{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://raw.githubusercontent.com/FUlyankin/r_probability/master/end_seminars/sem_6/student_teacher_dist.png\" height=\"300\" width=\"600\"> \n",
    "\n",
    "# <center> R для тервера и матстата. <br>  <br> 6.3 Проверка гипотез. Поющие коты и AБ-тесты. </center>\n",
    "\n",
    "Данный ноутбук является конспектом по курсу «R для теории вероятностей и математической статистики» (РАНХиГС, 2017-2018). Автор ноутбука [вот этот парень по имени Филипп.](https://vk.com/ppilif) Если у вас для него есть деньги, слава или женщины, он от этого всего не откажется. Ноутбук распространяется на условиях лицензии [Creative Commons Attribution-Share Alike 4.0.](https://creativecommons.org/licenses/by-sa/4.0/) При использовании обязательно упоминание автора курса и аффилиации. При наличии технической возможности необходимо также указать активную гиперссылку на [страницу курса.](https://fulyankin.github.io/R_probability/) На ней можно найти другие материалы. Фрагменты кода, включенные в этот notebook, публикуются как [общественное достояние.](https://creativecommons.org/publicdomain/zero/1.0/)\n",
    "\n",
    "---------\n",
    "\n",
    "В этой тетрадке мы посмотрим чего эдакого рисёрчеры в крупных компаниях проверяют на ежедневной основе. Делать это мы будем на примере поющих котов."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. В целом про АБ-тесты\n",
    "\n",
    "Этот параграф писался на основе [вот этой виньетки.](https://yadi.sk/i/FlQe3QHt3WiYyp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Во всех сферах бизнеса постоянно требуется улучшать его ключевые показатели. Идеи улучшения могут быть совершенно разными. Обычно их очень много. Хочется проверить какие из них будут работать, а какие нет. Тестировать идеи нужно на реальных пользователях. Выделяется группа пользователей, которой показывается некоторое новшество. Когда наберётся достаточно информации, проверяется гипотеза об улучшении ключевой метрики. Схема такой проверки называется A/Б-тестом. \n",
    "\n",
    "### Что за улучшение и метрики\n",
    "\n",
    "Итак, мы придумали идею, которая должна улучшить мир. Чтобы сделать вывод реально ли улучшает наша идея мир, мы должны выбрать какой-то показатель и посмотреть вырастет он или упадёт. Такие показатели называются метриками. Чаще всего при проведении А/Б-теста мы пытаемся понять улучшилось ли состояние бизнеса и поэтому используем метрики, связанные с деньгами. \n",
    "\n",
    "Например, увеличились ли продажи, когда мы изменили алгоритм рекомендации товаров. Стали ли люди донатить больше денег, когда мы усложнили прохождение уровня в игре. Выросли ли продажи, когда мы провели маркетинговую компанию и тп. \n",
    "\n",
    "Метрики, связанные с деньгами бывают очень грубыми. Они могут слабо реагировать на небольшие изменения или после внесения изменений может потребоваться очень много времени, чтобы измерить их. Из-за этого часто используют промежуточные метрики, который, с одной стороны достаточно чувствительны к изменениям, а с другой, хорошо согласуются с бизнес-показателями, которые в реальности требуется измерить. Например, при внесении изменений на сайт с арендой квартир в качестве такой метрики можно взять \"среднее количество визитов на сайт в день\" или \"среднее число уникальных пользователей\" или \"количество репостов сайта в социальных сетях\".\n",
    "\n",
    "### Где используются А/Б тесты \n",
    "\n",
    "* Любые сайты, независимо от их профиля, используют механизм A/Б-тестирования для принятия решения о внесении каких-то изменений. Аналогично тестируются любые изменения дизайна или функциональности в приложениях или играх. \n",
    "* Работоспособность лекарств. Тех, кто согласен принять участие в тесте, делят на две части. Одной дают плацебо, другой реальное лекарство. После смотрят какая доля людей в обеих группах поправилась и делают выводы об эффективности.\n",
    "* Перед тем как автоматизировать какой-то процесс с помощью алгоритма машинного обучения, всегда проверяется с помощью А/Б-теста будет ли он работать в реальности лучше, чем человек. \n",
