артериальное давление контрольной группы (набора пациентов, которым вводилось плацебо). Вторая выборка — артериальное давление тестовой группы (набора пациентов, которым вводилось лекарство). Нужно проверить, влияет ли вводимое лекарство на артериальное давление?"
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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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   "source": [
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    "Конечно, мы можем решать такую задачу с помощью T-test. Но артериальное давление от введения лекарства по некоторым разрезам пациентов может стать выше, по некоторым ниже, и среднее может не измениться. Что же делать?"
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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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   "source": [
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    "Мы можем воспользоваться критерием однородности. Он позволяет проверить, действительно ли наблюдаемые выборки получены из одного и того же неизвестного распределения. Давайте формализуем постановку задачи критерия однородности. \n",
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    "\n",
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    "Пусть есть 2 реализации выборки: \n",
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    "- $x_1, \\dots, x_n$: реализация выборки $X$ случайных величин $X_1, \\dots, X_n$, каждая из которых распределена как $\\mathcal{P}_X$.\n",
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    "- $y_1, \\dots, y_m$: реализация выборки $Y$ случайных величин $Y_1, \\dots, Y_m$, каждая из которых распределена как $\\mathcal{P}_Y$.\n",
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    "\n",
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    "Критерий согласия проверяет равенство истинных распределений:\n",
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    "\n",
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    " - $H_0: \\mathcal{P}_X = \\mathcal{P}_Y$\n",
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    " - $H_1: \\mathcal{P}_X \\neq \\mathcal{P}_Y$.\n",
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    " \n",
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    "Либо, [аналогично](https://stats.stackexchange.com/questions/136658/why-does-a-cumulative-distribution-function-cdf-uniquely-define-a-distribution), равенство их функций распределения:\n",
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    "\n",
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    " - $H_0: F_X = F_Y$\n",
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    " - $H_1: F_X \\neq F_Y$."
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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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    "tags": []
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   },
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   "source": [
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    "## Критерий Колмогорова-Смирнова"
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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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    "tags": []
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   },
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   "source": [
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    "### Два вида однородности"
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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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   "source": [
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    "\n",
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    "При проверке гипотезы однородности двух выборок $X_1, X_2, \\dots, X_n$ и $Y_1, Y_2, \\dots, Y_m$ стоит понять, с чем мы имеем дело: реализациями независимых между собой случайных величин или парными повторными наблюдениями.\n",
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    "\n",
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    "В качестве примера можем рассмотреть другую постановку задачи определения влияния лекарства на артериальное давление пациентов. \n",
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    "\n",
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    "Давайте сравним две постановки эксперимента:\n",
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    "1. Первая выборка — артериальное давление контрольной группы (набора пациентов, которым вводилось плацебо). Вторая выборка — артериальное давление тестовой группы (набора пациентов, которым вводилось лекарство). То есть случайные величины, из которых получена выборка, независимы.\n",
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    "2. Первая выборка — артериальное давление пациентов до введения лекарства. Вторая выборка — артериальное давление тех же самых пациентов после введения лекарства. Cлучайные величины $Х_і$ и $Y_і$ нельзя считать независимыми, так как они относятся к одному и тому же человеку.\n",
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    "\n",
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    "Критерий, который мы будем рассматривать в дальнейшем, относится только к первой постановке: все случайные величины $X_1, X_2, \\dots, X_n,Y_1, Y_2, \\dots, Y_m$ независимы в совокупности. Использовать критерий для парных повторных наблюдений будет ошибкой. В дальнейшем мы обязательно это проверим.\n",
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    "\n"
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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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   "source": [
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    "### Придумываем статистику"
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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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   "source": [
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    "Постановка задачи очень напоминает простой критерий согласия, который в случае непрерывной функции распределения мы решать уже научились. Давайте вспомним, как же мы строили статистику в критерии согласия Колмогорова?"
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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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   "source": [
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    "> В критерии согласия Колмогорова для проверки того, что реализация выборки $x_1, x_2, \\dots, x_n$ получена из распределения $\\mathcal{P}_0$ с функцией распределения $F_0$ мы использовали статистику $$\n",
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    "    D_n = \\underset{x \\in \\mathbb{R}}{\\sup} |\\widehat{{F_X}_n}(x) - F_0(x)|\n",
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    "$$ \n",
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    "> Эта статистика показывала наибольший модуль разности между эмпирической и теоретической функциями распредения."
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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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   "source": [
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    "В критерии однородности вместо известной функции распределения $F_0$ у нас имеется 2 неизвестных функции распределения $F_X$ и $F_Y$, которые мы также можем приблизить эмпирическими функциями распределения $\\widehat{{F_X}_n}$ и $\\widehat{{F_Y}_m}$. Давайте приспособим статистику из критерия согласия Колмогорова для нашего нового критерия однородности:\n",
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    "$$D_{nm} = \\underset{x \\in \\mathbb{R}}{\\sup} |\\widehat{{F_X}_n}(x) - \\widehat{{F_Y}_m}(x)|,$$ \n",
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    "\n",
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    "где $\\widehat{{F_X}_n}(x) = \\frac{1}{n}\\sum_i[X_i \\leqslant x]$, и $\\widehat{{F_Y}_m}(x) = \\frac{1}{m}\\sum_i[Y_i \\leqslant x]$."
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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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   "source": [
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    "Очевидно, что слишком большое расстояние будет противоречить гипотезе $H_0$."
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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": 5,
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   "metadata": {
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    "tags": []
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   },
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   "outputs": [],
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   "source": [
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    "x_axis = numpy.arange(start=-3, stop=3, step=0.001)\n",
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    "\n",
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    "# аппроксимируем CDF распределения, из которого семплирована наша выборка\n",
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    "# эмпирическая функция распределения:\n",
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    "X = norm().rvs(100)\n",
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    "Y = norm().rvs(100)\n",
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    "\n",
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    "emp_cdf_X = []\n",
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    "emp_cdf_Y = []\n",
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    "for x in x_axis:\n",
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    "    cdf_X= sum([int(b <= x) for b in X]) / len(X)\n",
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    "    emp_cdf_X.append(cdf_X)\n",
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    "    cdf_Y = sum([int(b <= x) for b in Y]) / len(Y)\n",
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    "    emp_cdf_Y.append(cdf_Y)"
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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": 6,
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   "metadata": {
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    "tags": []
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   },
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   "outputs": [
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    {
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     "data": {
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      "image/png": 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\n",
233
      "text/plain": [
234
       "<Figure size 1152x576 with 1 Axes>"
235
      ]
236
     },
237
     "metadata": {
238
      "needs_background": "dark"
239
     },
240
     "output_type": "display_data"
241
    }
242
   ],
243
   "source": [
244
    "pyplot.figure(figsize=(16, 8))\n",
245
    "\n",
246
    "\n",
247
    "pyplot.plot(x_axis, emp_cdf_X, color = 'white', linestyle = '-', \n",
248
    "            linewidth=2.0, label='empirical cdf for X')\n",
249
    "pyplot.plot(x_axis, emp_cdf_Y, color = 'salmon', linestyle = '-',  \n",
250
    "            linewidth=2.0, label='empirical cdf for Y')\n",
251
    "\n",
252
    "pyplot.legend(loc='best')\n",
253
    "pyplot.title(\"Empirical distributions of 2 samples\")\n",
254
    "pyplot.xlabel(\"X\")\n",
255
    "pyplot.ylabel(\"Cumulative probability\")\n",
256
    "\n",
257
    "pyplot.show()"
258
   ]
259
  },
260
  {
261
   "cell_type": "markdown",
262
   "metadata": {},
263
   "source": [
264
    "Мы видим на графике эмпирические функции распределения для двух выборок. Как же нам понять, достаточно ли большое расстояние между ними, чтобы мы могли отвергнуть гипотезу о равенстве распределений?"
265
   ]
266
  },
267
  {
268
   "cell_type": "markdown",
269
   "metadata": {},
270
   "source": [
271
    "### Распределение статистики"
272
   ]
273
  },
274
  {
275
   "cell_type": "markdown",
276
   "metadata": {},
277
   "source": [
278
    "[Н. В. Смирнов](https://ru.wikipedia.org/wiki/%D0%A1%D0%BC%D0%B8%D1%80%D0%BD%D0%BE%D0%B2,_%D0%9D%D0%B8%D0%BA%D0%BE%D0%BB%D0%B0%D0%B9_%D0%92%D0%B0%D1%81%D0%B8%D0%BB%D1%8C%D0%B5%D0%B2%D0%B8%D1%87_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)) в 1939 году показал, что при выполнении следующих условий:\n",
279
    "1. Случайные величины $X_1, X_2, \\dots, X_n$ независимы и имеют общую функцию распределения $F_X$.\n",
280
    "2. Случайные величины $Y_1, Y_2, \\dots, Y_m$ независимы и имеют общую функцию распределения $F_Y$.\n",
281
    "3. Функции распределения $F_X$ и $F_Y$ неизвестны, но принадлежат множеству всех **непрерывных функций распределения**.\n",
282
    "4. Все компоненты случайного вектора ($X_1, \\dots, X_n, Y_1, \\dots, Y_m$) **независимы** (условие, которое мы обсудили в разделе \"Два вида однородности\")."
