Lectures 4-5. T-test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3c410b84",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import (\n",
    "    norm, binom, expon, t, chi2, pareto, ttest_1samp, ttest_ind, sem\n",
    ")\n",
    "from statsmodels.stats.api import CompareMeans, DescrStatsW\n",
    "from statsmodels.stats.proportion import proportion_confint\n",
    "import numpy as numpy\n",
    "from seaborn import distplot\n",
    "from matplotlib import pyplot\n",
    "import seaborn\n",
    "\n",
    "import sys\n",
    "sys.path.append('.')\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "97a8419a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def inverse_plot_colorscheme():\n",
    "    import cycler\n",
    "    def invert(color_to_convert): \n",
    "        table = str.maketrans('0123456789abcdef', 'fedcba9876543210')\n",
    "        return '#' + color_to_convert[1:].lower().translate(table).upper()\n",
    "    update_dict = {}\n",
    "    for key, value in pyplot.rcParams.items():\n",
    "        if value == 'black':\n",
    "            update_dict[key] = 'white'\n",
    "        elif value == 'white':\n",
    "            update_dict[key] = 'black'\n",
    "    \n",
    "    old_cycle = pyplot.rcParams['axes.prop_cycle']\n",
    "    new_cycle = []\n",
    "    for value in old_cycle:\n",
    "        new_cycle.append({\n",
    "            'color': invert(value['color'])\n",
    "        })\n",
    "    pyplot.rcParams.update(update_dict)\n",
    "    pyplot.rcParams['axes.prop_cycle'] = cycler.Cycler(new_cycle)\n",
    "    lec = pyplot.rcParams['legend.edgecolor']\n",
    "    lec = str(1 - float(lec))\n",
    "    pyplot.rcParams['legend.edgecolor'] = lec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fe03459c",
   "metadata": {},
   "outputs": [],
   "source": [
    "inverse_plot_colorscheme()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ec26d13",
   "metadata": {},
   "source": [
    "# Лекция 4-5. t-test\n",
    "\n",
    "На этой лекции мы продолжим изучать критерии для анализа средних значений выборок и познакомимся с новым критерием: t-test.\n",
    "\n",
    "Попробуем решить следующую задачу."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2445408",
   "metadata": {},
   "source": [
    "> 📈 **Задача**\n",
    ">\n",
    "> В нашей компании хотят перейти с одной СУБД на другую. Главным критерием для перехода является \"затраченное время в сутках на загрузку новых данных\". Если раньше для ежедневного обновления базы требовалось в среднем 10 часов, то хочется найти новую СУБД, в которой все это будет происходить быстрее, чем за 7 часов.\n",
    ">\n",
    "> Для этого было принято решение перенести все данные на новую тестируемую СУБД. В течение одной недели каждый день мы посчитаем время загрузки данных, и если в среднем на обновление будет уходить меньше 7 часов, то мы полностью перейдем на новую СУБД. Ваша задача придумать, как проверить гипотезу о том, что новая СУБД лучше старой.\n",
    "> ___\n",
    "> *СУБД - система управления базами данных*\n",
    ">\n",
    "> *БД - база данных*\n",
    "\n",
    "Получилась выборка:\n",
    "\n",
    "- `[6.9, 6.45, 6.32, 6.88, 6.19, 7.13, 6.76]` &mdash; время загрузки в новую БД по дням в часах."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02e33c7d",
   "metadata": {},
   "source": [
    "Для начала переформулируем условие на языке математики: есть выборка\n",
    "- $X_1, X_2, ..., X_7$ &mdash; время загрузки в часах новых данных в СУБД за каждый день эксперимента\n",
    "- Еще будем считать, что $X$ из нормального распредения."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0d028b2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Среднее время загрузки в СУБД: 6.65\n"
     ]
    }
   ],
   "source": [
    "X = numpy.array([6.9, 6.45, 6.32, 6.88, 6.09, 7.13, 6.76])\n",
    "print(f\"Среднее время загрузки в СУБД: {round(numpy.mean(X), 2)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c4111ad",
   "metadata": {},
   "source": [
    "Наша гипотеза звучит так:\n",
    "\n",
    "$H_0$: $E \\overline{X} \\geq 7\\ vs.\\ H_1: E \\overline{X} < 7$\n",
    "\n",
    "\n",
    "\n",
    "Кажется, что мы такое уже умеем решать: вспомним про z-критерий.\n",
    "\n",
    "--- \n",
    "**Z-критерий**\n",
    "\n",
    "$H_0: \\mu \\leq \\mu_0\\ vs.\\ H_1: \\mu > \\mu_0$\n",
    "- Статистика $Z(X) = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{\\sigma^2}}$\n",
    "- При достаточно большом размере выборки $Z(X) \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$ (по ЦПТ)\n",
    "- Односторонний критерий: $\\left\\{Z(X) \\geq z_{1 - \\alpha} \\right\\}$\n",
    "    - p-value = $1 - \\Phi(z)$, где z &mdash; реализация статистики $Z(X)$, $\\Phi(z)$ &mdash; функция распределения $\\mathcal{N}(0, 1)$\n",
    "- Двусторонний критерий: $\\left\\{Z(X) \\geq z_{1 - \\frac{\\alpha}{2}} \\right\\} \\bigcup \\left\\{Z(X) \\leq -z_{1 - \\frac{\\alpha}{2}} \\right\\} $\n",
    "    - p-value = $2\\cdot \\min \\left[{\\Phi(z), 1 - \\Phi(z)} \\right]$, где z &mdash; реализация статистики $Z(X)$\n",
    "---\n",
    "\n",
    "Тогда надо лишь посчитать следующую статистику: $\\sqrt{n}\\dfrac{\\overline X - 7}{\\sqrt{\\sigma^2}} \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$\n",
    "\n",
    "**Но есть одна проблема: мы не знаем $\\sigma^2$!**\n",
    "\n",
    "\n",
    "Что мы можем сделать? Правильно, попытаемся ее оценить! Благо придумывать оценку не надо, ее уже придумали за нас: $\\widehat{\\sigma^2} =S^2 = \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}}(X_i - \\overline X)^2$. Она является [несмещенной](https://ru.wikipedia.org/wiki/Несмещённая_оценка) и [состоятельной](https://ru.wikipedia.org/wiki/Состоятельная_оценка) оценкой дисперсии."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fa4b992c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Оценка sigma^2: 0.1367238095238095\n"
     ]
    }
   ],
   "source": [
    "# ddof = 1 -- Это значит, что делим не на n, а на n-1 в формуле выше\n",
    "print(f\"Оценка sigma^2: {numpy.var(X, ddof=1)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2590bf7",
   "metadata": {},
   "source": [
    "Давайте введем новый критерий T'-test, в котором мы подставим:\n",
    "\n",
    "- $T(X) := \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}} $\n",
    "- $T(X) \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$\n",
    "\n",
    "    \n",
    "Осталось проверить: **Правда ли что при $H_0$ распределение статистики T &mdash; стандартное нормальное?**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c387a0e9",
   "metadata": {},
   "source": [
    "Для этого я предлагаю посмотреть, как на самом деле будет распределена статиcтика $T(X) = \\sqrt{n}\\dfrac{\\overline{X}-\\mu_0}{\\sqrt{S^2}}$ в задаче, поставленной изначально. \n",
    "Для этого будем считать, что выборка $X$ состоит из 7 элементов и $X \\sim \\mathcal{N}$.\n",
    "\n",
    "- Мы $M$ раз нагенерируем выборку $X$ и посчитаем каждый раз статиcтику $T(X)$.\n",
    "- В итоге мы получим выборку размера $M$ для $T(X)$ и сможем построить гистограмму распределения. Отдельно построим распределение $\\mathcal{N}(0, 1)$. Если эмпирическое распределение визуально совпадет с теоретическим нормальным, значит все хорошо. А если нет, то так просто мы не можем заменить $\\sigma^2$ на $S^2$.\n",
    "    - Дополнительно посмотрим, что будет, если заменить $T(X)$ на $Z(X)$. Благо на искусственном примере мы знаем дисперсию.\n",
    "\n",
    "Для этого мы напишем единообразную функцию, которая сможет построить распределение для любой статистики, а не только для $T(X), Z(X)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9fe93bed",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_statistics(number_of_experiments, statistic_function, sample_size, sample_distr):\n",
    "    \"\"\"\n",
    "        Функция для генерации выборки некой статистики statistic_function, построенной по выборке из распределения sample_distr.\n",
    "        Возвращает выборку размера number_of_experiments для statistic_function.\n",
    "    \n",
    "        Праметры:\n",
    "            - number_of_experiments: число экспериментов, в каждом из которых мы посчитаем statistic_function\n",
    "            - statistic_function: статистика, которая принимает на вход выборку из распределения sample_distr\n",
    "            - sample_size: размер выборки, которая подается на вход statistic_function\n",
    "            - sample_distr: распределение изначальной выборки, по которой считается статистика\n",
    "    \"\"\"\n",
    "\n",
    "    statistic_sample = []\n",
    "    for _ in range(number_of_experiments):\n",
    "        # генерируем number_of_experiments раз выборку\n",
    "        sample = sample_distr.rvs(sample_size)\n",
    "\n",
    "        # считаем статистику\n",
    "        statistic = statistic_function(sample)\n",
    "\n",
    "        #сохраняем\n",
    "        statistic_sample.append(statistic)\n",
    "    return statistic_sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3edb3f62",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1584x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(8)\n",
    "\n",
    "sample_size=7\n",
    "M = 100000\n",
    "sample_distr = norm(loc=5, scale=3) # Пусть выборка из этого распределения\n",
    "\n",
    "T_X = lambda sample: numpy.sqrt(sample_size) * (numpy.mean(sample) - sample_distr.mean()) / numpy.sqrt(numpy.var(sample, ddof=1)) # или numpy.std\n",
    "Z_X = lambda sample: numpy.sqrt(sample_size) * (numpy.mean(sample) - sample_distr.mean()) / sample_distr.std()\n",
    "samples = {\n",
    "    \"T(X)\": sample_statistics(\n",
    "    number_of_experiments=M, statistic_function=T_X,\n",
    "    sample_size=sample_size, sample_distr=sample_distr),\n",
    "    \n",
    "    \"Z(X)\": sample_statistics(\n",
    "    number_of_experiments=M, statistic_function=Z_X,\n",
    "    sample_size=sample_size, sample_distr=sample_distr)\n",
    "}\n",
    "\n",
    "\n",
    "pyplot.figure(figsize=(22, 5))\n",
    "\n",
    "for i, name in enumerate([\"T(X)\", \"Z(X)\"]):\n",
    "    pyplot.subplot(1, 2, i + 1)\n",
    "    current_sample = samples[name]\n",
    "    l_bound, r_bound = numpy.quantile(current_sample, [0.001, 0.999])\n",
    "    \n",
    "    x = numpy.linspace(l_bound, r_bound, 1000)\n",
    "    pyplot.title(f'Распределение статистики {name}, sample size={sample_size}', fontsize=12)\n",
    "    distplot(current_sample, label='Эмпирическое распределение')\n",
    "    pyplot.plot(x, norm(0, 1).pdf(x), label='$\\mathcal{N}(0, 1)$')\n",
    "    pyplot.legend(fontsize=12)\n",
    "    pyplot.xlabel(f'{name}', fontsize=12)\n",
    "    pyplot.xlim((l_bound, r_bound))\n",
    "    pyplot.ylabel('Плотность', fontsize=12)\n",