    "* А/Б-тестирование встречается и в довольно неожиданных местах. При правительствах США и Великобритани есть небольшие группы, которые совместно с психологами-бихевиористами выдвигают гипотезы о том, как люди взаимодействуют с государством, и на основании таких гипотез проводятся эксперименты: например, небольшие изменения в дизайне налоговой формы, или изменения в способе записи на донорство или трансплантацию органов. Такие вещи, которые легко и очень дешево можно поменять, оказывается, приводят к тому, что государство может сэкономить миллионы.\n",
    "\n",
    "\n",
    "### Кекс про кока-колу\n",
    "\n",
    "Компания, выпускающая колу решила протестировать как повлияет на продажи увеличение количества сахара в напитке. Для этого была собрана фокус-группа, которой предложили на выбор два напитка: со стандартным содержанием сахара и увеличенным. Людям нужно было попробовать оба и выбрать тот, который им больше понравился. В результате этого исследования выяснилось, что большее количество людей предпочитает Кока-Колу с увеличенным количеством сахара. Было решено увеличить количество сахара в напитке для более широкой аудитории. Неожиданно продажи упали. __Вопрос:__ что пошло не так? \n",
    "\n",
    "__Ответ:__ Эксперты стали разбираться почему так произошло, ведь в рамках фокус-группы было показано, что больше сахара — это вкуснее. Выяснилось, что это исследование проходило не в тех самых условиях, в которых люди обычно пьют Кока-Колу. Если речь идёт всего лишь об одном стакане, то, действительно, людям нравится большее количество сахара. Однако если напиток употребляется постоянно в больших количествах, то больше сахара — хуже. Кажется, что это логично: сложно выпить большое количество очень сладкого напитка. Поэтому, когда проводятся исследования на фокус-группах, нужно следить за тем, чтобы условия были максимально приближены к настоящим.\n",
    "\n",
    "__Мораль:__ любые исследования, которые проводятся в реальности стоят денег и могут привести к потерям. Тестирование идей должно происходить в максимально приближённых к реальности условиях.\n",
    "\n",
    "\n",
    "### Подводные камни\n",
    "\n",
    "В целом, процесс A/Б-тестирования распадается на две большие части. Первая часть — это планирование эксперимента: как именно будет выглядеть A/Б-тест, как пользователей будут делить на группы, сколько будет длиться тест и многие другие вопросы, связанные с этим. Вторая часть — это непосредственно проверка гипотез, принятие решения о том, положительно или отрицательно влияют изменения на бизнес в целом. На этапе дизайна возникает огромное количество проблем. \n",
    "\n",
    "Мы уже обсудили первый подводный камень: любые изменения должны тестироваться в максимально приближенных к реальности условиях. Иначе можно потерпеть фиаско аналогичное Кока-Коле. \n",
    "\n",
    "Есть и другие проблемы. Например, всегда хочется как можно меньше времени тратить на эксперименты и проверить много идей сразу. В такой ситуации будет сложно понять какое именно изменение привело к улучшению. Нужно следить, чтобы один и тот же пользователь не попал сразу в несколько экспериментальных групп. \n",
    "\n",
    "Более того, может оказаться, что изменения взаимоуничтожают друг-друга. Одно улучшает метрики, второе всё портит. Если проводится много экспериментов сразу, нужно следить за тем, чтобы они не противоречили друг-другу. Например, известна история о том, как Google тестировал 41 оттенок синего в цвете ссылок в поисковой выдаче. Если допустить, что одновременно еще проводился бы эксперимент о том, как выбрать цвет страницы или цвет, на фоне которого показываются эти ссылки, очевидно, что они не должны быть тех же самых цветов, что и текст ссылок, иначе пользователь просто не сможет ничего прочитать. То есть пример подбора одновременно цвета текста и цвета фона, на котором он показывается, — это пример экспериментов, которые друг с другом не сочетаются.\n",
    "\n",
    "Для проведения эксперимента требуется небольшая группа пользователей, которой будут показаны изменения. Для того, чтобы результаты, полученные на этой группе, можно было обобщить на всю выборку, она должна быть репрезентативной. Мы уже обсуждали до этого чем череваты проблемы с выборками в плане оценок параметров. Те же проблемы всплывают и тут. С одной стороны экспериментальная группа должна быть рандомизирована. С другой стороны в ней должна быть сохранена стратификация. Так, если известно, что 2/3 пользователей продукта - женщины, то в экспериментальной группе должно быть 2/3 женщин. При дизайне эксперимента между двумя этими вещами должен быть сохранён баланс. При этом не стоит забывать про закон больших чисел. Если в выборке довольно много людей, то, скорее всего, она охватит все страты в нужных пропрорциях. \n",