283
   ]
284
  },
285
  {
286
   "cell_type": "markdown",
287
   "metadata": {},
288
   "source": [
289
    "А также при выполнении нулевой гипотезы $H_0: F_X = F_Y$ статистика \n",
290
    "\n",
291
    "$$\\sqrt\\frac{nm}{m+n} D_{mn} \\stackrel{d}{\\rightarrow} \\phi,$$ \n",
292
    "\n",
293
    "где $\\phi$ имеет распределение Колмогорова: \n",
294
    "\n",
295
    "$$F_\\phi(x) = \\begin{equation*} \n",
296
    " \\begin{cases}\n",
297
    "  \\sum\\limits_{k=-\\infty}^ \\infty (-1)^k e^{-2k^2 x^2}, &\\text{ $ x > 0$}\\\\\n",
298
    "   0, &\\text{ $ x < 0$}\n",
299
    " \\end{cases}\n",
300
    "\\end{equation*}$$"
301
   ]
302
  },
303
  {
304
   "cell_type": "markdown",
305
   "metadata": {},
306
   "source": [
307
    "Мы знаем статистику и ее распределение при нулевой гипотезе, а это значит, что мы овладели умением проверять гипотезу однородности с помощью нового критерия! \n",
308
    "\n",
309
    "Если статистика $\\sqrt {\\frac {nm}{m+n}}D_{mn}$ превышает квантиль распределения Колмогорова $K_{\\alpha}$ для заданного уровня значимости $\\alpha$ и достаточно больших $n$ и $m$, то нулевая гипотеза $H_0$ об однородности выборок отвергается на уровне значимости $\\alpha$."
310
   ]
311
  },
312
  {
313
   "cell_type": "markdown",
314
   "metadata": {},
315
   "source": [
316
    "# Применение критерия Колмогорова-Смирнова на практике"
317
   ]
318
  },
319
  {
320
   "cell_type": "markdown",
321
   "metadata": {},
322
   "source": [
323
    "Давайте еще раз сформулируем критерий и условия его применимости простыми словами.\n",
324
    "\n",
325
    "Мы берем наибольшее расхождение между эмпирическими функциями распределений, домножаем его на функцию от размеров выборок и сравниваем с квантилем распределения Колмогорова. Если статистика выше квантиля, то гипотеза отвергается. \n",
326
    "\n",
327
    "Нужно помнить, что выборки должны быть получены из непрерывных распределений и независимы!"
328
   ]
329
  },
330
  {
331
   "cell_type": "markdown",
332
   "metadata": {},
333
   "source": [
334
    "## Достаточный размер выборки для применимости критерия"
335
   ]
336
  },
337
  {
338
   "cell_type": "markdown",
339
   "metadata": {},
340
   "source": [
341
    "Давайте теперь попробуем применить вышеописанный критерий. Мы вычитали в книжке М. Б. Лагутина *\"Наглядная математическая статистика\"*, что критерий можно применять начиная с $n, m \\geq 20$. Проверим, так ли это?"
342
   ]
343
  },
344
  {
345
   "cell_type": "markdown",
346
   "metadata": {},
347
   "source": [
348
    "Будем решать задачу про влияние лекарства на артериальное давление для независимых выборок, поставленную в начале статьи."
349
   ]
350
  },
351
  {
352
   "cell_type": "markdown",
353
   "metadata": {},
354
   "source": [
355
    "Давайте проведем АА-тест на синтетических данных, которые мы смоделируем из какого-нибудь распределения. Например, возьмем в качестве распределения артериального давления пациентов гамма-распределение с параметрами $(5, 110)$. Нарисуем плотность такого распределения, чтобы вспомнить, как оно выглядит."
356
   ]
357
  },
358
  {
359
   "cell_type": "code",
360
   "execution_count": 7,
361
   "metadata": {
362
    "tags": []
363
   },
364
   "outputs": [
365
    {
366
     "data": {
367
      "image/png": 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\n",
368
      "text/plain": [
369
       "<Figure size 1152x576 with 1 Axes>"
370
      ]
371
     },
372
     "metadata": {
373
      "needs_background": "dark"
374
     },
375
     "output_type": "display_data"
376
    }
377
   ],
378
   "source": [
379
    "X = gamma(5, 110).rvs(1000000)\n",
380
    "\n",
381
    "pyplot.figure(figsize=(16, 8))\n",
382
    "\n",
383
    "pyplot.hist(X, bins = 300, color = 'white', density= True)\n",
384
    "pyplot.title(\"Gamma (5, 110)\")\n",
385
    "pyplot.xlabel(\"Arterial pressure\")\n",
386
    "pyplot.ylabel(\"Density\")\n",
387
    "\n",
388
    "pyplot.show()"
389
   ]
390
  },
391
  {
392
   "cell_type": "markdown",
393
   "metadata": {},
394
   "source": [
395
    "В контрольной группе n пользователей, которым ввели лекарство. В тестовой группе m пользователей, которым ввели плацебо. При этом лекарство воздействия на артериальное давление не имеет."
396
   ]
397
  },
398
  {
399
   "cell_type": "markdown",
400
   "metadata": {},
401
   "source": [
402
    "Проверять будем с помощью функции [kstest](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html) из пакета scipy.stats."
403
   ]
404
  },
405
  {
406
   "cell_type": "code",
407
   "execution_count": 8,
408
   "metadata": {
409
    "tags": []
410
   },
411
   "outputs": [],
412
   "source": [
413
    "MonteCarloResults= namedtuple('MonteCarloResults', ['positive_rate',\n",
414
    "                                                    'confint_left_bound',\n",
415
    "                                                    'confint_right_bound'])\n",
416
    "\n",
417
    "def gen_monte_carlo_exp_for_ks(n, m, alpha, N_runs, latent_dist_X, \n",
418
    "                               latent_dist_Y):\n",
419
    "    \"\"\"\n",
420
    "        Функция для проверки критерия Колмогорова-Смирнова\n",
421
    "            с помощью метода Монте-Карло\n",
422
    "            \n",
423
    "        Возвращает долю отвержений гипотезы, и доверительный интервал для этой доли\n",
424
    "    \n",
425
    "        Параметры:\n",
426
    "            - n: размер выборки X\n",
427
    "            - m: размер выборки Y\n",
428
    "            - alpha: уровень значимости\n",
429
    "            - N_runs: число экспериментов в методе Монте-Карло\n",
430
    "            - latent_dist_X: распределение выборки X\n",
431
    "            - latent_dist_Y: распределение выборки Y\n",
432
    "    \"\"\"\n",
433
    "    \n",
434
    "    positive = 0\n",
435
    "    \n",
436
    "    for _ in range(N_runs): \n",
437
    "\n",
438
    "        X = latent_dist_X.rvs(n)\n",
439
    "        Y = latent_dist_Y.rvs(m)\n",
440
    "    \n",
441
    "        pvalue = kstest(X, Y)[1]\n",
442
    "    \n",
443
    "        if pvalue<=alpha:\n",
444
    "            positive+=1\n",
445
    "            \n",
446
    "    positive_rate = positive/N_runs\n",
447
    "    confint = proportion_confint(count = positive, nobs = N_runs, \n",
448
    "                                 alpha = 0.05, method='wilson')\n",
449
    "        \n",
450
    "    return MonteCarloResults(**{'positive_rate': positive_rate, \n",
451
    "                                'confint_left_bound': confint[0], \n",
452
    "                                'confint_right_bound': confint[1]})"
453
   ]
454
  },
455
  {
456
   "cell_type": "code",
457
   "execution_count": 9,
458
   "metadata": {
459
    "tags": []
460
   },
461
   "outputs": [
462
    {
463
     "name": "stdout",
464
     "output_type": "stream",
465
     "text": [
466
      "FPR:  0.0337\n",
467
      "FPR confint:  (0.031287239432944404, 0.036291853392978767)\n"
468
     ]
469
    }
470
   ],
471
   "source": [
472
    "(positive_rate, \n",
473
    " confint_left_bound, \n",
474
    " confint_right_bound) = gen_monte_carlo_exp_for_ks(n = 20, \n",
475
    "                                                   m = 20,\n",
476
    "                                                   alpha = 0.05,\n",
477
    "                                                   N_runs = 20000,\n",
478
    "                                                   latent_dist_X = gamma(5, 110),\n",
479
    "                                                   latent_dist_Y = gamma(5, 110))\n",
480
    "\n",
481
    "print('FPR: ', positive_rate)\n",
482
    "print('FPR confint: ', (confint_left_bound, confint_right_bound))"
483
   ]
484
  },
485
  {
486
   "cell_type": "markdown",
487
   "metadata": {},
488
   "source": [
489
    "Видим, что получили $\\it{\\text{FPR}}$ меньше заявленной $\\alpha = 0.05$. Критерий корректен, но заниженный $\\it{\\text{FPR}}$ — это неприятно: его мощность будет меньше, чем у критерия с $\\it{\\text{FPR}}$ близким к $\\alpha$."