    "    pyplot.grid(linewidth=0.2)\n",
    "\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dee26223",
   "metadata": {},
   "source": [
    "Мы видим, что:\n",
    "- Z-test тут работает: $\\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{\\sigma^2}} \\sim \\mathcal{N}(0, 1)$.\n",
    "- Но вот для $T(X)$ это не так! **Они отличаются! А значит T'-критерий не подходит для изначальной задачи!** \n",
    "\n",
    "----\n",
    "\n",
    "### Почему такое произошло?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3d363e9",
   "metadata": {},
   "source": [
    "При создании критерия есть **2 шага**:\n",
    "1. Придумать статистику для критерия\n",
    "    - С этим мы успешно справились, придумав $T(X)$.\n",
    "2. Понять, как распределена статистика.\n",
    "    - И вот это самый сложный шаг, который не позволяет использовать любую придуманную статистику. Нужно также понимать ее распределение.\n",
    "    - И с этим, как мы увидели, мы провалились для $T(X)$. Нормальное распределение не подошло.\n",
    "\n",
    "Но почему $T(X) = \\sqrt{n}\\dfrac{\\overline X - \\mu}{\\sqrt{S^2}}$ не распределена нормально, хотя $\\sqrt{n}\\dfrac{\\overline X - \\mu}{\\sqrt{\\sigma^2}} \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$? Почему при замене $\\sigma^2$ на $S^2$ все испортилось? \n",
    "\n",
    "**Дело в том, что $S^2$ &mdash; это случайная величина!**\n",
    "\n",
    "Вспомним, как мы выводили Z-критерий?\n",
    "1. Мы посчитали, что $\\overline X \\sim \\mathcal{N}(\\mu, \\sigma^2)$. Из ЦПТ или, в случае выше, из свойств нормального распределения.\n",
    "2. Далее, все также из свойств этого распределения следует, что если мы вычтем константу или поделим на константу, то нормальное распределение не превратится в другое: поэтому $\\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{\\sigma^2}} \\sim \\mathcal{N}(0, 1)$.\n",
    "\n",
    "**Но мы ничего не знаем про** $\\dfrac{\\overline{X}}{\\sqrt{\\eta}}$, где $\\overline{X} \\sim \\mathcal{N}, S^2 := \\eta \\sim P$, где P неизвестно. Мы не знаем пока никаких теорем, которые хоть как-то доказывали, что тут также останется нормальное распределение."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7a6046a",
   "metadata": {},
   "source": [
    "Давайте посмотрим на распределение $\\sqrt{S^2}$ на все том же нормальном распределении."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "31f2f191",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "\n",
    "\n",
    "S2 = lambda sample: numpy.std(sample, ddof=1)\n",
    "S2_sample = sample_statistics(\n",
    "    number_of_experiments=M, statistic_function=S2,\n",
    "    sample_size=sample_size, sample_distr=sample_distr\n",
    ")\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title('Распределение $\\sqrt{S^2}$', fontsize=12)\n",
    "distplot(S2_sample, label='Эмпирическое распределение')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel('$\\sqrt{S^2}$', fontsize=12)\n",
    "pyplot.ylabel('Плотность распределения', fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd8a8d86",
   "metadata": {},
   "source": [
    "Мы видим, что оно не симметрично и непонятно как распределено. Поэтому, когда мы некую величину из нормального распределения делим на несимметричное непонятное распределение, мы и получаем, что наша статистика $T$ не из нормального распределения.\n",
    "\n",
    "Так что давайте выведем критерий, который поможет решить изначальную задачу!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "550730cf",
   "metadata": {
    "tags": []
   },
   "source": [
    "## T-test\n",
    "\n",
    "Давайте решим проблему шага 2 в создании критерия и найдем распределение статистики $T = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}}$. Для того, чтобы это узнать, нам потребуется несколько фактов:\n",
    "\n",
    "1. Пусть $X_1 \\ldots X_n \\sim \\mathcal{N}(\\mu, \\sigma^2)$\n",
    "\n",
    "2. Пусть $\\xi_1 \\ldots \\xi_n \\sim \\mathcal{N}(0, 1)$. Тогда $\\eta=\\xi_1^2 +\\ ... +\\xi_n^2 \\sim \\chi^2_n$, &mdash; [**хи-квадрат распределение с $n$ степенями свободы**](https://ru.wikipedia.org/wiki/Распределение_хи-квадрат).\n",
    "    - Тогда $\\underset{i=1}{\\overset{n}{\\sum}}\\left(\\xi_i - \\overline \\xi \\right)^2 \\sim \\chi^2_{n-1}$. [Док-во](https://en.wikipedia.org/wiki/Cochran%27s_theorem) для крепких духом, и любящих линейную алгебру.\n",
    "\n",
    "    - $S^2_X = \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}}(X_i - \\overline X)^2 $\n",
    "\n",
    "    - $\\xi_i := \\dfrac{X_i - \\mu}{\\sigma} \\sim \\mathcal{N}(0, 1)$. Тогда $S^2_{\\xi} = \\dfrac{1}{\\sigma^2}S^2_X$.\n",
    "<!--     $$\\begin{align}\n",
    "    S^2_{\\xi} &= \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}}\\left(\\xi_i - \\overline \\xi \\right)^2 =\n",
    "            \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}} \\left(\\dfrac{X_i-\\mu}{\\sigma} - \\underset{i=1}{\\overset{n}{\\sum}}\\left[\\dfrac{X_i-\\mu}{n\\sigma}\\right] \\right)^2 = \\\\\n",
    "             &= \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}} \\left(\\dfrac{X_i}{\\sigma} - \\dfrac{\\mu}{\\sigma} - \\underset{i=1}{\\overset{n}{\\sum}}\\left[\\dfrac{X_i}{n\\sigma}\\right] + \\dfrac{n\\mu}{n\\sigma} \\right)^2 =\\\\\n",
    "             &= \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}} \\left(\\dfrac{X_i}{\\sigma} -\\dfrac{\\overline X_i}{\\sigma} \\right)^2 = \\dfrac{1}{\\sigma \\cdot(n - 1)}\\underset{i=1}{\\overset{n}{\\sum}} \\left(X_i - \\overline X_i \\right)^2 = \\dfrac{1}{\\sigma}S^2_X\n",
    "    \\end{align}\n",
    "    $$ -->\n",
    "    \n",
    "    - А значит $\\dfrac{(n - 1)\\cdot S^2_X}{\\sigma^2} = \\underset{i=1}{\\overset{n}{\\sum}}\\left(\\xi_i - \\overline \\xi \\right)^2 \\sim \\chi^2_{n-1}$\n",
    "\n",
    "3. Пусть $\\xi \\sim \\mathcal{N}(0, 1), \\eta \\sim \\chi^2_k$ и $\\xi$ с $\\eta$ независимы. Тогда статистика $\\zeta = \\dfrac{\\xi}{\\sqrt{\\eta/k}} \\sim t_{k}$ &mdash; из [распределения Стьюдента](https://ru.wikipedia.org/wiki/Распределение_Стьюдента) с k степенями свободы.\n",
    " \n",
    "    - $\\xi := \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sigma} \\sim \\mathcal{N}(0, 1)$\n",
    "    - $\\eta := \\dfrac{(n - 1)\\cdot S^2_X}{\\sigma^2} \\sim \\chi^2_{n-1}$\n",
    "    - $\\xi$ и $\\eta$ [независимы](https://math.stackexchange.com/questions/4165803/overlinex-and-s2-are-independent)\n",
    "    - Тогда\n",
    "    $$\\begin{align}\n",
    "        T = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}} = \\frac{\\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sigma}}{\\sqrt{\\dfrac{(n - 1)\\cdot S^2_X}{(n - 1)\\sigma^2}}} = \\dfrac{\\xi}{\\sqrt{\\dfrac{\\eta}{n-1}}} \\sim t_{n - 1}\n",
    "    \\end{align}$$\n",
    "\n",
    "**Итого:**\n",
    "\n",
    "Придуманная нами статистика $T = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}} \\sim t_{n - 1}$ &mdash; взята из распределения Стьюдента с n - 1 степенью свободы. **Но только в случае, если изначальная выборка из нормального распределения!**\n",
    "\n",
    "Теперь нам достаточно данных, чтобы построить критерий для нашей изначальной задачи:\n",
    "\n",
    "### T-test, критерий\n",
    "\n",
    "$H_0: \\mu =\\mu_0, X \\sim \\mathcal{N}\\ vs.\\ H_1: \\mu > \\mu_0$ или $X$ не из нормального распределения\n",
    "- Статистика $T(X) = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}}$\n",
    "- $T(X)  \\sim t_{n - 1}$\n",
    "- Односторонний критерий: $\\left\\{T(X) \\geq t_{n-1, 1 - \\alpha} \\right\\}$\n",
    "    - p-value = $1 - \\tau_{n-1}(z)$, где z &mdash; реализация статистики $T(X)$, $\\tau_{n-1}(z)$ &mdash; функция распределения $t_{n - 1}$\n",
    "- Двусторонний критерий: $\\left\\{T(X) \\geq t_{n-1, 1 - \\frac{\\alpha}{2}} \\right\\} \\bigcup \\left\\{T(X) \\leq -t_{n-1, 1 - \\frac{\\alpha}{2}} \\right\\} $\n",
    "    - p-value = $2\\cdot \\min \\left[{\\tau_{n-1}(z), 1 - \\tau_{n-1}(z)} \\right]$, где z &mdash; реализация статистики $T(X)$\n",
    "---\n",
    "\n",
    "Давайте теперь протестируем все наши теоретические исследования на практике!\n",
    "\n",
    "#### Python-библиотеки:\n",
    "- `scipy.stats.chi2(df=N)` &mdash; [библиотека](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html) для распределения хи-квадрат с N степенями свободы.\n",
    "- `scipy.stats.t(df=N)` &mdash; [библиотека](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.t.html) для распределения Стьюдента с N степенями свободы.\n",
    "- `scipy.stats.ttest_1samp`  &mdash; [реализованный T-критерий](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_1samp.html) в Python\n",
    "\n",
    "\n",
    "Для начала посмотрим на распределение Хи квадрат и на распределение $\\eta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d29146f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "\n",
    "\n",
    "eta_statistic = lambda sample: numpy.var(sample, ddof=1) * (sample_size - 1) / sample_distr.var()\n",
    "eta_sample = sample_statistics(\n",
    "    number_of_experiments=M, statistic_function=eta_statistic,\n",
    "    sample_size=sample_size, sample_distr=sample_distr\n",
    ")\n",
    "\n",
    "\n",
    "chi2_dist = chi2(df=sample_size-1) # Распределение chi2\n",
    "\n",
    "l_bound, r_bound = numpy.quantile(eta_sample, [0.001, 0.999])\n",
    "x = numpy.linspace(l_bound, r_bound, 1000)\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title('Распределение $\\eta$', fontsize=12)\n",
    "distplot(eta_sample, label='Эмпирическое распределение')\n",
    "pyplot.plot(x, chi2_dist.pdf(x), label='Chi2(n-1)')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel('$\\eta$', fontsize=12)\n",
    "pyplot.ylabel('Плотность распределения', fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11db4cc6",
   "metadata": {},
   "source": [
    "Видим, что все совпало!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "46d91c31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "\n",
    "\n",
    "T_X = lambda sample: numpy.sqrt(sample_size) * (numpy.mean(sample) - sample_distr.mean()) / numpy.std(sample, ddof=1)\n",
    "T_sample = sample_statistics(\n",
    "    number_of_experiments=M, statistic_function=T_X,\n",
    "    sample_size=sample_size, sample_distr=sample_distr\n",
    ")\n",
    "\n",
    "\n",
    "T_dist = t(df=sample_size-1) # Распределение T Стьюдента\n",
    "\n",
    "l_bound, r_bound = numpy.quantile(T_sample, [0.001, 0.999])\n",
    "x = numpy.linspace(l_bound, r_bound, 1000)\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title('Распределение $T(X)$', fontsize=12)\n",
    "distplot(T_sample, color='royalblue', label='Эмпирическое распределение')\n",
    "pyplot.plot(x, T_dist.pdf(x), c='green', label='T(n-1)')\n",