    "\n",
    "Эксперимент может ставиться на одних и тех же пользователях. Может оказаться важным как один и тот же пользователь реагирует на товар без изменений и с изменениями. Как вы помните, такие выборки называются связными. Возможно, что важен порядок предъевляемых изменений. Для того, чтобы понять влияние порядка изменений, можно попробовать использовать дизайн крест-накрест: половине пользователей показать сначала новый вариант, потом - старый, а другой половине - наоборот. \n",
    "\n",
    "Можно увидеть изменения там, где их нет. Например, если произошла выкатка на сайт новой кнопки, пользователи могут начать тыкать на неё из-за того, что они удивились новому изменению и хотят проверить что произойдёт. Мы при этом можем обрадоваться тому, что количество кликов увеличилось и решить, что это принесёт нам денег. Такую штуку можно детектировать с помощью обратного эксперимента. Пусть мы выкатили новую версию кнопки. Она показала себя лучше. Давайте расширим её до более большого числа пользователей, но при этом какой-то узкой группе людей продолжим показывать старую версию. Когда ажиотаж из-за любопытства стихнет, мы сможем удостовериться, что число кликов выросло из-за дизайна, проведя на длинном горизонте повторный А/Б-тест. \n",
    "\n",
    "Как мы с вами только что убедились, при проверке гипотез можно встреться с подводными камнями вообще везде. Иногда для того, чтобы определить насколько хорошим получился дизайн эксперимента, используют А/А-тест. Технология такого тестированя работает следующим образом: пользователей делят на две группы в соответствии с дизайном и показывают обеим группам старый вариант. Далее проверяют гипотезу о том, что метрики в группах совпадают. Если гипотеза не отвергается, всё круто. Если видны значимые изменения в метриках, у нашего дизайна есть проблемы. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Размер выборки \n",
    "\n",
    "Итак, дизайн эксперимента разработан, метрики выбраны. Вся экспериментальная структура устойчива и готова к пуску эксеримента. Осталось только решить сколько человек брать в выборку и как долго тест должен длиться. \n",
    "\n",
    "Задача определения объёма выборки тесто связана с тем, какой именно статистический инструмент будет использоваться для тестирования. Для каждого критерия подбор объёма осуществляется своим способом.\n",
    "\n",
    "Обычно, нужно понять какой минимальный размер эффекта мы хотим детектировать. Далее мы должны выбрать уровень значимости и размер ошибки второго рода. Далее, если взять статистический критерий и выразить из него величину $n$, можно понять при каких объёмах выборки этот размер будет улавливаться как значимый. Для различных критериев существуют калькуляторы мощности, в которые можно внести зафиксированные величины и получить на выход неизвестные. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. О котах и печеньках \n",
    "\n",
    "Давайте посмотрим на данные одной мобильной игрушки под названием \"Cookie Cats\", разработанной компанией <a href=\"http://tactile.dk\">Tactile Entertainment</a>. Это стандартный match-three пазл, где игрокам нужно соединять элементы одинаковых цветов, чтобы очистить поле и выиграть на уровне. И еще там есть поющие коты. Это важно. \n",
    "\n",
    "<p><a href=\"https://youtu.be/GaP5f0jVTWE\"><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/cookie_cats_video.jpeg\" style=\"width: 500px\"></a></p>\n",
    "\n",
    "По мере того, как игроки проходят уровни, они встречают ворота-блокеры, которые вынуждают их либо ждать длительное время, либо совершить внутриигровую покупку, чтобы продолжить играть. Помимо того, что эти ворота приносят разработчикам деньги от покупок, они еще и вынуждают игроков делать перерыв, в надежде на то, что те вернутся с новыми силами и снова начнут получать удовольствие от котиков. \n",
    "\n",
    "<p><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/cc_gates.png\" alt=\"\"></p>\n",
    "\n",