490
   ]
491
  },
492
  {
493
   "cell_type": "markdown",
494
   "metadata": {},
495
   "source": [
496
    "Давайте теперь проверим корректность критерия для стандартного нормального распределения вместо гамма-распределения:"
497
   ]
498
  },
499
  {
500
   "cell_type": "code",
501
   "execution_count": 10,
502
   "metadata": {
503
    "tags": []
504
   },
505
   "outputs": [
506
    {
507
     "name": "stdout",
508
     "output_type": "stream",
509
     "text": [
510
      "FPR:  0.0338\n",
511
      "FPR confint:  (0.031383645299605384, 0.03639540911910656)\n"
512
     ]
513
    }
514
   ],
515
   "source": [
516
    "(positive_rate, \n",
517
    " confint_left_bound, \n",
518
    " confint_right_bound) = gen_monte_carlo_exp_for_ks(n = 20,\n",
519
    "                                                   m = 20,\n",
520
    "                                                   alpha = 0.05,\n",
521
    "                                                   N_runs = 20000,\n",
522
    "                                                   latent_dist_X = norm(),\n",
523
    "                                                   latent_dist_Y = norm())\n",
524
    "\n",
525
    "print('FPR: ', positive_rate)\n",
526
    "print('FPR confint: ', (confint_left_bound, confint_right_bound))"
527
   ]
528
  },
529
  {
530
   "cell_type": "markdown",
531
   "metadata": {},
532
   "source": [
533
    "Результат аналогичный: критерий корректен, но доверительный интервал для FPR снова не включает $\\alpha$, что является симптомом заниженной мощности."
534
   ]
535
  },
536
  {
537
   "cell_type": "markdown",
538
   "metadata": {},
539
   "source": [
540
    "На самом деле, результат AA-теста не будет зависеть от формы распределений, поэтому для любых $n$ и $m$ мы можем с помощью метода Монте-Карло получить критические значения, которые будут давать $\\alpha$, близкую к требуемой: провести большое число экспериментов и взять наиболее экстремальные $\\alpha$ процентов. Таким образом, мы создадим свой табличный критерий, который будет корректен для фиксированных $n$ и $m$."
541
   ]
542
  },
543
  {
544
   "cell_type": "markdown",
545
   "metadata": {},
546
   "source": [
547
    "**Вывод: для небольших n и m критерий корректный, но имеет заниженный $\\it{\\text{FPR}}$.**"
548
   ]
549
  },
550
  {
551
   "cell_type": "markdown",
552
   "metadata": {},
553
   "source": [
554
    "Для какого размера выборки пациентов в нашем тесте $n$ и $m$ мы можем применить критерий, чтобы $\\it{\\text{FPR}}$ слабо отличался от $\\alpha$? Давайте вместе узнаем это с помощью метода Монте-Карло!"
555
   ]
556
  },
557
  {
558
   "cell_type": "code",
559
   "execution_count": 10,
560
   "metadata": {
561
    "tags": []
562
   },
563
   "outputs": [
564
    {
565
     "name": "stderr",
566
     "output_type": "stream",
567
     "text": [
568
      "100%|██████████| 10/10 [03:05<00:00, 18.57s/it]\n"
569
     ]
570
    }
571
   ],
572
   "source": [
573
    "FPR_list = []\n",
574
    "\n",
575
    "numpy_ceil = numpy.vectorize(math.ceil)\n",
576
    "\n",
577
    "# перебираем размер выборки с логарифмическим шагом\n",
578
    "for i in tqdm(numpy_ceil(numpy.geomspace(10, 3000, 10))):  \n",
579
    "    mmk_res = gen_monte_carlo_exp_for_ks(n = i, m = i, \n",
580
    "                                         alpha = 0.05,\n",
581
    "                                         N_runs = 30000,\n",
582
    "                                         latent_dist_X = gamma(1, 2),\n",
583
    "                                         latent_dist_Y = gamma(1, 2))\n",
584
    "    FPR_list.append([i, mmk_res])"
585
   ]
586
  },
587
  {
588
   "cell_type": "code",
589
   "execution_count": 14,
590
   "metadata": {
591
    "tags": []
592
   },
593
   "outputs": [
594
    {
595
     "data": {
596
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AAACOYYISAAAAAAAAgGP+D9LEGVKzD+TsAAAAAElFTkSuQmCC",
597
      "text/plain": [
598
       "<Figure size 1600x800 with 1 Axes>"
599
      ]
600
     },
601
     "metadata": {},
602
     "output_type": "display_data"
603
    }
604
   ],
605
   "source": [
606
    "pyplot.figure(figsize=(16, 8))\n",
607
    "\n",
608
    "\n",
609
    "pyplot.plot([elem[0] for elem in FPR_list], \n",
610
    "            [elem[1].positive_rate for elem in FPR_list], \n",
611
    "            color = 'white', linewidth=3.0, label='FPR')\n",
612
    "pyplot.fill_between([elem[0] for elem in FPR_list], \n",
613
    "                    [elem[1].confint_left_bound for elem in FPR_list], \n",
614
    "                    [elem[1].confint_right_bound for elem in FPR_list], \n",
615
    "                    color = 'violet', alpha = 0.3, label='FPR confint')\n",
616
    "pyplot.plot([elem[0] for elem in FPR_list], numpy.array([0.05]*len(FPR_list)),\n",
617
    "            color = 'yellow', linestyle = 'dashed', \n",
618
    "            linewidth=3.0, label='alpha')\n",
619
    "\n",
620
    "pyplot.legend(loc='best')\n",
621
    "pyplot.title(\"FPR dependence on sample size\")\n",
622
    "pyplot.xlabel(\"Sample size\")\n",
623
    "pyplot.ylabel(\"FPR\")\n",
624
    "pyplot.ylim(bottom=0)\n",
625
    "\n",
626
    "pyplot.show()"
627
   ]
628
  },
629
  {
630
   "cell_type": "markdown",
631
   "metadata": {},
632
   "source": [
633
    "**Вывод: видим, что начиная с размера выборки ~1000 истинная $\\alpha$ попадает в доверительный интервал FPR. Но и для меньшего размера выборки критерий можно использовать: вряд ли нас сильно огорчит FPR в 4.5% вместо требуемых 5%. Для размера выборки менее 50 критерий уже стоит использовать осторожно: FPR может быть значительно ниже заявленного.**"
634
   ]
635
  },
636
  {
637
   "cell_type": "markdown",
638
   "metadata": {},
639
   "source": [
640
    "Давайте теперь посмотрим, что происходит с мощностью. Поменяем распределение для второй выборки и посчитаем TPR:"
641
   ]
642
  },
643
  {
644
   "cell_type": "code",
645
   "execution_count": 54,
646
   "metadata": {
647
    "tags": []
648
   },
649
   "outputs": [
650
    {
651
     "name": "stderr",
652
     "output_type": "stream",
653
     "text": [
654
      "100%|██████████| 8/8 [00:59<00:00,  7.42s/it]\n"
655
     ]
656
    }
657
   ],
658
   "source": [
659
    "TPR_list = []\n",
660
    "\n",
661
    "for i in tqdm(numpy_ceil(numpy.geomspace(50, 4000, 8))):\n",
662
    "    mmk_res = gen_monte_carlo_exp_for_ks(n = i, m = i, \n",
663
    "                                         alpha = 0.05, N_runs = 10000,\n",
664
    "                                         latent_dist_X = gamma(1, 2), \n",
665
    "                                         latent_dist_Y = gamma(1.1, 2))\n",
666
    "    TPR_list.append([i, mmk_res])"
667
   ]
668
  },
669
  {
670
   "cell_type": "code",
671
   "execution_count": 57,
672
   "metadata": {
673
    "tags": []
674
   },
675
   "outputs": [
676
    {
677
     "data": {
678
      "image/png": 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",
679
      "text/plain": [
680
       "<Figure size 1600x800 with 1 Axes>"
681
      ]
682
     },
683
     "metadata": {},
684
     "output_type": "display_data"
685
    }
686
   ],
687
   "source": [
688
    "pyplot.figure(figsize=(16, 8))\n",
689
    "\n",
690
    "\n",
691
    "pyplot.plot([elem[0] for elem in TPR_list],\n",
692
    "            [elem[1].positive_rate for elem in TPR_list],\n",
693
    "            color = 'white', linewidth=2.0, label='TPR')\n",
694
    "pyplot.fill_between([elem[0] for elem in TPR_list],\n",
695
    "                    [elem[1].confint_left_bound for elem in TPR_list],\n",
696
    "                    [elem[1].confint_right_bound for elem in TPR_list],\n",
697
    "                    color = 'salmon', alpha = 0.5, label='TPR confint')\n",
698
    "\n",
699
    "pyplot.legend(loc='best')\n",
700
    "pyplot.title(\"TPR dependence on sample size\")\n",
701
    "pyplot.xlabel(\"Sample size\")\n",
702
    "pyplot.ylabel(\"TPR\")\n",
703
    "pyplot.ylim(bottom=0)\n",
704
    "\n",
705
    "pyplot.show()"
706
   ]
707
  },
708
  {
709
   "cell_type": "markdown",
710
   "metadata": {},
711
   "source": [
712
    "**Вывод: мощность стремится к 1 с увеличением размера выборки.**"
713
   ]
714
  },
715
  {
716
   "cell_type": "markdown",
717
   "metadata": {
718
    "tags": []
719
   },
720
   "source": [
721
    "## Зависимые выборки"
722
   ]
723
  },
724
  {
725
   "cell_type": "markdown",
726
   "metadata": {},
727
   "source": [
728
    "Что же будет происходить, если условие о независимости выборок не выполняется? Давайте проведем AA-тест и проверим корректность такого критерия."