    "pyplot.plot(x, norm(0, 1).pdf(x), c='yellow', label='$\\mathcal{N}(0, 1)$')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel('$T(X)$', fontsize=12)\n",
    "pyplot.ylabel('Плотность распределения', fontsize=12)\n",
    "pyplot.xlim((l_bound, r_bound))\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47967ecb",
   "metadata": {},
   "source": [
    "Здесь видно, что распределение Стьюдента практически идеально описывает данные, в то время как нормальное распределение более \"центрировано\": площадь в центре больше.\n",
    "\n",
    "Теперь, как вызвать встроенный t-test в Питоне:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "297ecf1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=11.510815172646131, pvalue=2.8759451265260583e-20)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Как вызывать критерий\n",
    "ttest_1samp(norm(loc=0, scale=1).rvs(100), popmean=-1, alternative='greater')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6548433d",
   "metadata": {},
   "source": [
    "### Доверительный интервал\n",
    "\n",
    "Будет приведено 2 метода вывода доверительного интервала.\n",
    "\n",
    "#### 1 метод\n",
    "\n",
    "Вспомним определение из второй лекции:\n",
    "\n",
    "> Пусть есть статистика $Q$ и критерий $\\psi(Q)$ для проверки гипотезы $H_0: \\theta = m$ уровня значимости $\\alpha$.\n",
    ">\n",
    "> Тогда доверительный интервал для $\\theta$ уровня доверия $1 - \\alpha$: множество таких m, что критерий $\\psi(Q)$ не отвергает для них $H_0$.\n",
    "\n",
    "\n",
    "Пусть $\\mu$ &mdash; истинное среднее выборки. Мы также знаем, что при $H_0: \\sqrt{n}\\dfrac{\\overline X - m}{\\sqrt{S^2}} \\sim t_{n - 1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39fb8942",
   "metadata": {},
   "source": [
    "Нас интересуют такие $m$, что:  $\\left\\{-t_{n-1, 1 - \\frac{\\alpha}{2}} < \\sqrt{n}\\dfrac{\\overline X - m}{\\sqrt{S^2}} < t_{n-1, 1 - \\frac{\\alpha}{2}} \\right\\}$, в этом случае критерий не отвергнется.\n",
    "\n",
    "Распишем, чтобы в центре осталось только $m$: $\\left\\{\\overline X - \\dfrac{t_{n - 1, 1 - \\alpha/2} \\sqrt{S^2}}{\\sqrt{n}} < m < \\overline X + \\dfrac{t_{n - 1, 1 - \\alpha/2} \\sqrt{S^2}}{\\sqrt{n}}\\right\\}$. А значит наш доверительный интервал: $CI_{\\mu} = \\left(\\overline X \\pm \\dfrac{t_{n - 1, 1 - \\alpha/2} \\sqrt{S^2}}{\\sqrt{n}} \\right),$ где $S^2 = \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}}(X_i - \\overline X)^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7dae745",
   "metadata": {},
   "source": [
    "### 2 метод\n",
    "\n",
    "Докажем через [классическое определение](https://ru.wikipedia.org/wiki/Доверительный_интервал#Определение) доверительного интервала.\n",
    "\n",
    "> Доверительным интервалом для параметра $\\theta$ уровня доверия $1 - \\alpha$ является пара статистик $L(X), R(X)$, таких, что $P(L(X) < \\theta < R(X)) = 1 - \\alpha$.\n",
    "\n",
    "$$\\begin{align}\n",
    "    &T(X) = \\sqrt{n}\\dfrac{\\overline X - \\mu}{\\sqrt{S^2}} \\sim t_{n - 1} \\Rightarrow \\\\\n",
    "    &P\\left(-t_{n - 1, 1-\\alpha/2} < \\sqrt{n}\\dfrac{\\overline X - \\mu}{\\sqrt{S^2}} < t_{n - 1, 1-\\alpha/2} \\right) = 1 - \\alpha \\Leftrightarrow \\\\\n",
    "    &P\\left(\\overline X - \\dfrac{t_{n - 1, 1 - \\alpha/2} \\sqrt{S^2}}{\\sqrt{n}}  < \\mu < \\overline X + \\dfrac{t_{n - 1, 1 - \\alpha/2} \\sqrt{S^2}}{\\sqrt{n}} \\right) = 1 - \\alpha\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "\n",
    "А значит $CI_{\\mu} = \\left(\\overline X \\pm \\dfrac{t_{n - 1, 1 - \\alpha/2} \\sqrt{S^2}}{\\sqrt{n}} \\right)$. \n",
    "\n",
    "*Как вы видите, доказательства в обоих случаях практически идентичны.*\n",
    "\n",
    "\n",
    "В Питоне для построения есть специальная функция:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e990d35e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CI = [9.62, 10.39]\n"
     ]
    }
   ],
   "source": [
    "sample = norm(loc=10, scale=2).rvs(100)\n",
    "\n",
    "# sem -- standart error of the mean, sem = sqrt(S^2)/sqrt(n)\n",
    "left_bound, right_bound = t.interval(alpha=0.95, loc=numpy.mean(sample), df=len(sample)-1, scale=sem(sample)) \n",
    "print(f\"CI = [{round(left_bound, 2)}, {round(right_bound, 2)}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e205c68d",
   "metadata": {},
   "source": [
    "-----\n",
    "\n",
    "Вернемся к изначальной задаче. \n",
    "> 📈 **Задача**\n",
    ">\n",
    "> В нашей компании хотят перейти с одной СУБД на другую. Главным критерием для переходя является \"затраченное время в сутках на загрузку новых данных\". Если раньше для ежедневного обновления базы требовалось в среднем 10 часов, то хочется найти новую СУБД, в которой все это будет происходить бывстрее, чем за 7 часов.\n",
    ">\n",
    "> Для этого было принято решение перенести все данные на новую тестируемую СУБД. В течение одной недели каждый день мы посчитаем время загрузки данных, и если в среднем на обновление будет уходить меньше 7 часов, то мы полностью перейдем на новую СУБД. Ваша задача придумать, как проверить гипотезу о том, что новая СУБД лучше старой.\n",
    "\n",
    "Получилась выборка:\n",
    "\n",
    "- `[6.9, 6.45, 6.32, 6.88, 6.19, 7.13, 6.76]` &mdash; время загрузки в новую БД по дням в часах.\n",
    "\n",
    "Для начала переформулируем условие на языке математики: есть выборка\n",
    "- $X_1, X_2, ..., X_7$ &mdash; время загрузки в часах новых данных в СУБД за каждый день эксперимента\n",
    "- Еще будем считать, что $X$ из нормального распредения.\n",
    "\n",
    "$H_0$: $E \\overline{X} \\geq 7\\ vs.\\ H_1: E \\overline{X} < 7$\n",
    "\n",
    "\n",
    "\n",
    "Мы уже знаем, что если выборка нормальна, то мы можем использовать T-test. Тогда\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "816b21e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = numpy.array([6.9, 6.45, 6.32, 6.88, 6.09, 7.13, 6.76])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0cd29efb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=-2.5247934680450737, pvalue=0.022497429172957096)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_1samp(X, popmean=7, alternative='less')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88027db2",
   "metadata": {},
   "source": [
    "Мы видим, что на уровне значимости 2.5% критерий отвергся, а значит переход на новую СУБД удовлетворяет условиям: загрузка быстрее 7 часов!\n",
    "Построим теперь доверительный интервал, чтобы понять, в каких границах у нас будет эффект."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f42ec21c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CI = [6.31, 6.99]\n"
     ]
    }
   ],
   "source": [
    "left_bound, right_bound = t.interval(alpha=0.95, loc=numpy.mean(X), df=len(X)-1, scale=sem(X)) \n",
    "print(f\"CI = [{round(left_bound, 2)}, {round(right_bound, 2)}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0bccc8a",
   "metadata": {},
   "source": [
    "Отлично! В среднем загрузка будет от 6 до 7 часов.\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86148c3b",
   "metadata": {},
   "source": [
    "Так, мы научились решать задачу оценки среднего выборки, когда дисперсия неизвестна, но выборка из нормального распределения. Теперь научимся решать следующую задачу:\n",
    "\n",
    "\n",
    "> 📈 **Задача**\n",
    ">\n",
    "> Вы придумали идею для стартапа в Москве, где курьеры собирают заказы для клиентов и отвозят им на дом. Маржа от заказа в вашем стартапе &mdash; X ₽, а стоимость работы курьера &mdash; 1К ₽.\n",
    "Специфика вашего стартапа такова, что есть большой риск возврата без оплаты. С учетом стоимостей, инвесторы готовы проспонсировать вам инфраструктуру и привлечение клиентов, если вы покажете, что у вас будет прибыль.\n",
    ">\n",
    "> Из данных у вас есть принесенные деньги от каждого пользователя. Иногда положительная величина, иногда отрицательная.\n",
    "\n",
    "Переформулируем задачу на языке статистики:\n",
    "- $X_1, X_2, ..., X_N$ &mdash; выборка прибыли от пользователя.\n",
    "\n",
    "$H_0$: $E \\overline{X} \\leq 0\\ vs.\\ H_1: E \\overline{X} > 0$\n",
    "\n",
    "Посмотрим на данные:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0ebeece4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-718.  657.  693.  391. -644.  421.  265. -108. 1956. -684. -753. -725.\n",
      " -341. -796. -662.  257. -719. 5184. -739. -291. -427.  283.   10.  500.\n",
      " -713. -458.   60. -756.  333. -537. -744.  254. -555. -780. -329. -560.\n",
      "  936. -742. -784.  213.  299. -678. -736.   24.  264.  293. -490. 2667.\n",
      " -605. -799. -797. -743.  347. -718. -508. -766. 1395.  392.  -62. -510.\n",
      "  237. -785. -745. -781. 3232. -727.  204. 2987.  244. -757.  -78.   10.\n",
      "  364.   -7. -440.  520.  203.  282.  685.  589. -724.  -48.  263. -457.\n",
      " -796. -708. -798.  488. -677. -690.  786. -770.  659. -679. -309. -731.\n",
      "  288. 1047. -796. -721.]\n"
     ]
    }
   ],
   "source": [
    "profits = numpy.loadtxt('profit_from_user.out', delimiter=',')\n",
    "print(profits[:100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "98c403a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "average profit = 58.4868\n",
      "n = 5000\n"
     ]
    }
   ],
   "source": [
    "print(f\"average profit = {profits.mean()}\")\n",
    "print(f\"n = {profits.shape[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3f3a67b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "seaborn.distplot(profits)\n",
    "pyplot.grid(linewidth=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cdc18c7",
   "metadata": {},
   "source": [
    "\n",
    "В отличие от предыдущей задачи тут 2 отличия:\n",
    "- Изначальная выборка не из нормального распределения\n",
    "- Выборка достаточно крупная: не 7 элементов, а уже 5000.\n",
    "\n",
    "Так, а что мы уже умеем решать?\n",
    "\n",
    "\n",
    "|                          | маленькая выборка | большая выборка |\n",
    "|--------------------------|-------------------|-----------------|\n",
    "| нормальное распределение | t-test            | t-test          |\n",
    "| любое распределение      |                   |                 |\n",
    "\n",
    "А сейчас мы выведем критерий для ячейки: \"любое распределение, большая выборка\". Мы снова будем выводить распределение для $T(X)$ статистики.\n",
    "\n",
    "\n",
    "## T'-test\n",
    "\n",
    "Вспомним, что у нас изначально была идея в Z-тесте вместо статистики Z, в которой дисперсия известна, использовать критерий T, где дисперсия оценена на данных. И использовать нормальное распределение. Только в первой задаче этот критерий нам не помог. Но что, если бы выборка была большой? Могли бы мы использовать нормальное распределение для приближения?\n",
    "\n",
    "\n",