    "Но возникает вопрос - когда и где ставить эти ворота? Изначально первые ворота стояли на 30-м уровне игры, однако в этом ноутбуке мы будем анализировать АБ-тест, в котором разработчики передвинули ворота на 40-й уровень. В частности мы будем смотреть влияние этого изменения на такой важный показатель как \"retention\" или удержание игроков, который расчитывается как отношение уникальных игроков, зашедших в игру на 1-й, 2-й, ... N-й день после установки ко всем игрокам, установившим приложение в этот день.  Данные можно скачать по [ссылке.](https://yadi.sk/i/3KxFDTIT3WiZ3Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>userid</th><th scope=col>version</th><th scope=col>sum_gamerounds</th><th scope=col>retention_1</th><th scope=col>retention_7</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>116    </td><td>gate_30</td><td>  3    </td><td>FALSE  </td><td>FALSE  </td></tr>\n",
       "\t<tr><td>337    </td><td>gate_30</td><td> 38    </td><td> TRUE  </td><td>FALSE  </td></tr>\n",
       "\t<tr><td>377    </td><td>gate_40</td><td>165    </td><td> TRUE  </td><td>FALSE  </td></tr>\n",
       "\t<tr><td>483    </td><td>gate_40</td><td>  1    </td><td>FALSE  </td><td>FALSE  </td></tr>\n",
       "\t<tr><td>488    </td><td>gate_40</td><td>179    </td><td> TRUE  </td><td> TRUE  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " userid & version & sum\\_gamerounds & retention\\_1 & retention\\_7\\\\\n",
       "\\hline\n",
       "\t 116       & gate\\_30 &   3       & FALSE     & FALSE    \\\\\n",
       "\t 337       & gate\\_30 &  38       &  TRUE     & FALSE    \\\\\n",
       "\t 377       & gate\\_40 & 165       &  TRUE     & FALSE    \\\\\n",
       "\t 483       & gate\\_40 &   1       & FALSE     & FALSE    \\\\\n",
       "\t 488       & gate\\_40 & 179       &  TRUE     &  TRUE    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "userid | version | sum_gamerounds | retention_1 | retention_7 | \n",
       "|---|---|---|---|---|\n",
       "| 116     | gate_30 |   3     | FALSE   | FALSE   | \n",
       "| 337     | gate_30 |  38     |  TRUE   | FALSE   | \n",
       "| 377     | gate_40 | 165     |  TRUE   | FALSE   | \n",
       "| 483     | gate_40 |   1     | FALSE   | FALSE   | \n",
       "| 488     | gate_40 | 179     |  TRUE   |  TRUE   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  userid version sum_gamerounds retention_1 retention_7\n",
       "1 116    gate_30   3            FALSE       FALSE      \n",
       "2 337    gate_30  38             TRUE       FALSE      \n",
       "3 377    gate_40 165             TRUE       FALSE      \n",
       "4 483    gate_40   1            FALSE       FALSE      \n",
       "5 488    gate_40 179             TRUE        TRUE      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library('dplyr')  # библиотека для работы с таблицами\n",
    "\n",
    "# Загружаем табличку с данными \n",
    "df = read.csv('/Users/fulyankin/Yandex.Disk.localized/R/R_prob_data/cookie_cats.csv', sep=',', dec='.',\n",
    "               colClasses=c(\"retention_1\"='logical',\"retention_7\"='logical'))\n",
    "\n",
    "head(df, 5)  # шапка таблицы"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>90189</li>\n",
       "\t<li>5</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 90189\n",
       "\\item 5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 90189\n",
       "2. 5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 90189     5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dim(df)   # размер таблицы"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Данные для АБ-теста\n",
    "\n",
    "Итак, собраны данные по 90189 игрокам, которые установили игру во время запущенного теста. У нас есть следующие переменные:\n",
    "\n",
    "<ul>\n",
    "<li><code>userid</code> - уникальный номер, идентифицирующий каждого игрока.</li>\n",
    "<li><code>version</code> - был ли пользователь отнесен к контрольной группе (<code>gate_30</code> - ворота на 30-м уровне) или к тестовой (<code>gate_40</code> - ворота на 40-м уровне).</li>\n",
    "<li><code>sum_gamerounds</code> - число сессий, сыгранных игроком в течение первых 14 дней после установки игры.</li>\n",
    "<li><code>retention_1</code> - вернулся ли игрок после <strong>первого</strong> дня с момента установки?</li>\n",
    "<li><code>retention_7</code> - вернулся ли игрок после <strong>седьмого</strong> дня с момента установки?</li>\n",
    "</ul>\n",
    "\n",
    "Когда игрок устанавливает игру, он/она случайным образом относятся либо к группе gate_30, либо gate_40. На всякий случай, давайте проверим, действительно ли их примерно поровну в каждой из группу."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>version</th><th scope=col>n</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>gate_30</td><td>44700  </td></tr>\n",