729
   ]
730
  },
731
  {
732
   "cell_type": "markdown",
733
   "metadata": {},
734
   "source": [
735
    "### Функция для проверки корректности критерия при зависимых выборках"
736
   ]
737
  },
738
  {
739
   "cell_type": "markdown",
740
   "metadata": {},
741
   "source": [
742
    "Напишем функцию, которая проверяет корректность критерия с помощью метода Монте-Карло. \n",
743
    "\n",
744
    "Она будет генерировать из некого \"начального\" распределения $\\mathcal{P}_{\\it{\\text{init}}}$ выборку размера $n$, а затем накладывать на нее 2 разных выборки из некого распределения \"шума\": $\\mathcal{P}_{\\it{\\text{noise}}_X}$ и $\\mathcal{P}_{\\it{\\text{noise}}_Y}$. \n",
745
    "\n",
746
    "То есть: $$ X \\sim \\mathcal{P}_{init} + \\mathcal{P}_{\\it{\\text{noise}}_X},$$\n",
747
    "$$ Y \\sim \\mathcal{P}_{\\it{\\text{init}}} + \\mathcal{P}_{\\it{\\text{noise}}_Y}.$$\n",
748
    "\n",
749
    "Если распределения шума одинаковы для обеих выборок ($\\mathcal{P}_{\\it{\\text{noise}}_X}$ = $\\mathcal{P}_{\\it{\\text{noise}}_Y}$), то итоговые выборки получены из одинакового распределения, и нулевая гипотеза выполняется.\n",
750
    "\n",
751
    "Понятно, что в такой постановке выборки $X$ и $Y$ будут зависимы, поскольку реализация выборки из распределения $\\mathcal{P}_{\\it{\\text{init}}}$ будет одна и та же."
752
   ]
753
  },
754
  {
755
   "cell_type": "code",
756
   "execution_count": 40,
757
   "metadata": {
758
    "tags": []
759
   },
760
   "outputs": [],
761
   "source": [
762
    "def gen_monte_carlo_exp_for_ks_dependent_samples(n, alpha, N_runs, init_dist,\n",
763
    "                                                 noise_dist_X, noise_dist_Y):\n",
764
    "    \"\"\"\n",
765
    "        Функция для проверки критерия Колмогорова-Смирнова для зависимых \n",
766
    "            выборок с помощью метода Монте-Карло.\n",
767
    "            \n",
768
    "        Проверка осуществляется для зависимых выборок \n",
769
    "            с одинаковым числом наблюдений n.\n",
770
    "            \n",
771
    "        Генерируется общая реализация выборки init_sample, далее из нее \n",
772
    "            с помощью наложения шума из распределений noise_dist_X и \n",
773
    "            noise_dist_Y получаются выборки X и Y.\n",
774
    "            \n",
775
    "        Возвращает долю отвержений гипотезы, и доверительный интервал\n",
776
    "            для этой доли\n",
777
    "    \n",
778
    "        Параметры:\n",
779
    "            - n - размер выборок\n",
780
    "            - alpha: уровень значимости\n",
781
    "            - N_runs: число экспериментов в методе Монте-Карло\n",
782
    "            - init_dist: \"начальное\" распределение выборки\n",
783
    "            - noise_dist_X: распределение шума выборки X\n",
784
    "            - noise_dist_Y: распределение шума выборки Y\n",
785
    "    \"\"\"\n",
786
    "    \n",
787
    "    positive = 0\n",
788
    "    \n",
789
    "    for _ in range(N_runs): \n",
790
    "\n",
791
    "        init_sample = init_dist.rvs(n)\n",
792
    "        X = init_sample+noise_dist_X.rvs(n)\n",
793
    "        Y = init_sample+noise_dist_Y.rvs(n)\n",
794
    "    \n",
795
    "        pvalue = kstest(X, Y)[1]\n",
796
    "    \n",
797
    "        if pvalue<=alpha:\n",
798
    "            positive+=1\n",
799
    "        \n",
800
    "    positive_rate = positive/N_runs\n",
801
    "    confint = proportion_confint(count = positive, nobs = N_runs, \n",
802
    "                                 alpha = 0.05, method='wilson')\n",
803
    "        \n",
804
    "    return MonteCarloResults(**{'positive_rate': positive_rate,\n",
805
    "                                'confint_left_bound': confint[0],\n",
806
    "                                'confint_right_bound': confint[1]})"
807
   ]
808
  },
809
  {
810
   "cell_type": "markdown",
811
   "metadata": {},
812
   "source": [
813
    "### Крайний случай проверки критерия для зависимых выборок"
814
   ]
815
  },
816
  {
817
   "cell_type": "markdown",
818
   "metadata": {},
819
   "source": [
820
    "Сначала рассмотрим крайний случай: отсутствие шума, когда $\\mathcal{P}_{\\it{\\text{noise}}_X}$ = $\\mathcal{P}_{\\it{\\text{noise}}_Y}$ и всегда принимает значение 0. Иными словами, выборка $Y$ \"копирует\" выборку $X$.\n",
821
    " \n",
822
    "Это может соответствовать такой постановке задачи: \n",
823
    ">Выборка $X$ — артериальное давление пациентов до введения лекарства. Выборка $Y$ — артериальное давление тех же самых пациентов после введения лекарства. При этом лекарство эффекта не имеет.\n",
824
    " \n",
825
    "Выборки $X$ и $Y$ будут зависимыми, и при этом будут распределены одинаково (т.е. нулевая гипотеза выполняется)."
826
   ]
827
  },
828
  {
829
   "cell_type": "code",
830
   "execution_count": 41,
831
   "metadata": {
832
    "tags": []
833
   },
834
   "outputs": [
835
    {
836
     "name": "stdout",
837
     "output_type": "stream",
838
     "text": [
839
      "FPR:  0.0\n",
840
      "FPR confint:  (0.0, 0.0003839983706765959)\n"
841
     ]
842
    }
843
   ],
844
   "source": [
845
    "(positive_rate,\n",
846
    " confint_left_bound,\n",
847
    " confint_right_bound) = gen_monte_carlo_exp_for_ks_dependent_samples(n = 600,\n",
848
    "                                                                     alpha = 0.05,\n",
849
    "                                                                     N_runs = 10000,\n",
850
    "                                                                     init_dist = norm(),\n",
851
    "                                                                     noise_dist_X  = norm(0,0),\n",
852
    "                                                                     noise_dist_Y =  norm(0,0))\n",
853
    "\n",
854
    "print('FPR: ', positive_rate)\n",
855
    "print('FPR confint: ', (confint_left_bound, confint_right_bound))"
856
   ]
857
  },
858
  {
859
   "cell_type": "markdown",
860
   "metadata": {},
861
   "source": [
862
    "Видим, что $\\it{\\text{FPR}} = 0$, то есть критерий никогда не отвергает нулевую гипотезу $H_0$. Почему так происходит? Потому что эмпирические функции распределения в точности совпадают. Проверим это на выборке размера 600."