    "1. Будем рассматривать ту же статистику $T = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}}$\n",
    "2. $\\xi := \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{\\sigma^2}} \\stackrel{d}{\\rightarrow} \\mathcal{N}(0, 1)$. По ЦПТ сходимость есть только по [распределению](https://en.wikipedia.org/wiki/Convergence_in_distribution).\n",
    "3. Тогда $T = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}} = \\xi \\cdot \\sqrt{\\dfrac{\\sigma^2}{S^2}}$. Обозначим $\\phi := \\sqrt{\\dfrac{\\sigma^2}{S^2}}$\n",
    "    - Помните, в начале лекции было сказано, что $S^2$ &mdash; лучшая оценка для дисперсии? Все дело в том, что она является [состоятельной оценкой](https://ru.wikipedia.org/wiki/Состоятельная_оценка) $\\sigma^2$. По-другому это можно записать так: $S^2$ [сходится по вероятности](https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_probability) к $\\sigma^2$. То есть $S^2  \\stackrel{p}{\\rightarrow} \\sigma^2$ \n",
    "    - А в этом случае существует [теорема](https://en.wikipedia.org/wiki/Continuous_mapping_theorem), утверждающая, что $\\phi = \\dfrac{\\sigma^2}{S^2}  \\stackrel{p}{\\rightarrow} 1$.\n",
    "4. $T = \\xi \\cdot \\phi$.\n",
    "    - $\\xi \\stackrel{d}{\\rightarrow} \\mathcal{N}(0, 1)$\n",
    "    - $\\phi  \\stackrel{p}{\\rightarrow} 1$\n",
    "    - И тут вступает в силу еще одна [теорема](https://en.wikipedia.org/wiki/Slutsky%27s_theorem): $T = \\xi \\cdot \\phi \\stackrel{d}{\\rightarrow} 1\\cdot \\mathcal{N}(0, 1)$. Та же сходимость, что и в ЦПТ!\n",
    "    - **То есть статистика $T$ точно также нормально распределена!**\n",
    "    \n",
    "    \n",
    "Итого, если выборка большая, то мы можем считать, что $T(X) \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$.\n",
    "\n",
    "---\n",
    "\n",
    "Заметим, что в случае \"нормальное распределение, большая выборка\" работают сразу 2 критерия: t-test и t'-test. Это значит, что если $T(X) \\overset{H_0}{\\sim} t_{n - 1}$ и $T(X) \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$, то $t_{n - 1} \\approx \\mathcal{N}(0, 1)$.\n",
    "- Формально же, если степень свободы в t-распределении равна бесконечности, то это нормальное распределение! $\\lim_{n\\rightarrow \\infty}t_{n} = \\mathcal{N}(0, 1)$\n",
    "\n",
    "А если $t_{n - 1} \\approx \\mathcal{N}(0, 1)$, то мы вместо T'-критерия мы можем использовать T-критерий! **Из того, что мы теоретически можем использовать T'-test, на практике мы можем использовать и T-test!**\n",
    "\n",
    "---\n",
    "\n",
    "А значит мы заполнили еще 1 ячейку в таблице:\n",
    "\n",
    "|                          | маленькая выборка | большая выборка |\n",
    "|--------------------------|-------------------|-----------------|\n",
    "| нормальное распределение | t-test            | t-test, t'-test |\n",
    "| любое распределение      |                   | t'-test, t-test |\n",
    "\n",
    "\n",
    "### T'-test, критерий\n",
    "\n",
    "$H_0: \\mu =\\mu_0\\ vs.\\ H_1: \\mu > \\mu_0$\n",
    "- Статистика $T(X) = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}}$\n",
    "- При достаточно большом размере выборки $T(X) \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$ (по ЦПТ и куче вспомогательных теорем)\n",
    "- Односторонний критерий: $\\left\\{T(X) \\geq z_{1 - \\alpha} \\right\\}$\n",
    "    - p-value = $1 - \\Phi(z)$, где z &mdash; реализация статистики $T(X)$, $\\Phi(z)$ &mdash; функция распределения $\\mathcal{N}(0, 1)$\n",
    "- Двусторонний критерий: $\\left\\{T(X) \\geq z_{1 - \\frac{\\alpha}{2}} \\right\\} \\bigcup \\left\\{T(X) \\leq -z_{1 - \\frac{\\alpha}{2}} \\right\\} $\n",
    "    - p-value = $2\\cdot \\min \\left[{\\Phi(z), 1 - \\Phi(z)} \\right]$, где z &mdash; реализация статистики $Z(X)$\n",
    "---\n",
    "\n",
    "\n",
    "Проверим наш критерий на крупных выборках:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1d899d69",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(8)\n",
    "\n",
    "sample_size=2000\n",
    "M = 10000\n",
    "sample_distr = expon(loc=5, scale=300)\n",
    "\n",
    "T_X = lambda sample: numpy.sqrt(sample_size) * (numpy.mean(sample) - sample_distr.mean()) / numpy.std(sample, ddof=1)\n",
    "T_sample = sample_statistics(\n",
    "    number_of_experiments=M, statistic_function=T_X,\n",
    "    sample_size=sample_size, sample_distr=sample_distr)\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "l_bound, r_bound = numpy.quantile(T_sample, [0.001, 0.999])\n",
    "\n",
    "\n",
    "x = numpy.linspace(l_bound, r_bound, 1000)\n",
    "pyplot.title(f'Распределение статистики T(X), sample size={sample_size}', fontsize=12)\n",
    "distplot(T_sample, label='Эмпирическое распределение')\n",
    "pyplot.plot(x, norm(0, 1).pdf(x), label='Экспоненциальное распределение')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel(f'{name}', fontsize=12)\n",
    "pyplot.xlim((l_bound, r_bound))\n",
    "pyplot.ylabel('Плотность', fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ff0f842",
   "metadata": {},
   "source": [
    "Мы видим, что распределения совпали! А на нормальном распределении, где в первый раз были различия на маленькой выборке?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5afd1ae3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "numpy.random.seed(8)\n",
    "\n",
    "sample_size=2000\n",
    "M = 30000\n",
    "sample_distr = norm(loc=5, scale=300)\n",
    "\n",
    "T_X = lambda sample: numpy.sqrt(sample_size) * (numpy.mean(sample) - sample_distr.mean()) / numpy.std(sample, ddof=1)\n",
    "T_sample = sample_statistics(\n",
    "    number_of_experiments=M, statistic_function=T_X,\n",
    "    sample_size=sample_size, sample_distr=sample_distr)\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "l_bound, r_bound = numpy.quantile(T_sample, [0.001, 0.999])\n",
    "\n",
    "\n",
    "x = numpy.linspace(l_bound, r_bound, 1000)\n",
    "pyplot.title(f'Распределение статистики T(X), sample size={sample_size}', fontsize=12)\n",
    "distplot(T_sample, label='Эмпирическое распределение')\n",
    "pyplot.plot(x, norm(0, 1).pdf(x), label='$\\mathcal{N}(0, 1)$')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel(f'{name}', fontsize=12)\n",
    "pyplot.xlim((l_bound, r_bound))\n",
    "pyplot.ylabel('Плотность', fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ca265ad",
   "metadata": {},
   "source": [
    "Тоже самое: статистика из нормального распределения! То есть в первый раз нам не повезло, что размер выборки был маленьким("
   ]
  },
  {
   "cell_type": "markdown",
   "id": "558ef7eb",
   "metadata": {},
   "source": [
    "### Доверительный интервал\n",
    "\n",
    "Выводится также, как и у t-test:\n",
    "\n",
    "$CI_{\\mu} = \\left(\\overline X \\pm \\dfrac{z_{1 - \\alpha/2} \\sqrt{S^2}}{\\sqrt{n}} \\right)$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "221b663a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CI = [289.96, 316.15]\n"
     ]
    }
   ],
   "source": [
    "sample = expon(scale=300).rvs(2000) # E sample = scale = 300\n",
    "left_bound, right_bound = norm.interval(alpha=0.95, loc=numpy.mean(sample), scale=sem(sample)) \n",
    "print(f\"CI = [{round(left_bound, 2)}, {round(right_bound, 2)}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d987490b",
   "metadata": {},
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "999af83b",
   "metadata": {},
   "source": [
    "Ну вот теперь кажется же самое время решать исходную задачу!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7bc5a8a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CI = [14.04, 102.94]\n"
     ]
    }
   ],
   "source": [
    "left_bound, right_bound = norm.interval(alpha=0.95, loc=numpy.mean(profits), scale=sem(profits)) \n",
    "print(f\"CI = [{round(left_bound, 2)}, {round(right_bound, 2)}]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5925afa",
   "metadata": {},
   "source": [
    "Да, выручка положительна! Значит мы нашли инвесторов для нашего стартапа :)\n",
    "\n",
    "Единственное но: **а правда ли, что наша выборка достаточно большая? И T'-test тут работает?** Ответ на этот вопрос мы получим на следующем занятии."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfb58f24",
   "metadata": {},
   "source": [
    "## Какой критерий в итоге использовать на практике? T-test или T'-test?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69c86b7e",
   "metadata": {},
   "source": [
    "Для начала определимся, когда какой критерий лучше использовать?\n",
    "\n",
    "1. Если выборка размера 60, то уже $t_{59} \\approx \\mathcal{N}(0, 1)$. \n",
    "    - Посмотрим на распределения Стьюдента и нормального:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e10cd6fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nGbcg+ZWbbuyFF15gzZo1Sb1MV1wZ4B8TE5M0L0+ePP/q8Tp37hyhoaFpTHytmJgYS36soSu+i0iW1bN+SR5vdQuz/FpxV1w7Lvvnhe0zYcWrEH0gYw6acAn+nG1OhaoS2/QF3qz0IJ8mNGf03XNZXv9HXpq7lQVbj2fM8UWyie3bt7NgwQLGjBnDzp07k+afPXsWgNDQUOLi4gC4cOFC0mn9K/LmzXtNIZYeoaGhScfNTCqyRCTLKRgaxMTOt2CUb07zy/04418I9i+F5S/BP9syL8iJHfB1Nyh5O+eajeWZkgP5wGjBe93+S7MqK3lh3p+cv6xeLbFWanuYMtOLL77Ipk2beOutt5LmXbp0iT179lCxYkVOnToFmAVZzZo1k9YpU6YMQUFB/PXXX17JUaVKFbZs2eKVfaWGp7fVERHJFC2rF2HOY834sdRT9EsYzZkzp+Dz1jCtc+YWWO4OrYUpLeDrbhy9YNA57gX2VHuEBY/ewx3lCliTScQH7N27l2+++YYRI0ZcM3/RokU0atQo6fm0adNo27YtDRs2JCQkhHHjxvHdd98lDXr/7LPP+Oyzz1I8TmBgIEFBQf96fEWjRo1YvHixt16Wx1RkiUiWEBJo560uNRn+YEceMF5nOi1h7fswuTEcWG11PNPuxfDRnRhbvuF9Z2eGBLzKqwM68FzrKgTYbVanE8mSxo0bR+7cua+ZN3nyZHr06JH0fMeOHQwdOpRp06Zx4sQJQkNDGTZsWNLyEiVKsGbNmhSPsXv3bmJjYylevDg//vgjsbGxlCpVCoAiRYpQtWpV5syZ4+VXdnM6XSgiliuSN5hP+9ZjVcHujIztgvPSSZjT3hyIntXEnYc5D8HfP7KzzTu04BXG3T6VLyNnM/Sr3zl3WTftlZytTJky1zw/cuQIuXJde1Hg7du3s2XLFtq3b8/cuXMB+Prrr/n666//tb+AgACKFSvG559/7vEx4eoV35966ilee+01S26orSJLRCxVrVhePujbkJcCH2dFYj3YOQcWPAaXs/hFLrd/D4d/I77DR4wpO5jOkeWZOWwSgz9fx8HTl6xOJ5Llufdk3UhCQgJVq1ZN83GeeuqpNG+bXjpdKCKWaValEB8OaclQ/3GscN4Ki0fBrD5Zv8C64vwx+KoD/DKRb40mvJhnLF8Oa85tpTL2/qsi4htUZImIJQY0LMNTPTrQ2fEKuxKLwTc94Lf03cDVEoYBP70Ccx9mnbMqfRnHxIH30b5WMauTiYjFVGSJSKYb06oyTVp14f64Fzl52YAp95mDyn3ZH1NhWmf2O/LTMf5lBnW9nwEN/z1ORERyDhVZIpKpxrSqTLGGPekVP5rLpw/Bp03h+GarY3nHvpXwv3uJjrlEx9jnuadVV/rfWdrqVCJiERVZIpJpxrSsTGTDHjwaPwznwbXwvxZw7ojVsbzrxE74b1PiT+ylX9yTNLuvC/1UaInkSCqyRCRTjG5ZiVJ3dePR+GEYh9bBtK7m5RCyowtR8GU7Ek7uoU/cU7Ro3Yk+d5S2OpWIZDIVWSKS4Ua2qETZu7rxcPwjOA9vMAushGx+mYNLp81C69R++sSOpHWbjvS+vZTVqUQkE6nIEpEM9WjTClS6uyvD4h7BeWQTTOsC8ResjpU5Lp6CL9sRd+YwvWJH0r7t/XSrW8LqVCKZbvXq1dSqVeu6yxo1asThw4eTnlesWJE//viD8+fP88gjj2RKvuHDh/P66697fb8qskQkw3S5rTi1m3RmSNwIEo9vhamdIC7G6liZ68IJ+KItcdHH6BE7iq7tO9C4UkGrU4lkmP3799O0adOk523atCEmJobNmz37gcuoUaNYsWIFefPmZdKkSR4f98UXXyQ+Pp6YmBhiYmI4e/bsNVeCb9OmDdu2bSMmJoY1a9ZQpUqVpGWffvopPXr0oGBB7/5tqsgSkQzRsHwEPTq0ZUjcoyRG7YSv7s++Y7BuJuYf+LwNcedO0i/+KcZ0b0m1YnmtTiWSKYYOHcpXX33l8fqlSpVi+/btaTrWN998Q2hoKKGhoYSFhbF//34Aypcvz7Rp0xg6dChhYWHMnz+fefPmJd16Jy4ujsWLF9O7d+80HTclKrJExOsqFwnlxZ7N6R8/kviYU+YpwthzVseyVsxxjKmdOB9nMNg5hv/0vYfIsFw3307Eh3z55ZeULFmS+fPnExMTw8iRI2nSpAk///xz0jrBwcF89tlnnDlzhu3bt1O3bt2kZcuXL+eee+7h/fffJyYmhgoVKnglV4sWLVi1ahVr1qwhMTGRCRMmEBkZSaNGjZLWWblyJa1bt/bK8a5QkSUiXlUkbzDv97uboc4xRCcEYEztbP7aTuD0HowZD3LYKMjTAaP5pN/t5A3WLWQl++jduzeHDh2ibdu2hIaGsnDhQpxOJ0ePHk1a58UXX6RcuXKUK1eOFi1a0KdPn6RlTZs2ZdWqVQwfPpzQ0FD+/vtvRo8eTXR0dIqTu7Zt23L69Gn+/PNPhgwZcs0ym812zWObzUb16tWT5u3cuZOaNWt6tT301y0iXpMnyJ9P+zXghaBR7E2MhG86w8ldVsfKWg7+ijFnGBs7/Y/JYU/wUa+L9J2ynoREw+pk4qtajociNTL2GP9sgyVPp3qzsLAwYmKuHYfZtWtXhg0bllQkvffee7zwwgsp7mPChAlMmDDhpseaOXMmkydPJioqivr16zN79mzOnj3L9OnTWbZsGRMmTKBRo0b8+uuvjB49msDAQEJCQpK2j4mJIV++fKl+jTeiniwR8Qo/G7zXvTZf5R/Br9SC+Y+aV0CXf9v2LSx/mXnGXfxWcgivdMjgL0gRi0RHRxMaGnrNvGLFil3za8KDBw965Vg7d+7k+PHjOJ1O1q5dy6RJk+jUqRMAu3fvpk+fPrz//vscP36ciIgIduzYwZEjVy+GHBoayrlz3h3WoJ4sEfGKR5tVZHf5Acx0NIWf34DN06yOlLWtehPCS/NenV68VecEDx4+y/T1h6xOJb4oDT1MGckwrvbK7tmzB5vNRrFixTh27BgAx48fp0SJEuzYsQOAkiVL3nB/Tz/9NM8880yKy5MXce453E8Rzp49m9mzZwOQL18+BgwYwIYNG5KWV6lShS1bttzk1aWOerJEJN2aVilE7cYdeSPhAfhzNqx41epIvmHBY7DvZ8bED6BL29bUKhFmdSKRdIuKiqJs2bIAJCQksGzZsmsGmM+cOZOnn36asLAwIiMjb3otrPHjxyf9YvB60xXt2rUjLMz8G6pbty7Dhw9n3rx5Scvr1KmDn58fERERTJ48mXnz5rF79+6k5Y0aNWLxYu/eqN7TIqslsBvYA4y5zvKhwDZgM7AaqOqaXxq47Jq/Gfg4HVlFJAsqVSCEkV2b8XDcMHP81dzhVkfyHU4HfNsPR8xJhiU8zus976ZA7kCrU4mky/jx43nuueeIjo7mySef5JNPPqFXr15Jy1966SUOHjzI/v37+fHHH1N1eYcb6datG3v27CEmJoYvv/ySiRMnXrPvd999l7Nnz7J7926io6MZNGhQ0rKgoCDuu+8+vvjiC69kSWIYxs0mu2EYew3DKGsYRqBhGFsMw6iabJ28bo/bGYaxxPW4tGEYf3pwjKRpw4YNBpChU3h4uBEeHp7hx8kpk9oz57ZprgC7MffRJkbVF383bE8fNshf1vJMPtmekbcatudPGnePXWlMHdTAsPvZrM/k623qg5OnbVq5cmXLs6Z2Wr16tVGrVq1MPabdbjfsdrtH6w4fPtyYMGFCmtrdMIyNKdU0nozJqofZg7XP9XwG0B7Y4baO+xUGc7sOLCLZ3PiONZhR4GF2OMvDd93hzL6bbyT/dvR3jMWj+aXNO9QpNYiRLc7y+mL9KlOyj4YNG1od4Ybef//9DNmvJ0VWJHDY7fkRoP511nsYeAIIBJq4zS8D/IFZiD0HrLrRwex2O+Hh4R7ESrsr52zFO9Se3ucLbdr91iLE13iQrx3NCN7wAblOrIUM/ttNK19oT2Pv91za0ZB3q3RkSsO9dImeybLdp62OlSJfaFNf42mb+vn5JV2pXFLm7Tby8/NLdX3izYHvHwDlgNGYxRTAcaAkUBuzAJsOXO9eEoOBjcDGiIgIL0YSkYxQpXBu7m3cmGcT+uF/aBXBa9+yOpLPswEhK57F79QuHokbRv+WDSiWL8jqWCKSDp70ZB0F3G8bX9w1LyUzgI9cj+NcE8DvwF6gImZB5W6yayIqKspIfgXXjJJZx8kp1J7elxXbNCTQztOt6zM04TEcMScwZvTh7KWs2+PiLiu2579Mf5CLQ3/myaAneKHVIXp8sopEZ9YdgeETbepjbtamhQsXJjExMZPS+D5vtZXT6Uz1592TnqwNQAXM036BQDdgXrJ13G8u1Br42/W4IHClv66saz0N2hDxYS+0rcr/8g3nqFEQY1Y/8JECy2dE78f4fhg7KMeKYoMY0aS81YlEJI08KbIcwHDgB2AnMBPYDowD2rnWGe6atxnztGAf1/y7ga2u+d9iXurhjJeyi0gmu69GEXLV6cYc513w8wQ4vN7qSNnTrgXw++dMdrShTuMO1C2dNce6iTUSEhLIlUs3F89MAQEBOByOVG/n6RXfF7kmd+43Gno0he1muyYR8XGRYbkY3rEZneP6wZG15hXLJeMseRpK38Hj4Q/xZbe/6PbuQs5fTv3/5CX7OXHiBJGRkRw9epTLly9bHSfbs9lsFC5cOE233NFtdUTkpvxs8OYDdXjG9giX4xPhu8Hg1JiQDJVwCWPWAE4PWs47uYbz2v2HGT59k9WpJAu4csPlYsWKERAQYHGarMvPzzxZ53Q6072vixcvcurUqVRvpyJLRG7q4XvKs674ADYnVob5/eGs7rGXKf7ZirF8HEvvfYV7qvag620nmbnx8M23k2wvJiYmqdiS67tyuQUrf5yhexeKyA3ViMxHw3ta856jA2z52rw3oWSete/D3hWMje9JrzbNKB6usTgivkJFloikKNDux8tdG/CY42Gz92rRSKsj5TyGAXOGkhB3kZGMYHznOthsVocSEU+oyBKRFD3WrAIz8w/mOAUxvhsMcTo9YYmYfzDmjmAXZdlUqh+9GpSyOpGIeEBFlohcV83i+ah+V3umJzaDtR/ocg1W27UAts3ivYT76dCyBSXzh1idSERuQkWWiPxLkL8f47rezsiEQfid/ht+esXqSAKwaCTGpTM84xzG+C61ddpQJItTkSUi//J484rMCB9MlFEA5/cPgSPW6kgCcDka5/zH2GUrw4YS/el7R2mrE4nIDajIEpFr1CkZRpU72/N1YlPzNOGRDVZHEne7FsLWmUxK6EDbe1tQuoBOG4pkVSqyRCRJkL8fY7s0YGT8IGyn/oIVr1odSa5n8SiMS2cY43yI17rcqtOGIlmUiiwRSfJIkwp8HTaEE+TH+H6oThNmVZejcc57lL9sZVhfvC896uvXhiJZkYosEQGgUuFQbrmrLV8nNoFfJ8HR362OJDeyexFs/YZJCR3o2LIZhfMGWZ1IRJJRkSUi+NngpU638qxjIH7R+2DleKsjiSeWjMGIPcdLDGVs+xpWpxGRZFRkiQg9G5RiVdF+HLYVxTnvUZ0m9BWXzuBcPIYtVORUpR60qFbY6kQi4kZFlkgOVzRfMB1aNOdjRxv4Yyrs/8XqSJIaW2fC3p94LaEbD7e7m9Agf6sTiYiLiiyRHG5s+xqMZSjG5XPw43NWx5G0WPA4sYk23g8ezKiWla1OIyIuKrJEcrCW1YsQVbEHW6mAc/FouBxtdSRJi+gDGCvG86NRj4L1OnFrqXCrE4kIKrJEcqzQIH+Gtbub8fEPwN7lsG2W1ZEkPdZ+gC1qG8/F9+G5jvUIsOviWSJWU5ElkkM9cW9FJgUNJtZpgwVPWB1H0svpwJg7glOE833+gQxoWMbqRCI5nooskRyoWrG8FK3fiaVGXYwV4yH6gNWRxBuObYLfPuYrRzMaN2lJsXzBVicSydFUZInkMDYbPN/hVl5K6I3fiR3m/Qkl+/jpVWwXoxhnDOK5trp2loiVVGSJ5DBdbyvBqqJ9OW4rhHPBE+B0WB1JvCn+As7Fz7CDspyu/CCNKxa0OpFIjuVpkdUS2A3sAY/Krp4AACAASURBVMZcZ/lQYBuwGVgNVHVb9rRru91AizQnFZF0CwsJ4IGWTfjY0Ro2T4dDa62OJBlh+3fY9q3g9YSujGh/B0H++ve0iBU8+cuzAx8ArTCLp+5cW0QBTAdqALWAN4C3XfOrAt2AapiF2oeu/YmIBUa2qMxb/gMx4i/B0hesjiMZyFj4FJecgUwNHcjQRuWsjiOSI3lSZNXD7InaB8QDM4D2ydY57/Y4N2C4Hrd3rR8H7Hftp1468opIGtUqEUbeOl1YY9yCc9k4uHjS6kiSkU7vwfh1Et8576Zeo9aUzB9idSKRHMeT+y9EAofdnh8B6l9nvYeBJ4BAoInbtuuSbRt5o4PZ7XbCwzP2QnphYWEZuv+cRu3pfd5uUz8bPNepPg85ehJwahu5936PLYP/zrKSnPoZNbb+lwu1uzE2zwDGdfqdx7/902v7zqltmpHUpt6VFdrTmyfqPwDKAaOB1N6bYzCwEdgYERHhxUgiAtCpZmF+KNCLk4QTvPx5bIbT6kiSCWyOywSteIm/KcmeUt1oXCG/1ZFEchRPerKOAiXcnhd3zUvJDOCjVG472TURFRVlREdnzq09Mus4OYXa0/u80aZhIQE0b3g/DzhawaYvidm1wgvJfFOO/Iz+/g22yp14q3xHpjb+iUWbvifO4b0iO0e2aQZTm3qXle3pSU/WBqACUAbzVGA3YF6ydSq4PW4N/O16PM+1fpBr+wrA+nTkFZFUerx5Rd7yHwBx52HZWKvjiAWMRaOJddr5Kk9/Bt5V1uo4IjmGJ0WWAxgO/ADsBGYC24FxQDvXOsNd8zZjjsvq45q/3bX+DmAJ5ritRC9lF5GbqFI0lAJ1u7DOqI5z2cu6AXROFb0fY817zHE25PbG91FUV4IXyRSenC4EWOSa3Ln//vvRG2z7qmsSkUz2dLs6jEroid+JbTh//8zqOGKlVW9jr/0gr4X2Z3Sr1Tw2Y5PViUSyPV2hTiSbanNLUX4v3od/bAVxLhwJGuyesyVcInHJc+ygDJeq96BeGQ2CF8loKrJEsqFcAXb6tb6bjxxtYNssXdldTNu/w3ZwDRMSuvJU+/rY/WxWJxLJ1lRkiWRDDzUux6e5BuJwJOrK7nINY9EozpGbhQX60b1uiZtvICJppiJLJJspkT8XNe5qzxJnPZy/vAnnj1kdSbKSqD9hw//40tGMdvc2JywkwOpEItmWiiyRbGb0fdV5xdkH+9kDsPZ9q+NIVrTiNWxx53nLfwCPNqtodRqRbEtFlkg20qBsfk5U7s1eSpC4eAw44qyOJFnR5Wicy8bxm1GNAnW7UL5QHqsTiWRLKrJEsgk/GzzatgFvJ3TEtnc57F5sdSTJyn7/HPuJP3nd0YNRbWpanUYkW1KRJZJNdLmtBIsi+nHRCMZY8ozVcSSrM5wkLhrDMVsh/irbh8YVC1qdSCTbUZElkg3kCfKnw73NmOpoirFxCpzcZXUk8QUHVmHbNZ/3E9oxtG1D/HVJBxGvUpElkg08fE95PggagF9cDKx4zeo44kOMH54jzmlnVr5+9GxQyuo4ItmKiiwRH1cyfwil7ujEamcNEle8pvsTSupEH8BY+wGznY1o1qylLukg4kUqskR83Mj7qvO6sxf207thw/+sjiO+6Jc3sV86wdv2/oxoWsHqNCLZhoosER/WoGx+/qnch0MUJXHx0+B0WB1JfFH8BRKXvsQmoxL563XTJR1EvERFloiP8rPBI21v5z8J9+O3ZynsWW51JPFlm6djj9rK644ePNW6ltVpRLIFFVkiPqpjneIsjOjPJSMQ55KnrY4jvs5wkrhwFP/YIthdri93V4iwOpGIz1ORJeKDcgXYub9lc2Y47sFY/1849bfVkSQ7OLQW2445fJTQlqFtGmLXJR1E0kVFlogPGtyoLB8H9ccWHwM/T7A6jmQjxtIXiXP68V3+/nS9rbjVcUR8moosER9TJG8wle/qzCrnLST+NF6XbBDvij6AsfZDZjvu4r7mLckT5G91IhGfpSJLxMc80aIqbxi98I/eCxt1yQbJAKvewi/2DJMCBzC0cTmr04j4LBVZIj6kRmQ+Ltfsw34icSx5FhITrI4k2VHceRKXv8p6owql7nyAyLBcVicS8UkqskR8yGNt6vJ2QifsB36B3YutjiPZ2aYv8D+1i4nOHjzRqrrVaUR8koosER/Rolphfi0+gHPkNi88KpKRnIk4Fj/NIYpwplpfapcIszqRiM9RkSXiAwLsNnre14QvHM2x/TEVov60OpLkBHt/wm/PUt5NuJ8RbW+3Oo2Iz/G0yGoJ7Ab2AGOus/wJYAewFVgOuN/KPRHY7JrmpTmpSA7Wq0EpvgodgOGIw/jpZavjSA7iXPIMF40gfiran/tqFLE6johP8aTIsgMfAK2AqkB313/d/QHcBtwCfAu84bbsMlDLNbVLZ16RHCdvLn9ub9qBH511SfzlHbhwwupIkpOc+gtj4xSmOZrSrVVzAu06ASLiKU/+Wuph9mDtA+KBGUD7ZOusAC65Hq8DdAU7ES8Z3qQi/7H3xT/mKKx93+o4khOtfB1bwkU+z9Of3neUuvn6IgKAJ1eZiwQOuz0/AtS/wfoDAPefPQUDGwEH8Dow50YHs9vthIeHexAr7cLCNIDTm9Se3nelTYuHBZGvQS+2J5Yh95oRhIbmAvRz+tTSZzS9nMT+Nomf7nqWB5p2YtmeL7AF57E6VLajz6l3ZYX29Ha/b0/M04YT3eaVcs17EPgPcL0r2w3GLMQ2RkTopqQiVwxpXIm3ErsRdGILAbvnWx1HcrCgLV8QGHOYt219GHhnSavjiPgET3qyjgIl3J4Xd81LrhnwLNAIiEu2PZinG1cCtYG9ybad7JqIiooyoqMz5zYhmXWcnELt6V01I0PZU643Jxz5YX434qLPWB3J5+kzmk6Ln2V31y+x1XyAvJve4VB0rNo0A6hNvcvK9vSkJ2sDUAEoAwQC3fj3rwRrA59gDmx3H5UbDgS5HkcAd2L+ClFEbqJP0zp8nNAG+445cPg3q+OIwI65+B/5jbcTH2BQ48pWpxHJ8jwpshzAcOAHYCcwE9gOjOPqrwUnAnmAWVx7qYYqmKcBt2AOjn8dFVkiN9WiSgEWRvQn3ulH4tIXrY4jksSxeAynCWNXmT7UKZ7X6jgiWZqnt1df5JrcveD2uFkK2/0K1EhtKJGcLMjfj3sb3cMAx10Y6yZB9AGrI4lcdXQTfttm8mn19nzcdD4//XkQw7A6lEjWpAueiGQxfe4ozeRc/fCPPwur3rI6jsi/OJe9hMNpMCf/ANrVLGZ1HJEsS0WWSBaSP3cgVZt0Z52zGv6/vgOx56yOJPJv544Q8PunzHXeSetWbQny11eJyPXoL0MkC3m4WRXeoRfBZ/cQtG261XFEUhS88WMCY0/xSfAA+jcsY3UckSxJRZZIFlGuYG6ctw7gIEXxX/kKNiPR6kgiKbIlXMR/9UR+NypRtnFPCuQOtDqSSJajIkski3ikdT0mOTsRsH8F/gdXWh1H5KYCd8wi8NR23qUnw++tbnUckSxHRZZIFnB72QJsLjeUGCMXCYufxmZ1IBEP2Awn8Yue4QiFuFxnEOUL6VY7Iu5UZIlYzGaDPm2b8ZWjGbZNX8KJnVZHEvHcvpUE7PmBDxwdGN7mdqvTiGQpKrJELNaxdiTfFhiMzRGL86dXrY4jkmoJS57lkhHAhjJDubN8AavjiGQZKrJELBQc4Efjlp1Z5rwNx89vwsWTVkcSSb1Tf+O3cQpfO+6hV9uW+Ol8twigIkvEUgPuKs9HQf0JjDkC6z60Oo5ImiWuGI9fwgWmhw+h063FrY4jkiWoyBKxSKHQIIo06s8OozTxS54HR5zVkUTS7nI0jhUT+MVZkztbdCMk0G51IhHLqcgSscjwlrV41+hO4LH1sP07q+OIpN/6yQSd28+kwP4MbFzR6jQillORJWKBqkXzcrzGME4RRvyC0VbHEfGOxATiFj3DXiOSvHcOpmi+YKsTiVhKRZaIBQa3a8z/Eu8j4M9v4Ngmq+OIeM/uRQQdXsX7RheGtbrV6jQillKRJZLJmlYpxNLIYSQ6E0n4cazVcUS8Lm7BaM4ZIeyvNpwakfmsjiNiGRVZIpnI389G2zYdWei8HWPVf+D8MasjiXhf1Hbsm6fyheNe+rdrbnUaEcuoyBLJRN3rl2JKnsEEXfoH55r3rI4jkmEcy17G5ohlYdFhtKhW2Oo4IpZQkSWSSfLm8qdC84FsNcoRt+R5SLhkdSSRjHPxJIk/v8Ey5600b9ONQLu+biTn0adeJJMMbVaDD/x6EHxiM2ybZXUckQxnrP2I4JhDfBoykJ53lrU6jkimU5ElkgnKROTmQt0RRJGf2PkjwTCsjiSS8RLjiV30LLuNkhRtMpT8uQOtTiSSqVRkiWSCwe0a819nG4J2fAuH11sdRyTz7JxH8JE1fMgDDG2pSzpIzqIiSySDNSwfwarSj+JMTDTHYonkMLHzR3HWyM3Rmo9SqXCo1XFEMo2nRVZLYDewBxhzneVPADuArcByoJTbsj7A366pT5qTivggu5+Nth26sshZH2PV27pkg+RMUX8SsPlLpibeS/8OLa1OI5JpPCmy7MAHQCugKtDd9V93fwC3AbcA3wJvuObnB14E6gP1XI/D051axEd0rVuKz0OHEHzxCImrdckGybnil76M3XGRBZEjaFKlkNVxRDKFJ0VWPcwerH1APDADaJ9snRXAld+jrwOKux63AJYCZ4Bo12P9M0ZyhLzB/pS99yF2GqWJXfgMOGKtjiRinUuncSx/jVXOW2jathcBdpvViUQynL8H60QCh92eH8HsmUrJAGDxDbaNvNHB7HY74eEZ29kVFhaWofvPadSe1ze0aTU+sj9IaNR67Md/wZaKz7Xa1LvUnt6XljY1/v4Wx52D+TTvYAY2XcqMDYdvvlEOos+pd2WF9vT2wPeemKcNJ6Zyu8HARmBjRESElyOJZL6S4cH8c8swoo3csGws+je7CNicDlg2lgNGEULuGEx4Lk/+nS/iuzz5hB8FSrg9L+6al1wz4FmgERDntm3jZNuuvM62k10TUVFRRnR0tAex0i+zjpNTqD2veqLT/bzkbEHQlqnE/L0mzftRm3qX2tP7Ut2m0XMJqbWUj8t04pE7ZvL6t79kTDAfps+pd1nZnp70ZG0AKgBlgECgGzAv2Tq1gU+AdsAJt/k/APdiDnYPdz3+IX2RRbK2uysW5MeST+CXcInYH1+yOo5IlnNp/iguOwP4+5anqFo0r9VxRDKMJ0WWAxiOWRztBGYC24FxmEUVmKcH8wCzgM1cLcLOAC9jFmobXNuc8VJ2kSwnwG6jaYf+rHLegmP5K3DptNWRRLKeM/vw/+1DZjsb0b1TJ6vTiGQYT0+IL3JN7l5we9zsBttOcU0i2d6Dd1Zmcsggcp/dxcX1/7U6jkiWFb9iArlqd2NmwRG0vuVHFm693igUEd+mK76LeElEnkByNXmCoxTk4vdPgDPR6kgiWVf8RWIXPs02oyzV2w4nOEBfR5L96FMt4iX92zTiMzqQ+685cDDtg91Fcgpj22xC//mNyQG96Ne0ttVxRLxORZaIF1SPzMvmKqNwJiZyccHTVscR8Rkx3z/BWSOEc7ePIjIsl9VxRLxKRZaIF3To1IsfjXrYfpmo+xOKpEbUn+Ta/DkzjHvp3aGN1WlEvEpFlkg6tatdmukFhpPnwgHiV0+yOo6Iz7n0wzgC48+xvMyTNChXwOo4Il6jIkskHfIE+VOy9ZPsM4pxYe5TkBhvdSQR3xN7FsfSsaw3qtCo0zD8/XSPBMkeVGSJpEO/++7kf/5dyXvgB/h7qdVxRHyWY+MX5D29hf+FDOTBu6tbHUfEK1RkiaRRhUJ5+KvWsziccP77J62OI+LbDIPz347gtBGKo/GzFAoNsjqRSLqpyBJJo45d+/KDUR/7qolw7rDVcUR83/HN5Nn2BTNoQa+O7W6+vkgWpyJLJA3uq1WarwuOIO+FfcT+8q7VcUSyjZhFYwmOj2Z52dHUK6NB8OLbVGSJpFLuQDtF2zzDIaMwMbMfhcQEqyOJZB+x50hY/CybjQrc3uVxDYIXn6YiSySVet53D1/530/43rkY+3+xOo5ItpPwx9eEn1zPFyF96Xp3TavjiKSZiiyRVChbMDc7az+PLTGB6O9HWh1HJNuKnvkIMUYuLjd+gYJ5NAhefJOKLJFUaNdtKL8YtbCvfA0uRFkdRyT7OrmLPH9M5nua0q1zF6vTiKSJiiwRD7W+rRJfFxhO+LmdXFrzkdVxRLK9c0teITTuH34oM4YGFYpYHUck1VRkiXggby5/Qu57iZNGPqJnDgNnotWRRLK/+ItcnvM4fxklqNb5OYL89ZUlvkWfWBEPdL+/E9/6tSDfn5/D0U1WxxHJMRw7F1Hg0GK+CnqAB1rcbXUckVRRkSVyE7VLRfBzpefIE3+S6PkvWB1HJMc5Pesx/BLj+bvuK5QqEGJ1HBGPqcgSuQG7n41aDzzHLqMk8XOfgPgLVkcSyXli/sF/xcuspQYtuz9mdRoRj6nIErmBjk3v5OuQByl05Efiti+wOo5IjnVhzSdEnN3CrIiHuPe2KlbHEfGIiiyRFBTJF8zRO18Fp4MT34ywOo5IzmYYnP56KOeMEAJbvUbeYH+rE4nclIoskRS0efARfqUWwT+/CjHHrY4jkuMZUTsI3/wxC+xN6NT5QavjiNyUp0VWS2A3sAcYc53ldwObAAfQOdmyRGCza5qXtpgimatJnSp8V3gEBc9t4+wvuiaWSFZxauHLhMceZnmF56hdrpjVcURuyJMiyw58ALQCqgLdXf91dwjoC0y/zvaXgVquqV1ag4pklry5/LG3eZPzRi5OTx8EhtPqSCJyhSOWi7Me4pBRmLJdx+vaWZKlefLprIfZg7UPiAdmAO2TrXMA2Aro20h8XoduQ1jq15DwDf/BGbXT6jgikkz83lUU/Wsa3wW14/62HayOI5IiT0YORgKH3Z4fAeqn4hjBwEbMU4mvA3NutLLdbic8PDwVu0+9sLCwDN1/TpOd2rN2+eIsLjWSwpf+Ju63TzL8s5iS7NSmWYHa0/usbtPLy8cTVqY5G2q+zK07NrHvxDlL83iD1W2a3WSF9syMftZSwG3Ag8B/gHLXWWcwZiG2MSIiIhMiifxbsL8fwS1e4oyRF8f8J7A5HVZHEpEU2OIvELh0DHspTrkOz+BnszqRyL950pN1FCjh9ry4a56nrqy7D1gJ1Ab2JltnsmsiKirKiI6OTsXu0y6zjpNT+Hp7dn2gDzP9mxK57UOO7vzF6jiA77dpVqP29D5L23T9bEpUa8vsUp1pXe875i1ZYl0WL9Ln1LusbE9PerI2ABWAMkAg0A3PfyUYDgS5HkcAdwI7UplRJMNVLlWU1VWep2DsAY7OHWt1HBHx0OEZj5M78Rx/NXidyAKhVscRuYYnRZYDGA78AOwEZgLbgXFc/bVgXcyxWl2AT1zLAapgngbcAqzAHJOlIkuylAC7jbLd3+K4UYCLs4aAI87qSCLiqcvR2Bc9yS7K0KDXy1anEbmGp5fMXeSa3LnfKXcD5mnE5H4FaqQhl0imaXN/D74Pbk3J3Z9xaO86q+OISCpF//4dpW57gHlFe9Gi6QJ+WL7M6kgigK74Ljlc5dLF+bX6OArHHeDQrOtdZ1dEfMHBr4aSO/Ec++56h2IF8lkdRwRQkSU5WIDdRmT3SZwywrgwYyA4Yq2OJCJpdSka+4JH+ZuS1OnzhtVpRAAVWZKDteg8mOVBTSi5/UMu7t9gdRwRSafTf8yn3KFvWZi3K81b6AYjYj0VWZIjVS5fljVVnqP45d3s/26s1XFExEv2Tn2UAo4odt0+kWKFClgdR3I4FVmS4wTY/Qh/4EMuGsFET+sHuuioSPYRfwG+H8YRClG197vYdJFSsZCKLMlxmnZ7jLUBt1Ni81tcPLL95huIiE85tf0nKu77kmV52tKkdXer40gOpiJLcpRq1W5hdYWRlLm4mb3zNDhWJLvaPX0UxeIPsPW21yhVvMTNNxDJACqyJMcICQ7C6PhfMAyiPu8DhtPqSCKSURxxXJ7Rn7NGKIV7fYpdNzcUC6jIkhzj9v5vsMNeiYIrR3Hp5AGr44hIBove9ztlt0xkfdDtNO6h6+BJ5lORJTlCvcZt+alQb6pFzWP/z1OtjiMimWT33DeoFLOO1eWeoGrN+lbHkRxGRZZkewULFeZgo/9Q1HGcXVMesjqOiGQmw+DwlD6EGJeIbf8puXPnsTqR5CAqsiR7s0Gpvv/jjC0M2+z+JMZdsDqRiGSyS9H/kH/pY+zzK0Xt/u9aHUdyEBVZkq3d0eUJNobcRfVd73J0p27+LJJT7f31e2ofm87qAp25tXk3q+NIDqEiS7KtstXqsanqGKpe/p0/vnnZ6jgiYrGtnz1G6YS97L1jIoWLl7M6juQAKrIkWwrJk4+Ejp+R27jEsc96g2FYHUlELJaYEEfc132ItwUQ1vsr7P4BVkeSbE5FlmRLlQZ9xlF7MQr98BBnTxyxOo6IZBHH922j0m/PsDuwGnU0PksymIosyXZqd3qKP/I1pf7+D9m5brHVcUQki/lj8RTqn5zNhmI9qNbkQavjSDamIkuylRLV7uDPGmOodfk31n35nNVxRCSL+uO/w6jo+IuDd71JgRIVrY4j2ZSKLMk2gkLDie/0OQWMsxye0htD47BEJAXxcbHETu+Jn80gtPd0/AKCrY4k2ZCKLMkebDbKDprKGb8CFF4yhNMn/7E6kYhkcYf27abqulEcCKhA9QEfWh1HsiEVWZItVOv2CjvzNuSuff9hy2/LrY4jIj5i3ZJp3HNyKluLdKJSq2FWx5FsRkWW+LxSd3Rme6XhNLy4lJVTX7E6joj4mF8/fYzaCZvYW+9lCle9y+o4ko2oyBKflrdENU40f5/Kzr/ZPrk/TqfGYYlI6sTFJxA15UGKcIr4zl8SFF7M6kiSTXhaZLUEdgN7gDHXWX43sAlwAJ2TLesD/O2a+qQtpsi/+eUKI6T3THLb4mBGD6LPnbc6koj4qGPHj1NkUT/i/EIoMvhb8A+yOpJkA54UWXbgA6AVUBXo7vqvu0NAX2B6svn5gReB+kA91+PwtMcVcbH5UWrI15wOKEKN1cPZ9dduqxOJiI/buOFXGv35HAdzVaN8v8lWx5FswJMiqx5mD9Y+IB6YAbRPts4BYCvgTDa/BbAUOANEux63THtcEVOZByawP+wOWh1+mxXL5lsdR0SyiSWzP6VN9BfsiexAyVaPWx1HfJy/B+tEAofdnh/B7JnyxPW2jbzRBna7nfDwjO3sCgsLy9D95zSZ3Z5hdR9gf+XBtIxdzLq5H2X458UK+ox6l9rT+7Jzm26e8TINB1Vmbb3nKRF9kAu7V2TKcbNzm1ohK7RnVhn4PhjYCGyMiIiwOotkYcHl7uTw7a9wm3Mbe79+ioREDXQXEe+6GO/gwrfDKGc7zOkWH+BfuIrVkcRHedKTdRQo4fa8uGueJ44CjZNtu/I66012TURFRRnR0dEe7j59Mus4OUVGt2dA4UrE3/cxJW0nuPTlg/x9MPvf+FmfUe9Se3pfdm3T6OhoGnzfk3P3zyO+0+dEv3cXxERl2rHFe6xsT096sjYAFYAyQCDQDZjn4f5/AO7FHOwe7nr8Q+pjSo4XUoC8A74nl5+TEot6s2P/IasTiUg2t27LNuqtfYi4gHwUGTIXAkKsjiQ+xpMiywEMxyyOdgIzge3AOKCda526mOOtugCfuJaDOeD9ZcxCbYNrmzNeyi45hX8whYfO4UJgQRr/MYKf12+0OpGI5BDzf1hCx73PcSJPJYoOmA62rDLKRnyBp5+WRUBFoBzwqmveC1zt0dqAeSowN1AAqOa27RSgvGv6LJ15Jaex2SjS53NO5K3Og0fG8e3cOVYnEpEcZsa0/9Iz+gOOF7mHwl3esjqO+BCV5JKlRXR8k39KtKLX+f8y/fMPrI4jIjmQw2kw55OxdIqbQ1TV/oQ3e9LqSOIjVGRJlhXW8hlO1RhI54T5LPjkWeIcyS/DJiKSOc7HOlg/+WHuda4muuEL5GnQ1+pI4gNUZEmWlKfhEM42GM19zpVs+HgIZy7GWx1JRHK4w6cvcOzzPtzJZi61eJvgGsmvyy1yLRVZkuUE1+rCxaav05iNHJrSn4OnL1odSUQEgD8PnYIZPanptxdHx//iX66R1ZEkC1ORJVmKf8XmJLT/mNv8dhE/ozd/HjltdSQRkWus2XWYYgv7UM7vH+w9ZkBkHasjSRalIkuyjpL1sXWbSiW/IxSc34dfd3l6zVsRkcy1cP0Obls1kEL2C+Tq9z0UrGR1JMmCVGRJ1lCiHoF95lDCfoZav/Rn0ca/rE4kInJD05b9RtstDxHqbxAyaBFEVLQ6kmQxKrLEesXrEth3DpH+52ixYSDTl/9udSIREY989P0y+v79MLkD7eQatFiFllxDRZZYq/htBPabS6T/edr+MZiPFqyxOpGIiMcMA96cvpBB+0aQJ+hKoVXB6liSRajIEutE3kpg37kU84+h49YhvDfnF6sTiYikmtOACVPn89CBR8kd5E/wQBVaYlKRJdaIvJXAfvMoGnCBbjse4u3vfrY6kYhImiU6DcZ/NY8Rhx8nT3CgCi0BVGSJFco2xr/fAooGXKDX7uFMmPkThmF1KBGR9ElINHjl8zk8cexx8gQHEDjoRyha0+pYYiEVWZK5qrTF3nMW5QNOMeCvhxg/Y5kKLBHJNuITnbw05XtGHXuMgkGJBAxYBKXutDqWWERFlmSe2j2xdf2CmvYDdP1zCGOn/0SiUxWWiGQvcQ4nz0+Zy4iDD1Mq4Cz23t9DxZZWxxILqMiSTGG7Yzi0/4CG9u00/30w42b9iuorEcmu4hxOnv3iR/r/NYzq/kewdZ8G5Zt44AAAFAFJREFUt3S1OpZkMhVZkrFsNmzNx2Lc+yqt/dZRe/UQJsz7w+pUIiIZzuE0eG76z9y/bSi323dBx0+hwTCrY0kmUpElGcc/GHuXzzHufJwH7csotuxh3vtxh9WpREQyjdOAsd+up/GGh2nptx5ajsfW+k3ws1sdTTKBiizJGLkL4t9/Ic4q7RhjnwoLHufTX/ZYnUpExBKvzd9MxZ8fZrB9AUbdQdh7fANBoVbHkgymIku8r2Bl/If8hL1oDd71e4v1015i+m+HrE4lImKp95b/RfSc0bxs/xSjbBP8B/4I+YpbHUsykIos8a6y92AftJSw0FA+SXyeTydP4qddJ6xOJSKSJcz6/Qg/fPE6H9leIyiiFPbBP0GxOlbHkgyiIku8wgC481HoNZtygWd598KTPPfBl2w7es7qaCIiWcrqPad45+NPmJzwNIVz27ANWAK1elgdSzKAiixJNyMwD5dafwTNx9HavoFn/9/enYdHVZ9tHP9OZrIRyAKBCCFA2JSASNhUVNaiUBVE4RXFVvrSUrXUWm3VYuuClUsqVbRCLS1YEBWoilIFBQUEwk4QhEAgCdlDyL5vk5n3jzPWyEshwiQnmbk/13WuzHLmzD0PM8yTc36/k5xf8uCSj8gsqjI7mohIi3TiTBmPvb6GPxc/wvW2k3DHEirGzsdp9TM7mrhRY5usCUAikAQ8eZ77/YE1rvv3Aj1ct/cAqoCvXMsblx5VWqTwvpRP/xB7r5t5yraK6+If46f/+JLSKrvZyUREWrQzpdXMWvIp0xMf4QHremqvvpeKaWshONLsaOImjWmyrMBiYCIQA9zj+tnQLKAI6A28AixocF8yMMi1PHCZeaUliZmMZfZW2oWGs8L6AkkfvcgfPjxKXb3OMioi0hiVtfU8/M4BfL54liW2l/Ht1BefB7ZD9Eizo4kbNKbJGo6xhyoFqAVWA5PPWWcysMJ1+T1gHGBxU0ZpaXzbwG2L4H9WMtAvm7fsj/P3NWtZsz/D7GQiIq3Skm3JbFi3knctc+keWAU//gjGPQ0+NrOjyWVozL9eJNDw2zMTuPYC69iBEqCD63o0cAgoBX4P7LjQk1mtVsLCwhoR69KFhoY26fY9mb1jfyonvoYjNJrZ1vWMP7ucZ7ZkUlhpa/J/N2+i96h7qZ7up5q637FC+NO6OF77QQ6rQn7Ompsew9ZnHG0+/RXWkjSz47U6LeE92tQD33OAbkAs8CjwDhB8nvVmAweAA+Hh4U0cSS6FEwvVg39G+d3rCA0J5W2/+XSO/zMPvnOYwkqNvxIRcYfs0jpmv7Wf60+8wF99XyGgUy/KZmygJmYaGojR+jRmT1YWENXgelfXbedbJ9O1zRCgAGNmf41rnYMY47P6YjRUDS11LeTm5jqLiooa/wouQ3M9T6sXEgWT/gK9xjCefTxet5h5/9zJjlP5gPH3uUD1bAqqqXupnu6nmrpfUVERj7xTwKRrslk3JZG5ljnsH/8SlV1ugE8ehcoCsyO2Kma+RxvTZO0H+mAc9ssCpgP3nrPOeuB+YDcwFdiC0WB1BAqBeqCnazsp7gguzcBigWE/hR88h7/Nh2ds/yAyZQ33rP2K/PJas9OJiHi09YezOZTxIYumZ7C3y338ud9U6qNvgo2Pw9fvmR1PGqExhwvtwBzgM+A4sBY4BswDJrnWWYYxBisJ47DgN6d5GAkcwTh9w3sYswsL3ZRdmlKH3jBzA/xwIdfaTrHR93FSNy1m5pv71GCJiDSTjMIq7n4jDsvOV/jEby4xAflw1zK4ZzUEdzE7nlxEY6ctbHAtDT3d4HI1MO08j3vftUhr4WOD6+fAmN8RaKljnu0N+uSs54H3DnMyt9zsdCIiXsfucLLg00Q2J+SyaOoptre/iwV9plH30F7Y/AeIXwFOjdhqiXTGd/lWz9HwYByMf46x1q/Y7PcYKZuXctdfd6nBEhExWXx6Mbe/9iX2na+zyf8Jhvimwu2vwqzPIVJ//7Al0gk4xBjYfst8iJlEJ3s2830X0iHrC+7/1xGS89RciYi0FDV2By9+eoKNR3P407QUEsIn8OwVd1Pys60Q/xZ88SxU5JsdU1zUZHkz30AY8TDc+Gt8fWCOz2ruta7n9U+O8dbuVBza+ywi0iIdzizh9td2MntUNl+M2scS5538c9B0HDGTYOt8OLAM6uvMjun11GR5Ix8bxP4IRj8B7Tozrj6O59u8y86Dh5mw8QQFFRrYLiLS0tXWO3h9SxLr4rP4w20ZzIjZzpOOGeyfuACu/Tls+SMc+0DjtUykJsubWCwQMwXG/h469OKq2mM877eUwJx9zFlxlPj0YrMTiojI95RVXMUDqw4ysk8aL046RXr7G3im7VTSpy6HGx+Bz5+DpM/NjumV1GR5i74TYPTvoMsgImtPM8/3JWJqdvPqupOsPZChQ4MiIq3c9lP5TFy0gx9dn866MQfY6TuKee2nUHDf+5C6E7a9CKkX/Mt24mZqsjyZxQf6T4GbHoWIAbSvzeb31sWM9t3O0k0n+cWuVKrrHGanFBERN6mtd7Bs52nW7s/g56PS2HLDLtZZxrEwcjLlMz+GjL2wfSGc2mR2VK+gJssTWX1h4HS48dfQoRcRNan81rqYCQFxrNqVzJhtyZRUaUCkiIinKquxs3BTIit3p/KrcWnsHbqNtY5RvBpxK8Uz/gVnjsCOVyDhQ3Dql+2moibLk7SNgKE/gSE/gXZX0K36JHN9X+EG9vDu7jTG7Eghr6zm4tsRERGPcLashqc+PMob25N5cFQKOwdvYSM38FLYbZyd9iYUPQv7/26c/qFa43LdTU2WJ4gcYswk6T8FrH4MqtrLo75vMtAZz4ptqTwZd5riSu25EhHxVhmFVcxdd5RXvzjF7JEpbBm2g+3W4SwKGMvJm/8IY+bC4TWw729w9rjZcT2GmqzWKiAUrp4KsfdBl1h87eXc4fiMhwK34l99mpWbUnloTzrlNXazk4qISAuRW1rD8x8fZ/HWZGaOSOada+PI8+vNa7Vj2RR7D/VDfwJpcXBoFSR8BLUVZkdu1dRktSYWC0SPhtgZ0O92sAXQueoUsyzLmR60k2Ons1jwUSqbE3Kp13RBERH5Lworanl580kWb03i1oHHeXDE18yPfJ8V1TfxVsRICu74K0z8ExxbZzRcGXvNjtwqqclqDSKHwIA7IeYOCOmKf10JEx2f81O/OKItyfz7SDbTdqVyPKfM7KQiItKK1NgdfBCfxQfxWQzuFsr9IxKJi/mYo7Z+LK0ZwZaBU7EP/jEUpsDRD4yTm+YeMzt2q6Emq6XqPAj63wH974Sw7vjU13JNzQFmWt/nFv94Dqee4Z+fZbLh6xwqa+vNTisiIq1cfHox8elfERxoY9I1x/nFkH280vVd1tcNZ2XAMI7f9GsY+RvISzSarWMfQt4Js2O3aGqyWgqbP0SPhL4T4coJEByJxVHHgJpDzLBuYKL/QYqr81i/I5tbDmaSVlBpdmIREfFApVV2Vu1JY9WeNK6MaMe0ocd5c+BmbAGd+HftUN5pO5RTo54wTnBdeBpOboTEjZC2CxwaB9yQmiwzdegNPUdDr7HGT78gbPZKBtfFc5d1PeP9v6K8KpcNcTnM+Dqbo1ml5uYVERGvkphbxh8/Oc4LG44zpFsYtw48zKqrN0DAFWysi2VdwEC+HjYLx3UPGaeASNoCKVshZRsUp5sd33RqsppTcCR0HwE9RxlNVUgUAKE12Yy2fMkU3yNc559Ack4BWw7lMTPhDEcyS0yNLCIi4nTCgbQiDqQVMe/jBIZ2D2N8TDwvX9WJzmEd2OkYwAe1V7Oz742UD7jTeFBhCiRvhdNfQvpuKD9r7oswgZqspmLxgU79IOo66OZaQrsBEFBXwhDHEX5o/ZSbrMfo6JNDXHI+nx0/y5OJZ8kpqTY5vIiIyPk5nbA/tYj9qUXM33Cc7h3aMPaqeO69shOLotuTaY3iS3t/Nrbpx5HYu6kdNst4YEGy0Wyl74GMPVCQZGzMg6nJcgeLBcKioUssRA42fna+BvzaAtCuLp9YZwJjrFsYZk2klzWVI5mF7NpXwGPJ+RzOKKG2Xn/WQEREWp+0gkrejEvlzbhUAnx9GNI9jBG9tvNUrw70i+xAgqUn++x92Na2F0cG3Epl7H3GA6uLIfswZMdD9iHIioeSDHNfjJupyfq+AkKg41UQMQAi+sMVA6BTDPi3A8DmqCbansIwv+0M9U1lmCWRYGc2h9KLiE8v4sW0Yg6mFVFVpxmBIiLiWarrHMQlFRCXVABAO38bQ3qEMbhbGL/sHsY1XUPJ9YvioKMv+/x6cLBrNGk95uDw8TU2UFUMuUeN00TkHjWWvJNQW27iq7p0arLOx+pnHNprH20MTg/vC+F9jJ9tI/6zWmB9Gb0cqQzyi2OANZ2rfU7TzZ7GqbwijmaXsCerlCXpRSTnlXv6HlEREZH/p6zGzrbEPLYl5gFg9bFwZUQ7YruFMrhLCD+ODCY6IowUazRHHD05GtiVw5FRnI76ETXWNt9uqDQL8k9B/kljKUiBotPG4PoWPKPRK5ssp48vjnadIWQAhEZBSFdjEHpYDyzto3EGRxpjqlyC6kuJJourbAn0sX5Bb0sW/XzSqC/O5FRuOSdzy9iXW8byrBKS8yp0tnUREZHzqHc4ScgpJSHn29nyvlYLfSPaEdMlmCsj2nFrRDt6RwRjD4wiwdmNZGcXToV05kRQZ1J7DKPaJ+jbDTrsWEoycRaehqJUKMmEknQoyaTeWYZPxZnmf5ENNLbJmgC8CliBfwAvnnO/P7ASGAIUAHcDqa77fgfMAuqBh4HPLiuxG5Q9eIR6W+B3bgtzFBJlyaOnNY1uln109zlLd0suHWszKS3OITW/gtP5FSQWVLAxr4JTuWVU6CSgIiIil6Wu3smx7FKOZX/3NEXBgTb6dmpHdMcg+nYI4ubwIHqEBxHUvitnfLuQ5ogg3dmJtA4RpIR2JdMZS4lP6H8eXwoElqfBwoHN/Iq+1ZgmywosBsYDmcB+YD2Q0GCdWUAR0BuYDizAaLRiXNf7A12Az4G+GA2XaX5rW00HWw2RlnzaVGXjLMmioLScnOJqMooqSSqqZFtRFZlFVRRW1JoZVURExCuVVtn/c9qIhiwWCA/yp2tYoGtpw/XtA+kcEkhYSDDO4EjKAzqT7Qwn31bDSyblh8Y1WcOBJCDFdX01MJnvNlmTgWddl98DXgcsrttXAzXAadd2hgO7LzP3Zfly9UJKquwkZZ7VrD4REZFWxOmEvPIa8sprOJRRfN51/G0+9I3qRKCvtZnTfVdjmqxIoOGcykzg2gusYwdKgA6u2/ec89jICz2Z1WolLCysEbEu3ZkaX/DxJSg4hKCLry4XERoaevGV5HtRTd1L9XQ/1dT9VFP3KieQ8jqavKe4kJYy8H22ayE8PNzkKCIiIiKXrzFNVhYQ1eB6V9dt51sn07XNEIwB8I15LMBS10Jubq6zqKjoPKu4X3M9j7dQPd1PNXUv1dP9VFP3U03dy8x6+lx8FfYDfYBowA9jIPv6c9ZZD9zvujwV2AI4XbdPx5h9GO3azr7LTi0iIiLSwjVmT5YdmINx6gUrsBw4BswDDmA0UsuAtzAGthdiNFa41luLMUjeDvwCk2cWioiIiDSHxo7J2uBaGnq6weVqYNp/eewLrkVERETEazTmcKGIiIiIfE9qskRERESagJosERERkSagJktERESkCajJEhEREWkCFqfTaXaGc+UBac3wPOFAfjM8j7dQPd1PNXUv1dP9VFP3U03dqznq2R3oeL47WmKT1VwOAEPNDuFBVE/3U03dS/V0P9XU/VRT9zK1njpcKCIiItIE1GSJiIiINAFvbrKWmh3Aw6ie7qeaupfq6X6qqfuppu5laj29eUyWiIiISJPx5j1ZIiIiIk3G25us54EjwFfAJqCLuXFavZeAExg1XQeEmhvHI0wDjgEONOPockwAEoEk4EmTs3iC5cBZ4KjZQTxEFLAVSMD4vP/K3DgeIQDYBxzGqOlzZoTw9sOFwUCp6/LDQAzwgHlxWr2bgS2AHVjguu0J8+J4hH4YDdbfgN9gTEeW78cKnATGA5nAfuAejC80uTQjgXJgJTDA5CyeoLNriQfaAQeBO9B79HJYgCCM96kvsBOjed3TnCG8fU9WaYPLQYBXd5xusAmjwQLjjdzVxCye4jjGHhi5dMMx9mClALXAamCyqYlav+1AodkhPEgORoMFUIbxuY80L45HcGI0WGA0Wb6Y8B3v7U0WwAtABjADeNrkLJ7kf4GNZocQwfiyymhwPRN9gUnL1QOIBfaanMMTWDGGA50FNmNCTb2hyfocY9zAucs3v8k+hXE8/G1gjhkBW5mL1ROMmtoxaioX15iaiojnawu8DzzCd4+0yKWpBwZhHFUZjgmHtm3N/YQm+EEj13sb2AA804RZPMHF6jkTuA0Yhw6/NlZj36NyabIwfpH6RlfXbSItiS9Gg/U28IHJWTxNMcbEggk082QNb9iTdSF9GlyejDEzTi7dBOBxYBJQaXIWkW/sx/isRwN+wHRgvamJRL7LAizDGIv1sslZPEVHvp3hHogx8aXZv+O9fXbh+8CVGLO30jBmFuo33EuXBPgDBa7re9Bszcs1BfgLxn8YxRjjC24xNVHr9ENgEcYYjeUYYzHl0r0LjAbCgVyMIwDLzAzUyt0I7AC+xvg+ApiLcXRFLs1AYAXGZ94HWAvMa+4Q3t5kiYiIiDQJbz9cKCIiItIk1GSJiIiINAE1WSIiIiJNQE2WiIiISBNQkyUiIiLSBNRkiYiIiDQBNVkiIiIiTUBNloiIiEgT+D8UXUo27VJA2AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = 59\n",