       "\t<tr><td>gate_40</td><td>45489  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " version & n\\\\\n",
       "\\hline\n",
       "\t gate\\_30 & 44700    \\\\\n",
       "\t gate\\_40 & 45489    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "version | n | \n",
       "|---|---|\n",
       "| gate_30 | 44700   | \n",
       "| gate_40 | 45489   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  version n    \n",
       "1 gate_30 44700\n",
       "2 gate_40 45489"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df %>% group_by(version) %>% summarise(n = n())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Распределение числа игровых сессий\n",
    "<p><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/mr_waffles_smiling.png\" style=\"width:200px; float:left\"> </p>\n",
    "<p>Похоже, что игроков действительно примерно поровну в каждой из групп, отлично!</p>\n",
    "<p>Фокус нашего анализа будет сосредоточен на удержании игроков (retention), но ради интереса давайте построим распределение числа игровых сессий, сыгранных игроками в течение их первой недели жизни в игре.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>sum_gamerounds</th><th scope=col>number_of_players</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0   </td><td>3994</td></tr>\n",
       "\t<tr><td>1   </td><td>5538</td></tr>\n",
       "\t<tr><td>2   </td><td>4606</td></tr>\n",
       "\t<tr><td>3   </td><td>3958</td></tr>\n",
       "\t<tr><td>4   </td><td>3629</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " sum\\_gamerounds & number\\_of\\_players\\\\\n",
       "\\hline\n",
       "\t 0    & 3994\\\\\n",
       "\t 1    & 5538\\\\\n",
       "\t 2    & 4606\\\\\n",
       "\t 3    & 3958\\\\\n",
       "\t 4    & 3629\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "sum_gamerounds | number_of_players | \n",
       "|---|---|---|---|---|\n",
       "| 0    | 3994 | \n",
       "| 1    | 5538 | \n",
       "| 2    | 4606 | \n",
       "| 3    | 3958 | \n",
       "| 4    | 3629 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  sum_gamerounds number_of_players\n",
       "1 0              3994             \n",
       "2 1              5538             \n",
       "3 2              4606             \n",
       "4 3              3958             \n",
       "5 4              3629             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library('ggplot2')  # Пакет для картинок\n",
    "\n",
    "# Подсчитываем число людей, сыгравших каждое количество раундов\n",
    "plot_df = df %>% group_by(sum_gamerounds) %>% summarise(number_of_players = n())\n",
    "\n",
    "head(plot_df,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UBAB6S/PAGdzAKtpuy2225OPM+aNSsg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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Рисуем распределение этих людей \n",
    "options(repr.plot.width=6, repr.plot.height=3)\n",
    "\n",
    "ggplot(plot_df[1:100,], aes(x=sum_gamerounds, y=number_of_players))+\n",
    "    geom_line()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Общее удержание первого дня (1-day retention)\n",
    "<p>На графике вверху мы видим, что некоторые игроки установили игру, но даже ни разу не поиграли (0 сессий), многие игроки закончили лишь пару сессий за первую неделю, а некоторые действительно подсели и сыграли более 80 раз!</p>\n",
    "<p>Конечно, мы хотим, чтобы игроки были заинтересованы в игрушке и возвращались в неё снова и снова. Обычная метрика, использующаяся в гейм-индустрии, чтобы измерить, насколько игрушка веселая и захватывающая, - это <em>удержание первого дня</em> (1-day retention): Процент игроков, которые вренулись и снова стали играть спустя 1 день после установки. Чем выше удержание первого дня, тем проще и дальше удерживать пользователей и строить себе большую базу фанатов.</p>\n",
    "<p>В качестве первого шага, давайте посмотрим, как в целом выглядит 1-day retention.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.445209504485026"
      ],
      "text/latex": [
       "0.445209504485026"
      ],
      "text/markdown": [
       "0.445209504485026"
      ],
      "text/plain": [
       "[1] 0.4452095"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(df$retention_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. 1-day retention по АБ-группам \n",