863
   ]
864
  },
865
  {
866
   "cell_type": "code",
867
   "execution_count": 42,
868
   "metadata": {
869
    "tags": []
870
   },
871
   "outputs": [],
872
   "source": [
873
    "x_axis = numpy.arange(start=-3, stop=3, step=0.001)\n",
874
    "\n",
875
    "# аппроксимируем CDF распределения, из которого семплирована наша выборка\n",
876
    "# эмпирическая функция распределения:\n",
877
    "init_sample = norm().rvs(600)\n",
878
    "X = init_sample\n",
879
    "Y = init_sample\n",
880
    "\n",
881
    "emp_cdf_X = []\n",
882
    "emp_cdf_Y = []\n",
883
    "for x in x_axis:\n",
884
    "    cdf_X= sum([int(b <= x) for b in X]) / len(X)\n",
885
    "    emp_cdf_X.append(cdf_X)\n",
886
    "    cdf_Y = sum([int(b <= x) for b in Y]) / len(Y)\n",
887
    "    emp_cdf_Y.append(cdf_Y)"
888
   ]
889
  },
890
  {
891
   "cell_type": "code",
892
   "execution_count": 43,
893
   "metadata": {
894
    "tags": []
895
   },
896
   "outputs": [
897
    {
898
     "data": {
899
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",
900
      "text/plain": [
901
       "<Figure size 1600x800 with 1 Axes>"
902
      ]
903
     },
904
     "metadata": {},
905
     "output_type": "display_data"
906
    }
907
   ],
908
   "source": [
909
    "pyplot.figure(figsize=(16, 8))\n",
910
    "\n",
911
    "\n",
912
    "pyplot.plot(x_axis, emp_cdf_X, color = 'white', linestyle = '-',\n",
913
    "            linewidth=1.0, label='empirical cdf for A')\n",
914
    "pyplot.plot(x_axis, emp_cdf_Y, color = 'salmon', linestyle = (0, (1, 3)),\n",
915
    "            linewidth=4.0, label='empirical cdf for B')\n",
916
    "\n",
917
    "pyplot.legend(loc='best')\n",
918
    "pyplot.title(\"Empirical distributions of dependent samples (w/o noise)\")\n",
919
    "pyplot.xlabel(\"X\")\n",
920
    "pyplot.ylabel(\"Cumulative probability\")\n",
921
    "\n",
922
    "pyplot.show()"
923
   ]
924
  },
925
  {
926
   "cell_type": "markdown",
927
   "metadata": {},
928
   "source": [
929
    "Видим, что график эмпирического распределения одной выборки находится в точности под графиком другой выборки."
930
   ]
931
  },
932
  {
933
   "cell_type": "markdown",
934
   "metadata": {},
935
   "source": [
936
    "### Общий случай проверки критерия для зависимых выборок"
937
   ]
938
  },
939
  {
940
   "cell_type": "markdown",
941
   "metadata": {},
942
   "source": [
943
    "Давайте теперь посмотрим, что же происходит, когда распределения шума одинаковые, но не принимают константное значение.\n",
944
    "\n",
945
    "В качестве распределений будем брать распределения из семейства нормальных, поскольку их удобно складывать.\n",
946
    "\n",
947
    "Возьмем $$\\mathcal{P}_{\\it{\\text{init}}} \\sim \\mathcal{N}(0,4^2),$$ \n",
948
    "$$\\mathcal{P}_{\\it{\\text{noise}}_X} \\sim \\mathcal{N}(0, 3^2),$$\n",
949
    "$$\\mathcal{P}_{\\it{\\text{noise}}_Y} \\sim \\mathcal{N}(0, 3^2).$$ \n",
950
    "\n",
951
    "Получается, что $$X \\sim \\mathcal{P}_{\\it{\\text{init}}} + \\mathcal{P}_{\\it{\\text{noise}}_X} = \\mathcal{N}(0, 3^2) + \\mathcal{N}(0,4^2) = \\mathcal{N}(0, 5^2),$$\n",
952
    "$$Y \\sim \\mathcal{P}_{\\it{\\text{init}}} + \\mathcal{P}_{\\it{\\text{noise}}_Y} = \\mathcal{N}(0, 3^2) + \\mathcal{N}(0,4^2) = \\mathcal{N}(0, 5^2)$$\n",
953
    "\n",
954
    "Выборки $X$ и $Y$ одинаково распределены и зависимы. Нулевая гипотеза выполнена."
955
   ]
956
  },
957
  {
958
   "cell_type": "code",
959
   "execution_count": 44,
960
   "metadata": {
961
    "tags": []
962
   },
963
   "outputs": [
964
    {
965
     "name": "stdout",
966
     "output_type": "stream",
967
     "text": [
968
      "FPR:  0.0048\n",
969
      "FPR confint:  (0.0036224922338521153, 0.006357819752465983)\n"
970
     ]
971
    }
972
   ],
973
   "source": [
974
    "(positive_rate,\n",
975
    " confint_left_bound,\n",
976
    " confint_right_bound) = gen_monte_carlo_exp_for_ks_dependent_samples(n = 600,\n",
977
    "                                                                     alpha = 0.05,\n",
978
    "                                                                     N_runs = 10000, \n",
979
    "                                                                     init_dist = norm(0,4),\n",
980
    "                                                                     noise_dist_X  = norm(0,3),\n",
981
    "                                                                     noise_dist_Y =  norm(0,3))\n",
982
    "\n",
983
    "print('FPR: ', positive_rate)\n",
984
    "print('FPR confint: ', (confint_left_bound, confint_right_bound))"
985
   ]
986
  },
987
  {
988
   "cell_type": "markdown",
989
   "metadata": {},
990
   "source": [
991
    "Видим, что $\\it{\\text{FPR}}$ также очень близок к 0. Давайте нарисуем эмпирические распределения, чтобы поближе посмотреть, что происходит."
992
   ]
993
  },
994
  {
995
   "cell_type": "code",
996
   "execution_count": 45,
997
   "metadata": {
998
    "tags": []
999
   },
1000
   "outputs": [],
1001
   "source": [
1002
    "x_axis = numpy.arange(start=-15, stop=15, step=0.001)\n",
1003
    "\n",
1004
    "# аппроксимируем CDF распределения, из которого семплирована наша выборка\n",
1005
    "# эмпирическая функция распределения:\n",
1006
    "init_sample = norm(0,4).rvs(600)\n",
1007
    "X = init_sample+norm(0,3).rvs(600)\n",
1008
    "Y = init_sample+norm(0,3).rvs(600)\n",
1009
    "\n",
1010
    "emp_cdf_X = []\n",
1011
    "emp_cdf_Y = []\n",
1012
    "for x in x_axis:\n",
1013
    "    cdf_X= sum([int(b <= x) for b in X]) / len(X)\n",
1014
    "    emp_cdf_X.append(cdf_X)\n",
1015
    "    cdf_Y = sum([int(b <= x) for b in Y]) / len(Y)\n",
1016
    "    emp_cdf_Y.append(cdf_Y)"
1017
   ]
1018
  },
1019
  {
1020
   "cell_type": "code",
1021
   "execution_count": 46,
1022
   "metadata": {
1023
    "tags": []
1024
   },
1025
   "outputs": [
1026
    {
1027
     "data": {
1028
      "image/png": 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1029
      "text/plain": [
1030
       "<Figure size 1600x800 with 1 Axes>"
1031
      ]
1032
     },
1033
     "metadata": {},
1034
     "output_type": "display_data"
1035
    }
1036
   ],
1037
   "source": [
1038
    "pyplot.figure(figsize=(16, 8))\n",
1039
    "\n",
1040
    "\n",
1041
    "pyplot.plot(x_axis, emp_cdf_X, color='white', label='empirical cdf for A')\n",
1042
    "pyplot.plot(x_axis, emp_cdf_Y, color='salmon', label='empirical cdf for B')\n",
1043
    "\n",
1044
    "pyplot.legend(loc='best')\n",
1045
    "pyplot.title(\"Empirical distributions of dependent samples (w/ noise)\")\n",
1046
    "pyplot.xlabel(\"X\")\n",
1047
    "pyplot.ylabel(\"Cumulative probability\")\n",
1048
    "\n",
1049
    "pyplot.show()"
1050
   ]
1051
  },
1052
  {
1053
   "cell_type": "markdown",
1054
   "metadata": {},
1055
   "source": [
1056
    "Эмпирические функции распределения отличаются слабо, поэтому нулевая гипотеза при проверке критерием для зависимых выборок редко отвергается."