    "t_dist = t(df=df)\n",
    "z_dist = norm(loc=0, scale=1)\n",
    "\n",
    "x = numpy.linspace(-3, 3, 100)\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title(f'Плотность распределения статистики T и N', fontsize=12)\n",
    "pyplot.plot(x, z_dist.pdf(x), label='N(0, 1)')\n",
    "pyplot.plot(x, t_dist.pdf(x), label=f't(df={df})')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26541440",
   "metadata": {},
   "source": [
    "- Мы видим, что эти 2 распределения визуально полностью совпадают, поэтому неважно, как посчитать: статистика $T\\sim \\mathcal{N}(0, 1)$ или $T\\sim t_n$.\n",
    "- **Но это не значит, что с N=60 T-test/T'-test работают корректно!** Если выборка не из нормального рапределения, они оба могут все еще ошибаться.\n",
    "\n",
    "2. Если выборка меньше 60, то безопасней использовать t-test, нежели t'-test.\n",
    "    - **У T-test FPR всегда будет меньше, чем у T'-test**. \n",
    "        - На FPR влияет процент случаев `pvalue < alpha`. У t-test pvalue $\\geq$ t'-test pvalue.\n",
    "        - `pvalue = t_distr.cdf(x)` или `pvalue = norm_dist.cdf(x)`. Поэтому, чем тяжелее хвост у распределения, тем больше p-value. А теперь посмотрим на примере:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "bca474df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "dark"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_array = [2, 5, 10, 20]\n",
    "x = numpy.linspace(-3, 3, 100)\n",
    "\n",
    "pyplot.figure(figsize=(10, 5))\n",
    "pyplot.title(f'CDF распределений T и N', fontsize=12)\n",
    "for df in df_array:\n",
    "    t_dist = t(df=df)\n",
    "    pyplot.plot(x, t_dist.cdf(x), label=f't(df={df})')\n",
    "\n",
    "z_dist = norm(loc=0, scale=1)\n",
    "pyplot.plot(x, z_dist.cdf(x), c='yellow', label='N(0, 1)')\n",
    "pyplot.legend(fontsize=12)\n",
    "pyplot.xlabel('X', fontsize=12)\n",
    "pyplot.grid(linewidth=0.2)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "898b822a",
   "metadata": {},
   "source": [
    "Как видно на графике, чем меньше степень свободы, тем выше линия на графике (при x < 0), а значит и больше cdf при фиксированном x. Поэтому и p-value будет больше.\n",
    "\n",
    "\n",
    "- Распределение Стьюдента с бесконечностью степеней свободы &mdash; это нормальное распределение: $t_{\\infty} = \\mathcal{N}(0, 1)$. Поэтому `norm(0, 1).cdf(x) = t_distr(df=infinity).cdf(x) < t_distr(df=N).cdf(x)`.\n",
    "\n",
    "Поэтому, если выборка небольшая, безопаснее использовать t-test. Но все еще не факт, что ваш критерий будет валиден!\n",
    "\n",
    "---\n",
    "\n",
    "Посмотрим еще раз на табличку \n",
    "\n",
    "|                          | маленькая выборка | большая выборка |\n",
    "|--------------------------|-------------------|-----------------|\n",
    "| нормальное распределение | t-test            | t-test, t'-test |\n",
    "| любое распределение      |                   | t'-test, t-test |\n",
    "\n",
    "Мы видим, что мы везде можем использовать t-test (а t'-test не всегда), и в случае маленьких выборок он безопаснее. **Поэтому t-test и стал намного более популярным, чем t'-test**. Но t'-test на практике может быть тоже полезен: \n",
    "- Не надо думать при реализации о степенях свободы.\n",
    "- Написать такой критерий на SQL будет сильно проще: вы можете использовать табличные значения в коде, чтобы понять, отвергся ли критерий.\n",
    "- Делать различные теоретические вычисления проще. \n",
    "- В нем сложнее ошибиться при реализации.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4d0890b",
   "metadata": {},
   "source": [
    "## MDE\n",
    "\n",
    "Вернемся к задаче со стартапом. Представим, что мы хотим запустить наш стартап в новом городе, например в Санкт-Петербуре. **Вопрос: можем ли мы собрать выборку не из 2000 людей, как мы делали с Москвой, а всего из 1000?**\n",
    "\n",
    "Что вообще нам мешает взять слишком маленькую выборку?\n",
    "- Например, если мы проверяем наш стартап на 1-2 пользователей, то мы ничего не можем сказать про наш истинный эффект, он может быть как больше 0, так и меньше. Будет слишком широкий доверительный интервал (из-за большой дисперсии в выборке, как мы видели в Москве), и нам нужен огромный эффект, чтобы его обнаружить: например, 1М рублей прибыли.\n",
    "    - Еще, возможно, мы не можем использовать критерий на такой маленькой выборке, но сейчас посчитаем, что t-test критерий валиден даже на маленькой выборке.\n",
    "- А если выборка состояла бы из бесконечного числа пользователей, то мы могли бы абсолютно точно сказать истинную прибыль от пользователя, даже если она равна 1 копейке.\n",
    "- Но оба эти случая нас не устраивают :( В первом - мы не сможем запустить стартап из-за слишком большого шума, а во втором - нам нужна вечность, чтобы проверить нашу гипотезу.\n",
    "\n",
    "И здесь нам поможет MDE (minimum detectable effect). Это такое истинное значение эффекта, что наш шанс его обнаружить равен $1-\\beta$ при использовании нашего критерия.\n",
    "   - Мы можем посмотреть, какой эффект мы сможем задетектировать при доставке 1000 пользователям, и от этого решить, подходит нам такая выборка, или нет. Например:\n",
    "        - Мы видим, что MDE 100 рублей. То есть с вероятностью $1-\\beta$ (на практике 80%) мы его обнаружим, **если такой эффект будет**. И с вероятностью 80% стартап запустится в Питере. Отлично, это нас устраивает, мы проверяем гипотезу на 1000 человек.\n",
    "        - Мы видим, что MDE 10000 рублей. Это, наоборот, слишком много: у нас 99% товаров стоят меньше 1000 рублей. Мы не наберем такой прибыли, стартап невыигрышный, нужно брать выборку большего размера.\n",
    "\n",
    "---\n",
    "\n",
    "\n",
    "От чего зависит MDE?\n",
    "- Ошибка 1 рода, или $\\alpha$.\n",
    "    - Например, при $\\alpha = 1$ мы найдем эффект и при размере выборки, равной 1 (мы просто всегда будем отвергать 0 гипотезу). А при $\\alpha = 0$ мы никогда не задетектируем эффект.\n",
    "- Мощность, или $1 - \\beta$.\n",
    "    - Следует из самого определения\n",
    "- От шума в данных, или от дисперсии.\n",
    "    - Чем более шумные данные, как мы знаем, тем шире доверительный интервал. А значит сложнее точно предсказать рамки для истинного эффекта, поэтому и MDE будет больше.\n",
    "- От размера выборки.\n",
    "    - Нас интересует не просто дисперсия в данных, а дисперсия среднего значения: она по той же логике должна быть как можно меньше. А что такое дисперсия среднего? Это $\\dfrac{\\sigma^2}{N}$, поэтому MDE также зависит от размера выборки.\n",
    "\n",
    "\n",
    "\n",
    "Теперь давайте выведем формулу исходя из того, что мы знаем все эти 4 параметра.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7758b93d",
   "metadata": {},
   "source": [
    "-----\n",
    "Для начала определимся с проверяемой гипотезой:  \n",
    "- $H_0: \\mu_0 = 0\\ vs. \\ H_1: \\mu_0 > 0$\n",
    "\n",
    "Обозначим \n",
    "- $S^2_{\\mu} := \\dfrac{S^2}{N}$ &mdash; оценка дисперсии среднего значения.\n",
    "- $S_{\\mu} = \\sqrt{\\dfrac{S^2}{N}}$ &mdash; оценка стандартного отклонения среднего значения, или SEM.\n",
    "\n",
    "Теперь, мы знаем, что \n",
    "- $\\overline X \\sim \\mathcal{N}(\\mu, S^2_{\\mu})$\n",
    "\n",
    "Нам надо найти $MDE=m$, такое, что:\n",
    "\n",
    "- если $\\overline X \\sim \\mathcal{N}(m, S^2_{\\mu})$, то в $1-\\beta$ проценте случаев для него отвергнется критерий. Проверяем мощность (зеленая площадь на графике).\n",
    "- если $\\overline X \\sim \\mathcal{N}(0, S^2_{\\mu})$, то критерий отвергнется для него в $\\alpha$ процентов случаев. Проверяем FPR (красная площадь на графике).\n",
    "\n",
    "\n",
    "<img src=\"https://raw.githubusercontent.com/dimalunin2016/pictures/main/download-3.png\" width=\"1500\" height=\"200\" />\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25db6829",
   "metadata": {},
   "source": [
    "\n",
    "То есть:\n",
    "\n",
    "- Пусть $B(X): P_{H_0}(\\overline X > B(X)) = \\alpha$. $B(X)$ &mdash; Граница критической области, красная граница на графике.\n",
    "- Тогда $P_{H_1}(\\overline X > B(X)) = 1-\\beta$. Зеленая область на графике. \n",
    "    - Или, что аналогично: $P_{H_1}(\\overline X - m > B(X) - m) = 1-\\beta$.\n",
    "    - Обозначим $\\xi := \\overline X - m$. $P_{H_0}(\\xi > B(X) - m) = 1-\\beta$. Рыжая плотность получается из синей вычитанием m. $\\xi$ из рыжей плотности, $\\overline X$ из синей.\n",
    "\n",
    "Надо решить эти 2 уравнения и мы получим выражение $m$ через все 4 параметра.\n",
    "\n",
    "1. $B(X)$ мы итак знаем. При $H_0$ наш критерий имеет следующий вид: $\\left\\{T(X) \\geq z_{1 - \\alpha} \\right\\} \\Leftrightarrow  \\left\\{\\sqrt{N}\\dfrac{\\overline X}{\\sqrt{S^2}} \\geq z_{1 - \\alpha} \\right\\} \\Leftrightarrow B(X) = z_{1 - \\alpha}\\sqrt{\\dfrac{S^2}{N}} = z_{1 - \\alpha}S_{\\mu} $\n",
    "\n",
    "2. $P_{H_0}(\\xi > z_{1 - \\alpha}S_{\\mu} - m) = 1-\\beta$. Работать с распределением $\\mathcal{N}(0, S^2_{\\mu})$ не очень удобно, гораздо проще с $\\mathcal{N}(0, 1)$. Для этого перехода достаточно перейти от $\\xi \\rightarrow \\dfrac{\\xi}{S_{\\mu}}$ по свойствам нормального распределения.\n",
    "\n",
    "- Обозначим $\\eta := \\dfrac{\\xi}{S_{\\mu}}$. Тогда \n",
    "$$\\begin{align}\n",
    "    &P_{H_0}(\\xi > z_{1 - \\alpha}S_{\\mu} - m) =\\\\ \n",
    "    &P_{H_0}(\\dfrac{\\xi}{S_{\\mu}} > \\dfrac{z_{1 - \\alpha}S_{\\mu} - m}{S_{\\mu}}) =\\\\\n",
    "    & P_{\\mathcal{N}(0, 1)}(\\eta > z_{1 - \\alpha} - \\dfrac{m}{S_{\\mu}}) = 1-\\beta\n",
    "\\end{align}\n",
    "$$\n",
    "- $\\Phi(C) = P(\\eta < C)$. Тогда \n",
    "    $$\\begin{align}\n",
    "    &1 - \\Phi \\left(z_{1 - \\alpha} - \\dfrac{m}{S_{\\mu}} \\right) = 1-\\beta \\Leftrightarrow\\\\ &z_{1 - \\alpha} - \\dfrac{m}{S_{\\mu}} = z_{\\beta},\n",
    "    \\end{align}\n",
    "    $$ \n",
    "    где $z_{\\beta} = \\Phi^{-1}(\\beta)$ &mdash; квантиль $\\beta$ нормального распределения.\n",
    "    - В конце мы как раз пользуемся тем, что $\\eta \\sim \\mathcal{N}(0, 1)$.\n",
    "- Финально мы получаем, что: $m = (z_{1 - \\alpha} - z_{\\beta}) \\cdot S_{\\mu} = |\\text{расп. симметрично}| = (z_{1 - \\alpha} + z_{1 - \\beta}) \\cdot \\sqrt{\\dfrac{S^2}{N}}$.\n",
    "\n",
    "### Итого:\n",
    "\n",
    "- $\\text{MDE} = (z_{1 - \\alpha} + z_{1 - \\beta}) \\cdot \\sqrt{\\dfrac{S^2}{N}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "612b4ad9",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "\n",
    "Вернемся к стартапу. Мы определились, что N = 1000, $\\alpha=5$%, $1-\\beta=80$%, а как узнать $S^2$? \n",