1057
   ]
1058
  },
1059
  {
1060
   "cell_type": "markdown",
1061
   "metadata": {},
1062
   "source": [
1063
    "### Сравнение критерия Колмогорова-Смирнова для зависимых и независимых выборок"
1064
   ]
1065
  },
1066
  {
1067
   "cell_type": "markdown",
1068
   "metadata": {},
1069
   "source": [
1070
    "Давайте теперь сравним результаты АА тестов: какой FPR и мощность в зависимости от размера выборки получится для \n",
1071
    "1. независимых выборок $$X, Y \\sim \\mathcal{N}(0, 5^2)$$\n",
1072
    "2. зависимых выборок из предыдущего пункта: $$X \\sim \\mathcal{P}_{\\it{\\text{init}}} + \\mathcal{P}_{\\it{\\text{noise}}_X} = \\mathcal{N}(0, 3^2) + \\mathcal{N}(0,4^2) = \\mathcal{N}(0, 5^2),$$\n",
1073
    "$$Y \\sim \\mathcal{P}_{\\it{\\text{init}}} + \\mathcal{P}_{\\it{\\text{noise}}_Y} = \\mathcal{N}(0, 3^2) + \\mathcal{N}(0,4^2) =  \\mathcal{N}(0, 5^2),$$\n",
1074
    "где реализация выборки из распределения $\\mathcal{P}_{\\it{\\text{init}}}$ общая для $X$ и $Y$."
1075
   ]
1076
  },
1077
  {
1078
   "cell_type": "markdown",
1079
   "metadata": {},
1080
   "source": [
1081
    "#### Сравнение $\\it{\\text{FPR}}$"
1082
   ]
1083
  },
1084
  {
1085
   "cell_type": "code",
1086
   "execution_count": 47,
1087
   "metadata": {
1088
    "tags": []
1089
   },
1090
   "outputs": [
1091
    {
1092
     "name": "stderr",
1093
     "output_type": "stream",
1094
     "text": [
1095
      "100%|██████████| 10/10 [02:56<00:00, 17.62s/it]\n"
1096
     ]
1097
    }
1098
   ],
1099
   "source": [
1100
    "FPR_list_independent = []\n",
1101
    "FPR_list_dependent = []\n",
1102
    "\n",
1103
    "# перебираем размер выборки с логарифмическим шагом\n",
1104
    "for i in tqdm(numpy_ceil(numpy.geomspace(50, 6000, 10))):  \n",
1105
    "    mmk_res_independent = gen_monte_carlo_exp_for_ks(n = i, m = i, \n",
1106
    "                                                     alpha = 0.05, \n",
1107
    "                                                     N_runs = 10000,\n",
1108
    "                                                     latent_dist_X = norm(0, 5),\n",
1109
    "                                                     latent_dist_Y = norm(0, 5))\n",
1110
    "    FPR_list_independent.append([i, mmk_res_independent])\n",
1111
    "    \n",
1112
    "    mmk_res_dependent = gen_monte_carlo_exp_for_ks_dependent_samples(n = i,\n",
1113
    "                                                                     alpha = 0.05,\n",
1114
    "                                                                     N_runs = 10000,\n",
1115
    "                                                                     init_dist = norm(0,4),\n",
1116
    "                                                                     noise_dist_X  = norm(0,3),\n",
1117
    "                                                                     noise_dist_Y =  norm(0,3))\n",
1118
    "    FPR_list_dependent.append([i, mmk_res_dependent])"
1119
   ]
1120
  },
1121
  {
1122
   "cell_type": "code",
1123
   "execution_count": 58,
1124
   "metadata": {
1125
    "tags": []
1126
   },
1127
   "outputs": [
1128
    {
1129
     "data": {
1130
      "image/png": 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",
1131
      "text/plain": [
1132
       "<Figure size 1600x800 with 1 Axes>"
1133
      ]
1134
     },
1135
     "metadata": {},
1136
     "output_type": "display_data"
1137
    }
1138
   ],
1139
   "source": [
1140
    "pyplot.figure(figsize=(16, 8))\n",
1141
    "\n",
1142
    "\n",
1143
    "pyplot.plot([elem[0] for elem in FPR_list_independent],\n",
1144
    "            [elem[1].positive_rate for elem in FPR_list_independent],\n",
1145
    "            color = 'white', linewidth=3.0, label='FPR independent samples')\n",
1146
    "pyplot.fill_between([elem[0] for elem in FPR_list_independent],\n",
1147
    "                    [elem[1].confint_left_bound for elem in FPR_list_independent],\n",
1148
    "                    [elem[1].confint_right_bound for elem in FPR_list_independent],\n",
1149
    "                    color = 'violet', alpha = 0.3, \n",
1150
    "                    label='FPR confint independent samples')\n",
1151
    "\n",
1152
    "pyplot.plot([elem[0] for elem in FPR_list_dependent],\n",
1153
    "            [elem[1].positive_rate for elem in FPR_list_dependent],\n",
1154
    "            color = 'white', linestyle = 'dashed', linewidth=3.0,\n",
1155
    "            label='FPR dependent samples')\n",
1156
    "pyplot.fill_between([elem[0] for elem in FPR_list_dependent],\n",
1157
    "                    [elem[1].confint_left_bound for elem in FPR_list_dependent],\n",
1158
    "                    [elem[1].confint_right_bound for elem in FPR_list_dependent],\n",
1159
    "                    color = 'skyblue', alpha = 0.3,\n",
1160
    "                    label='FPR confint dependent samples')\n",
1161
    "\n",
1162
    "pyplot.plot([elem[0] for elem in FPR_list_independent],\n",
1163
    "            numpy.array([0.05]*len(FPR_list_independent)),\n",
1164
    "            color = 'yellow', linestyle = 'dotted',\n",
1165
    "            linewidth=3.0, label='alpha')\n",
1166
    "\n",
1167
    "pyplot.legend(loc='best')\n",
1168
    "pyplot.title(\"FPR dependence on sample size: dependent vs independent samples\")\n",
1169
    "pyplot.xlabel(\"Sample size\")\n",
1170
    "pyplot.ylabel(\"FPR\")\n",
1171
    "\n",
1172
    "pyplot.show()"
1173
   ]
1174
  },
1175
  {
1176
   "cell_type": "markdown",
1177
   "metadata": {},
1178
   "source": [
1179
    "**Вывод: видим низкий $\\it{\\text{FPR}}$ для зависимых выборок. Доверительный интервал для $\\it{\\text{FPR}}$ не включает $\\alpha$ даже для большого размера выборки. Значит, мы будем терять в мощности критерия.**"
1180
   ]
1181
  },
1182
  {
1183
   "cell_type": "markdown",
1184
   "metadata": {},
1185
   "source": [
1186
    "#### Сравнение мощности"
1187
   ]
1188
  },
1189
  {
1190
   "cell_type": "markdown",
1191
   "metadata": {},
1192
   "source": [
1193
    "По низкому $\\it{\\text{FPR}}$ для зависимых выборок мы сделали вывод о том, что мы будем терять в мощности. Давайте теперь явно проверим, насколько существенны эти потери. Поменяем шум для распределения $Y$ на $$\\mathcal{P}_{\\it{\\text{noise}}_Y} \\sim \\mathcal{N}(0, 2^2).$$  Тогда выборка $Y$ будет порождена случайной величиной, распределенной как $\\mathcal{N}(0, 2^2) + \\mathcal{N}(0, 4^2) = \\mathcal{N}(0, 20)$"
1194
   ]
1195
  },
1196
  {
1197
   "cell_type": "code",
1198
   "execution_count": 49,
1199
   "metadata": {
1200
    "tags": []
1201
   },
1202
   "outputs": [
1203
    {
1204
     "name": "stderr",
1205
     "output_type": "stream",
1206
     "text": [
1207
      "100%|██████████| 10/10 [02:57<00:00, 17.76s/it]\n"
1208
     ]
1209
    }
1210
   ],
1211
   "source": [
1212
    "TPR_list_independent = []\n",
1213
    "TPR_list_dependent = []\n",
1214
    "\n",
1215
    "# перебираем размер выборки с логарифмическим шагом\n",
1216
    "for i in tqdm(numpy_ceil(numpy.geomspace(50, 6000, 10))):\n",
1217
    "    \n",
1218
    "    mmk_res_independent = gen_monte_carlo_exp_for_ks(n = i, m = i,\n",
1219
    "                                                     alpha = 0.05,\n",
1220
    "                                                     N_runs = 10000,\n",
1221
    "                                                     latent_dist_X = norm(0, 5),\n",
1222
    "                                                     latent_dist_Y = norm(0, 2*math.sqrt(5)))\n",
1223
    "    TPR_list_independent.append([i, mmk_res_independent])\n",
1224
    "    \n",
1225
    "    mmk_res_dependent = gen_monte_carlo_exp_for_ks_dependent_samples(n = i, \n",
1226
    "                                                                     alpha = 0.05,\n",
1227
    "                                                                     N_runs = 10000,\n",
1228
    "                                                                     init_dist = norm(0,4),\n",
1229
    "                                                                     noise_dist_X  = norm(0,3),\n",
1230
    "                                                                     noise_dist_Y =  norm(0,2))\n",
1231
    "    TPR_list_dependent.append([i, mmk_res_dependent])"
1232
   ]
1233
  },
1234
  {
1235
   "cell_type": "code",
1236
   "execution_count": 61,
1237
   "metadata": {
1238
    "tags": []
1239
   },
1240
   "outputs": [
1241
    {
1242
     "data": {
1243
      "image/png": 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16tXyer3BnA8++EDDhg1TYmLi0ZkM8DUSEhIkSc3NzZKkcePGKSIiolvdl5SUaP/+/d3qftu2baqvrw/mfPDBB0pISNDxxx8fzPnH9/h7Dv9vQChZrVbNnDlTdrtda9eupd7Rqz355JNasWKFPv74427HqXv0VgUFBaqqqtK+ffu0dOlS5eTkSKLm0TtdeOGF2rhxo1599VXV1dVp8+bNuuaaa4Ln+V3226P5eAxITU2VzWZTXV1dt+N1dXXKzMwM0aiA78bfa/ib6jszM7PbP1Ikye/3q7m5uVvO4d7jHz8DCAWLxaLHHntMa9as0Y4dOyQdqkm32622trZuuf9c9/+qpr8uJyEhQVFRUT0yH+DrDB8+XB0dHXK73frDH/6g6dOna9euXdQ7eq2ZM2dq7Nixmjdv3lfOUffojdavX6+rr75aU6dO1Zw5czRw4EB98sknio2NpebRKw0aNEhz5szRnj17dM4552jRokX6/e9/r6uuukoSv8seCVuoBwAAQG/25JNPavjw4Tr11FNDPRSgR5WUlGj06NFKSEjQpZdeqsWLF2vSpEmhHhbQI/r376+FCxdqypQpcrvdoR4OcFSsXLky+PO2bdu0fv167d+/XzNmzJDL5QrhyICeYbVatXHjRv3qV7+SJG3dulXDhw/XddddpyVLloR4dMcWVj4eAxobG+Xz+ZSRkdHteEZGhmpra0M0KuC78fca/qb6rq2t/cqT8sLCwpScnNwt53Dv8Y+fARxtjz/+uC644AKdccYZqqqqCh6vra1VZGRk8Hbsv/vnuv9XNf11OW1tberq6vrO5wN8E6/Xq3379mnz5s365S9/qaKiIt18883UO3qlcePGKSMjQ5s3b5bX65XX69Xpp5+um266SV6vV3V1ddQ9er22tjaVlpZq8ODB/F2PXqmmpkY7d+7sdmzXrl0aMGCAJH6XPRI0H48BXq9XmzZt0uTJk4PHLBaLJk+erLVr14ZwZMC/r7y8XDU1Nd3qOy4uTieddFKwvteuXaukpCSNHTs2mHPmmWfKarVq/fr1wZzTTjtNNtuXC7qnTJmi3bt3q7W19ehMBvgHjz/+uKZPn64zzzxTFRUV3c5t2rRJHo+nW90PGTJEubm53ep+xIgRSktLC+ZMmTJFbW1twX8ErV27ttt7/D2H/zfg+8BqtSoyMpJ6R6/08ccfa/jw4Ro9enQwNmzYoJdeekmjR4/Wxo0bqXv0ena7Xfn5+aqpqeHvevRKn376qYYOHdrt2JAhQ7R//35J/C57pEL+1BviX8eMGTOMy+UyV111lRk2bJj5wx/+YJqbm7s9KYwgvq9ht9vNqFGjzKhRo4wxxtxyyy1m1KhRJicnx0gyd955p2lubjY//OEPzfDhw81bb71l9u3bZyIjI4Pv8d5775lNmzaZ8ePHm5NPPtmUlJSYl156KXg+Pj7e1NTUmMWLF5vCwkIzY8YM43A4zLXXXhvy+RN9L5588knT0tJiTjvtNJORkRGMqKioYM5TTz1lKioqzOmnn27Gjh1rPv30U/Ppp58Gz1utVlNcXGxWrlxpRo4cac4++2xTV1dn7r///mBOXl6ecTgc5qGHHjJDhw41c+bMMV6v15x99tkh/w6IvhUPPPCAmThxosnNzTXDhw83DzzwgPH7/eass84yEvVO9I34x6ddS9Q90ftiwYIF5rTTTjO5ublmwoQJ5sMPPzT19fUmNTXVSNQ80fvihBNOMB6Px8ybN8/k5+ebH/3oR8bhcJjLL788mMPvst86Qj4A4lvGDTfcYCoqKkxXV5dZt26dOfHEE0M+JoL4NjFp0iRzOC+88EIw55577jE1NTXG5XKZjz76yBQUFHR7j6SkJPPSSy+Z9vZ209raap577jljt9u75YwYMcKsXr3auFwuc/DgQXPnnXeGfO5E34yvM3v27GBOZGSkeeKJJ0xTU5NxOBzmjTfeMBkZGd3eZ8CAAWbFihXG6XSa+vp6s2DBAhMWFtYtZ9KkSWbz5s2mq6vL7N27t9tnEMTRimeffdaUl5ebrq4uU1dXZz766KNg41Gi3om+Ef/cfKTuid4Wy5YtM1VVVaarq8scPHjQLFu2zAwaNCh4nponemOcf/75pri42LhcLrNz505zzTXXfCWH32X/dVi++AEAAAAAAAAAvlPs+QgAAAAAAACgR9B8BAAAAAAAANAjaD4CAAAAAAAA6BE0HwEAAAAAAAD0CJqPAAAAAAAAAHoEzUcAAAAAAAAAPYLmIwAAAAAAAIAeQfMRAAAAAAAAQI+g+QgAAIDvHWOMpk2b1iPvnZubK2OMRo0a1SPvDwAAgC/RfAQAAOiDUlNT9dRTT2n//v3q6upSTU2NVq5cqZNPPjnUQ+txBw8eVGZmprZv3x7qoQAAAPR6tlAPAAAAAEffG2+8oYiICM2ePVtlZWXKyMjQ5MmTlZKSEuqh9bhAIKC6urpQDwMAAKBPYOUjAABAH5OQkKDTTjtNc+fO1V//+lcdOHBAGzZs0IMPPqg//elPwbxbb71VxcXFcjgcOnDggJ588knZ7fbg+dmzZ6ulpUXnn3++du/eLafTqddee03R0dG66qqrVF5erubmZi1cuFBW65f/7CwvL9ddd92ll19+WQ6HQ5WVlbr++uu/ccz9+/fXH//4R7W0tKipqUlvv/22cnNzvzY/MTFRS5cuVX19vTo7O1VaWqqrr75a0ldvu37hhRdkjPlKTJo0SZIUERGhBQsWqLKyUg6HQ+vWrQueAwAAwDej+QgAANDHOBwOdXR06KKLLlJERMTX5gUCAd100006/vjjNXv2bJ155pl6+OGHu+XExMTopptu0qxZszR16lSdfvrpeuutt3TeeefpvPPO05VXXqmf/exnuvTSS7tdd8cdd6ioqEhjxozRgw8+qIULF+qss8467DhsNps++OADdXR0aOLEiTrllFPkcDi0cuVKhYeHH/aae++9V4WFhTr33HN13HHHac6cOWpsbDxs7s0336zMzMxgPPbYY6qrq9Pu3bslSU888YQmTJigWbNmaeTIkXrttde0cuVKDR48+Gu/OwAAAHzJEARBEARBEH0rLr74YtPU1GQ6OzvNmjVrzP33329GjBjxjddccsklpqGhIfh69uzZxhhjBg0aFDy2aNEi43A4jN1uDx57//33zaJFi4Kvy8vLzXvvvdftvZctW2ZWrFgRfG2MMdOmTTOSzBVXXGF27drVLT88PNw4nU4zZcqUw471nXfeMc8999xhz+Xm5hpjjBk1atRXzk2fPt10dnaak08+2UgyOTk5xuv1mn79+nXL++ijj8z9998f8v+OBEEQBEEQ3/dg5SMAAEAf9OabbyorK0sXXnihVq5cqdNPP12bN2/W7NmzgzmTJ0/WqlWrVFlZqfb2dr344otKTU1VdHR0MMfpdKqsrCz4uq6uThUVFXI6nd2Opaend/v8tWvXfuX1cccdd9ixjho1SoMHD1ZHR0cwmpubFRUVpfz8/MNes2jRIs2aNUtbtmzRQw89pAkTJvzL72T06NF68cUX9fOf/1yfffaZJGnEiBGy2WwqLS3t9vmTJk362s8GAADAl3jgDAAAQB/ldru1atUqrVq1Svfdd5+eeeYZ3XPPPVq8eLFyc3O1fPlyLVq0SL/61a/U3NysU089Vc8//7wiIiLkcrkkSV6vt9t7GmMOe+wf93w8UrGxsdq0aZOuuOKKr5xraGg47DUrV65Ubm6uzjvvPE2ZMkUff/yxnnzySd1xxx2Hzc/IyNC7776rZ599Vs8//3y3z/b5fBo3bpz8fn+3axwOx/95TgAAAH0FzUcAAABIknbu3KmLLrpIkjRu3DhZrVbdfvvtMsZIkmbMmPGdfdYPfvCDr7zetWvXYXM3b96smTNnqr6+Xh0dHd/6MxobG7VkyRItWbJEn3zyiRYsWHDY5mNkZKTeeecd7d69W7fddlu3c1u2bJHNZlN6errWrFnzrT8bAAAAh3DbNQAAQB+TnJysjz/+WFdccYVGjBihvLw8XXrppbrzzjv1zjvvSJL27t2riIgI3XjjjRo4cKD+4z/+Q9ddd913NoZTTjlFd9xxhwoKCnT99dfrsssu08KFCw+b+9JLL6mxsVHvvPOOTj31VOXl5WnSpElauHChsrOzD3vNPffcowsvvFD5+fkqLCzUBRdc8LXNzaefflo5OTm66aablJaWpoyMDGVkZCg8PFx79uzR0qVLtWTJEk2fPl15eXkaP368fvGLX+i88877zr4PAACA3ormIwAAQB/jcDi0fv163XrrrVq9erW2b9+ue++9V88884x+/vOfS5KKi4t16623au7cudq+fbuuuOIKzZs37zsbw+9+9zudcMIJ2rJli+666y7ddttt+vDDDw+b63K5dNppp+nAgQN68803tWvXLj333HOKiopSe3v7Ya/xeDyaP3++iouLtXr1avn9fs2aNeuwuZMmTVJWVpZ27dql2traYJx88smSpB//+MdasmSJfve736mkpERvv/22xo8frwMHDnw3XwYAAEAvZtGhJ88AAAAAR0V5ebkee+yxr13pCAAAgN6DlY8AAAAAAAAAegTNRwAAAAAAAAA9gtuuAQAAAAAAAPQIVj4CAAAAAAAA6BE0HwEAAAAAAAD0CJqPAAAAAAAAAHoEzUcAAAAAAAAAPYLmIwAAAAAAAIAeQfMRAAAAAAAAQI+g+QgAAAAAAACgR9B8BAAAAAAAANAj/j+jlQotLOkDdAAAAABJRU5ErkJggg==",
1244
      "text/plain": [
1245
       "<Figure size 1600x800 with 1 Axes>"
1246
      ]
1247
     },
1248
     "metadata": {},
1249
     "output_type": "display_data"
1250
    }
1251
   ],
1252
   "source": [
1253