    "\n",
    "На практике есть 3 способа: \n",
    "- Оценить на исторических данных. В данном случае это не подходит, потому что ранее стартапа в Питере не было.\n",
    "- Оценить по похожим данным. Например, в нашем случае, оценить дисперисию по Москве.\n",
    "- Как-то теоретически оценить. Самый плохой способ, который работает, если первые 2 не помогают.\n",
    "\n",
    "\n",
    "Посмотрим теперь MDE в нашей задаче."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "deca8d22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MDE при N=1000: 126.08268390090282\n"
     ]
    }
   ],
   "source": [
    "N = 1000\n",
    "S2 = numpy.var(profits)\n",
    "alpha = 0.05\n",
    "beta = 1 - 0.8\n",
    "\n",
    "MDE = (norm().ppf(1-alpha) + norm().ppf(1 - beta)) * numpy.sqrt(S2/N)\n",
    "print(f\"MDE при N={N}: {MDE}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9f9d9c2",
   "metadata": {},
   "source": [
    "А значит мы можем рассчитывать на точность лишь в 126 руб.\n",
    "\n",
    "----\n",
    "Для нас это слишком большой MDE: хочется, чтобы он был $\\leq$ 100 рублей, мы предполагаем, что это более вероятный истинный эффект, исходя из опыта с Москвой.\n",
    "\n",
    "\n",
    "Давайте теперь решим обратную задачу: Мы знаем MDE=100руб, $\\alpha=5$%, $1-\\beta=80$%, $S^2$, чему равно $N$? Выведем его из формулы MDE:\n",
    "\n",
    "$N = \\left(\\dfrac{z_{1 - \\alpha} + z_{1 - \\beta}}{\\text{MDE}}\\right)^2 S^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4691e976",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Минимальный размер выборки: 1590\n"
     ]
    }
   ],
   "source": [
    "S2 = numpy.var(profits)\n",
    "alpha = 0.05\n",
    "beta = 1 - 0.8\n",
    "mde = 100\n",
    "\n",
    "N = ((norm().ppf(1-alpha) + norm().ppf(1 - beta)) / mde)**2 * S2\n",
    "N = int(N) + 1\n",
    "print(f'Минимальный размер выборки: {N}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d44cacc",
   "metadata": {},
   "source": [
    "Тогда нам надо взять выборку размера примерно 1600 человек. \n",
    "\n",
    "Таким образом, сделав подготовительную работу, мы поняли, что 1000 человек это мало, 2000 человек &mdash; много для нашего MDE. И подобрали иделаьный размер выборки."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b24961a",
   "metadata": {},
   "source": [
    "# Двувыборочный T-test. Задача AB-тестирования\n",
    "\n",
    "> 📈 **Задача**\n",
    ">\n",
    "> У нас на сайте Авито есть услуги продвижения. Мы хотим начать давать на них скидки, чтобы привлечь больше людей и начать больше зарабатывать. Для этого было решено провести AB тест:\n",
    "> Одной половине пользователей мы не выдали скидок, а во второй половине мы выдали скидки всем новым пользователям. Надо понять, стали ли мы больше зарабатывать?\n",
    "\n",
    "\n",
    "Для решения этой задачи мы не можем использовать одновыборочный t-test. В этот раз у нас 2 выборки $A$ &mdash; контроль, и $B$ &mdash; тест.\n",
    "\n",
    "Наша гипотеза звучит так: \n",
    "$H_0: E A = E B\\ vs. H_1: E A < E B$\n",
    "\n",
    "1. **Обе выборки нормальны**. Тогда есть 2 критерия в зависимости от наших знаний про дисперсию:\n",
    "    - $\\sigma^2_A = \\sigma^2_B$. \n",
    "    \n",
    "    Тогда:\n",
    "        - $S^2_{full} = \\dfrac{(N - 1)S^2_A + (M - 1)S^2_B}{N + M - 2}$, где N, M -  размер контроля и теста соотвественно. А критерий выглядит следующим образом:\n",
    "        - $T(A, B) = \\dfrac{\\overline A - \\overline B}{S^2_{full}\\sqrt{1/N + 1/M}} \\overset{H_0}{\\sim} T_{n + m - 2}$\n",
    "   \n",
    "    - $\\sigma^2_A \\neq \\sigma^2_B$. \n",
    "    \n",
    "    Тогда:\n",
    "        - $T(A, B) = \\dfrac{\\overline A - \\overline B}{\\sqrt{S^2_{A}/N + S^2_{B}/M}} \\overset{H_0}{\\sim} T_{v}$\n",
    "            - где $v = \\dfrac{\\left(\\dfrac{S^2_{A}}{N} + \\dfrac{S^2_{B}}{M} \\right)^2}{\\left(\\dfrac{(S^2_{A})^2}{N^2(N - 1)} + \\dfrac{(S^2_{B})^2}{M^2(M-1)} \\right)} $\n",
    "2. **Хотя бы 1 выборка ненормальна**. Тогда вбой вступает нормальная аппроксимация при большом размере выборок, критерий T'-test:\n",
    "    - $T(A, B) = \\dfrac{\\overline A - \\overline B}{\\sqrt{S^2_{A}/N + S^2_{B}/M}} \\overset{H_0}{\\sim} \\mathcal{N}(0, 1)$\n",
    "    - Согласитесь, здесь намного проще формула, чем те, что выше? :) Поэтому для AB-тестирования самостоятельно легче реализовать именно t'-критерий, где вы не ошибетесь.\n",
    "    \n",
    "    \n",
    "-----\n",
    "\n",
    "Python-библиотеки:\n",
    "\n",
    "- `scipy.stats.ttest_ind` &mdash; 2-выборочный t-test [критерий](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ttest_ind.html#scipy.stats.ttest_ind)\n",
    "- `CompareMeans` &mdash; [класс](https://www.statsmodels.org/stable/generated/statsmodels.stats.weightstats.CompareMeans.html) для построения доверительных интервалов у t-test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bfbf5c89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=2.5645688722251325, pvalue=0.005237676356845092)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numpy.random.seed(42)\n",
    "X = expon(scale=1100).rvs(1000)\n",
    "Y = norm(loc=980, scale=30).rvs(1000)\n",
    "\n",
    "ttest_ind(X, Y, equal_var=False, alternative='greater')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "4c4359e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.010475352713690184"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ttest_ind(X, Y, equal_var=False).pvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "5af197a4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20.380593037118373, 153.1987434094658)\n"
     ]
    }
   ],
   "source": [
    "# Доверительный интервал\n",
    "\n",
    "cm = CompareMeans(DescrStatsW(X), DescrStatsW(Y))\n",
    "print(cm.tconfint_diff(usevar='unequal'))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b0da4c1",
   "metadata": {},
   "source": [
    "# О чем важно помнить\n",
    "\n",
    "При использовании t-test критериев, как одновыборочного, так и двувыборочного, важно помнить, что:\n",
    "\n",
    "- **Элементы выборок должны быть независимы!**\n",
    "    - Например, ваша выборка не можеть содержать несколько заказов одного пользователя. Они должны быть агрегированны, иначе критерии будут невалидны!\n",
    "- В двубырочном критерии **выборки теста и контроля должны быть независимы!**\n",
    "    - Иначе критерии точно также будут невалидны.\n",
    "    \n",
    "Более подробно к чему приводят ошибки с независимостью выборок мы рассмотрим на следующих лекциях."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5dfdd46",
   "metadata": {},
   "source": [
    "## Итог\n",
    "\n",
    "На этой лекции мы рассмотрели\n",
    "- Как строить критерии для оценки среднего в случае, если вы не знаете дисперсии изначального распределения?\n",
    "    \n",
    "|                          | маленькая выборка | большая выборка |\n",
    "|--------------------------|-------------------|-----------------|\n",
    "| нормальное распределение | t-test               | t-test, t'-test |\n",
    "| любое распределение      |  | t'-test, t-test |\n",
    "\n",
    "\n",
    "- Вывели доверительные интервалы 2-мя способами.\n",
    "- Показали, что по умолчанию лучше использовать T-test, как более безопасный критерий. \n",
    "- Вывели формулу MDE для одновыборочного критерия.\n",
    "    - А также ввели формулу для минимального размера выборки.\n",
    "- Посмотрели, какие есть критерии для AB-тестирования.\n",
    "- Уточнили, какие условия нужно наложить на выборку, чтобы критерии можно было бы корректно применять."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb5ec7dd",
   "metadata": {},
   "source": [
    "## Доп секция\n",
    "\n",
    "### Как выбрать $S^2$?\n",
    "\n",
    "В начале лекции мы взяли $\\widehat{\\sigma^2} = S^2 = \\dfrac{1}{n - 1}\\underset{i=1}{\\overset{n}{\\sum}}(X_i - \\overline X)^2$. А можно ли брать другую статистику для оценки дисперсии?\n",
    "\n",
    "- Для T-test нет, там все фиксировано. Теоретическая формула с t-распределением подходит только для описанной оценки дисперсии.\n",
    "- Для T'-test же все проще: *мы можем взять любую оценку* $\\widehat{\\sigma^2}$, которая является состоятельной оценкой $\\sigma^2$.\n",
    "    - В этом случае, проведя то же док-во, которое мы выводили ранее для T'-критерия, мы получим, что точно также $T(X) = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\widehat{\\sigma^2}} \\rightarrow \\mathcal{N}(0, 1)$. Так что при больших N неважно, какую состоятельную оценку дисперсии брать.\n",
    "    - Какие оценки являются состоятельными?\n",
    "        - $\\widehat{\\sigma^2} = \\dfrac{1}{n}\\underset{i=1}{\\overset{n}{\\sum}}(X_i - \\overline X)^2$\n",
    "        - $\\widehat{\\sigma^2} = \\dfrac{1}{n + 1}\\underset{i=1}{\\overset{n}{\\sum}}(X_i - \\overline X)^2$\n",
    "        - Так что неважно, на что вы делите: на $\\dfrac{1}{n}$ или $\\dfrac{1}{n-1}$, при больших n нет разницы.\n",
    "        \n",
    " "
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    "       \n",
    "### Смысл степени свободы\n",
    "\n",
    "Давайте разбираться, что это за зверь такой. Для начала мы поймем, как оно работает для хи квадрат:\n",
    "\n",
    "1. $\\eta = \\dfrac{(n - 1)\\cdot S^2_X}{\\sigma^2} = \\underset{i=1}{\\overset{n}{\\sum}}\\left(\\xi_i - \\overline \\xi \\right)^2 \\sim \\chi^2_{n-1}$, где $\\xi_i \\sim \\mathcal{N}(0, 1)$\n",
    "    \n",
    "    - Вспомним, что $\\underset{i=1}{\\overset{n}{\\sum}}\\left(\\xi_i - \\mu \\right)^2 = \\underset{i=1}{\\overset{n}{\\sum}}\\xi_i^2 \\sim \\chi^2_n$, это одно из возможных определей $\\chi_2$. И тут степеней свободы равно числу независимых параметров в системе: n. Каждое $\\xi_i$ случайно и не зависит от остальных.\n",
    "    - Но как только мы заменяем $\\mu$ на $\\overline \\xi$, то мы говорим, что мы фиксируем $\\overline \\xi$. Так что теперь наши $\\xi_i$ такие, что они дали оценку $\\mu$ как $\\overline \\xi$ и никакую другую.\n",
    "    - А если мы знаем среднее случайных величин, то теперь мы можем свободно менять лишь $n-1$ значение $\\xi_i: i \\in {1, ..., n-1}$. Оставшееся значение зафиксировано, и напрямую считается из среднего и n-1 оставшегося значения.\n",
    "\n",
    "\n",
    "\n",
    "2. $T = \\sqrt{n}\\dfrac{\\overline X - \\mu_0}{\\sqrt{S^2}} = \\dfrac{\\xi}{\\sqrt{\\dfrac{\\eta}{n-1}}} \\sim t_{n - 1}$\n",
    "    - Здесь степень свободы также берется из хи-квадрат, у которого она такая, потому что мы оценили мат. ож и на это потратили 1 степень свободы. \n",
    "\n",
    "**Итого** простая интерпретация степени свободы &mdash; число свободно меняемых параметров в статиcтике."
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