    "pyplot.figure(figsize=(16, 8))\n",
1254
    "\n",
1255
    "\n",
1256
    "pyplot.plot([elem[0] for elem in TPR_list_independent],\n",
1257
    "            [elem[1].positive_rate for elem in TPR_list_independent],\n",
1258
    "            color = 'white', linewidth=1.0, label='TPR independent samples')\n",
1259
    "pyplot.fill_between([elem[0] for elem in TPR_list_independent],\n",
1260
    "                    [elem[1].confint_left_bound for elem in TPR_list_independent],\n",
1261
    "                    [elem[1].confint_right_bound for elem in TPR_list_independent],\n",
1262
    "                    color = 'violet', alpha = 0.3,\n",
1263
    "                    label='TPR confint independent samples')\n",
1264
    "\n",
1265
    "pyplot.plot([elem[0] for elem in TPR_list_dependent],\n",
1266
    "            [elem[1].positive_rate for elem in TPR_list_dependent],\n",
1267
    "            color = 'white', linestyle = 'dashed',\n",
1268
    "            linewidth=1.0, label='TPR dependent samples')\n",
1269
    "pyplot.fill_between([elem[0] for elem in TPR_list_dependent],\n",
1270
    "                    [elem[1].confint_left_bound for elem in TPR_list_dependent],\n",
1271
    "                    [elem[1].confint_right_bound for elem in TPR_list_dependent],\n",
1272
    "                    color = 'skyblue', alpha = 0.3, \n",
1273
    "                    abel='TPR confint dependent samples')\n",
1274
    "\n",
1275
    "pyplot.legend(loc='best')\n",
1276
    "pyplot.title(\"TPR dependence on sample size: dependent vs independent samples\")\n",
1277
    "pyplot.xlabel(\"Sample size\")\n",
1278
    "pyplot.ylabel(\"TPR\")\n",
1279
    "\n",
1280
    "pyplot.show()"
1281
   ]
1282
  },
1283
  {
1284
   "cell_type": "markdown",
1285
   "metadata": {},
1286
   "source": [
1287
    "**Вывод: для зависимых выборок мы существенно теряем в мощности критерия по сравнению с независимыми. Несмотря на это, мощность все равно стремится к 1 с увеличением выборки. Критерий все равно валиден, и может помочь обнаружить эффект.**"
1288
   ]
1289
  },
1290
  {
1291
   "cell_type": "markdown",
1292
   "metadata": {},
1293
   "source": [
1294
    "Если вам встретится задача с зависимостью, можно попробовать провести AA-тест, и посмотреть, наcколько $\\it{\\text{FPR}}$ будет близок к $\\alpha$. Если $\\it{\\text{FPR}}$ сильно занижен, лучше применить другой критерий."
1295
   ]
1296
  },
1297
  {
1298
   "cell_type": "markdown",
1299
   "metadata": {},
1300
   "source": [
1301
    "## Выводы"
1302
   ]
1303
  },
1304
  {
1305
   "cell_type": "markdown",
1306
   "metadata": {},
1307
   "source": [
1308
    "Давайте подведем итог, что же мы сегодня узнали?\n",
1309
    "\n",
1310
    "Вывели критерий Колмогорова-Смирнова:\n",
1311
    "- Научились проверять, принадлежат ли две выборки одному распределению (при условии что выборки независимые и получены из непрерывных распределений).\n",
1312
    "\n",
1313
    "Протестировали применимость критерия для разных размеров выборки:\n",
1314
    "- Получилось, что с $n, m ≈ 1000$ наблюдаемый $\\it{\\text{FPR}}$ не отличается от заявленной $\\alpha$. \n",
1315
    "- Для меньшего размера выборки критерий применять также можно, но $\\it{\\text{FPR}}$ будет заниженным, что оказывает эффект на мощность критерия.\n",
1316
    "- При увеличении размера выборки мощность стремится к 1.\n",
1317
    "\n",
1318
    "Протестировали применимость критерия для зависимых выборок:\n",
1319
    "- Критерий для зависимых выборок корректен, но $\\it{\\text{FPR}}$ ниже $\\alpha$. \n",
1320
    "- Мы теряем в мощности по сравнению со случаем независимых выборок, но критерий все равно применим.\n",
1321
    "- При увеличении размера выборки мощность стремится к 1."
1322
   ]
1323
  },
1324
  {
1325
   "cell_type": "markdown",
1326
   "metadata": {},
1327
   "source": [
1328
    "## P.S.: важное замечание по применимости критериев однородности"
1329
   ]
1330
  },
1331
  {
1332
   "cell_type": "markdown",
1333
   "metadata": {},
1334
   "source": [
1335
    "Мы целую лекцию разбирались с критерием Колмогорова-Смирнова, но в реальной практике аналитика данных критерии однородности встречаются редко. \n",
1336
    "\n",
1337
    "Причина этого заключается в том, что аналитика как правило интересует количественная характеристика изменения распределения метрики. Чаще нам нужно будет понять, изменилось ли среднее всей выборки, либо среднее в каком-то разрезе?\n",
1338
    "\n",
1339
    "Результатом применения критерия однородности Колмогорова-Смирнова будет наличие изменения в распределении, без ответа на вопрос \"а какое именно изменение произошло?\". Стали ли тяжелее хвосты или произошел сдвиг распределения? На эти вопросы критерий Колмогорова-Смирнова ответить не сможет, в отличие от T-теста.\n",
1340
    "\n",
1341
    "При этом модельной задачкой в этой методичке была задачка из области медицины. В сфере медицины такой критерий будет более полезным, потому что наличие эффекта определенного лекарства на рассматриваемую метрику уже будет являться результатом: об этом как минимум стоит написать на упаковке лекарства.\n",
1342
    "\n",
1343
    "Помимо знания о том, в каких случаях критерий применим, вам также потребуется знание, в каких случаях он не применим. Поэтому, в следующий раз, когда кто-то вам скажет использовать критерий однородности Колмогорова-Смирнова в какой-то задаче, стоит хорошо подумать, прежде чем это сделать."
1344
   ]
1345
  }
1346
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1347
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1348
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1349
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1350
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1351
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1352
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1353
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1354
   "codemirror_mode": {
1355
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1356
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1357
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1358
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1359
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1360
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1361
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1362
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1363
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1364
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1365
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1366
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1367
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1368
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1369