    "<p><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/belle_cookie.png\" style=\"width:200px; float:right\"> </p>\n",
    "<p>Итак, немногим меьше половины всех игроков возвращяются к нам спустя один день после установки. Теперь давайте посмотрим, как отличается 1-day retention внутри наших тестовых групп.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>version</th><th scope=col>mean(retention_1)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>gate_30  </td><td>0.4481879</td></tr>\n",
       "\t<tr><td>gate_40  </td><td>0.4422827</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " version & mean(retention\\_1)\\\\\n",
       "\\hline\n",
       "\t gate\\_30 & 0.4481879\\\\\n",
       "\t gate\\_40 & 0.4422827\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "version | mean(retention_1) | \n",
       "|---|---|\n",
       "| gate_30   | 0.4481879 | \n",
       "| gate_40   | 0.4422827 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  version mean(retention_1)\n",
       "1 gate_30 0.4481879        \n",
       "2 gate_40 0.4422827        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df %>% group_by(version) %>% summarise(mean(retention_1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Должны ли мы быть уверены в разнице? \n",
    "<p>Похоже, что у нас есть небольшое ухудшение в удержании первого дня, если мы двигаем ворота к сороковому уровню (44.2%) в сравнеии с контрольной группой, где ворота остались на 30-м уровне (44.8%). Разница, конечно, невелика, но даже маленькие изменений в удержании могут иметь значительные последствия. Однако сейчас мы уверены, что различие есть в наблюдаемых данных, а будет ли вариант с воротами на сороковом уровне хуже в будущем?</p>\n",
    "<p>Есть несколько способов оценки нашей уверенности в наблюдаемых цифрах. \n",
    "Здесь мы попробуем воспользоваться $z$-критерием для проверки гипотезы о равенстве долей, а также бустрапом (bootstrap).  Бутсрап подразумевает, что мы будем последовательно ресэмплить с возвращением наш датасет (то есть выбирать случайную подвыборку из всего множества наблюдений) и для каждой выборки считать удержание первого дня. Дисперсия нашего 1-day retention при таком способе вычисления даст нам указание на то, насколько мы должны быть неуверены в оценках нашего удержания.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "iterations = 500 # число итераций"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>gate_30_mean</th><th scope=col>gate_40_mean</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.4511725</td><td>0.4379922</td></tr>\n",
       "\t<tr><td>0.4468566</td><td>0.4392336</td></tr>\n",
       "\t<tr><td>0.4486125</td><td>0.4418851</td></tr>\n",
       "\t<tr><td>0.4467628</td><td>0.4461677</td></tr>\n",
       "\t<tr><td>0.4453667</td><td>0.4446114</td></tr>\n",
       "\t<tr><td>0.4476762</td><td>0.4437294</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " gate\\_30\\_mean & gate\\_40\\_mean\\\\\n",
       "\\hline\n",
       "\t 0.4511725 & 0.4379922\\\\\n",
       "\t 0.4468566 & 0.4392336\\\\\n",
       "\t 0.4486125 & 0.4418851\\\\\n",
       "\t 0.4467628 & 0.4461677\\\\\n",
       "\t 0.4453667 & 0.4446114\\\\\n",
       "\t 0.4476762 & 0.4437294\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "gate_30_mean | gate_40_mean | \n",
       "|---|---|---|---|---|---|\n",
       "| 0.4511725 | 0.4379922 | \n",
       "| 0.4468566 | 0.4392336 | \n",
       "| 0.4486125 | 0.4418851 | \n",
       "| 0.4467628 | 0.4461677 | \n",
       "| 0.4453667 | 0.4446114 | \n",
       "| 0.4476762 | 0.4437294 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  gate_30_mean gate_40_mean\n",
       "1 0.4511725    0.4379922   \n",
       "2 0.4468566    0.4392336   \n",
       "3 0.4486125    0.4418851   \n",
       "4 0.4467628    0.4461677   \n",
       "5 0.4453667    0.4446114   \n",
       "6 0.4476762    0.4437294   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boot_1d_30 = rep(0, iterations)  # вектор для средних по воротам на 30 уровне\n",
    "boot_1d_40 = rep(0, iterations)  # вектор для средних по воротам на 40 уровне\n",
    "\n",
    "for(i in 1:iterations){\n",
    "    # генерируем таблицу с повторениями соответствующую по размерам оригинальной\n",
    "    boot_mean = sample_n(df, size = dim(df)[1], replace=TRUE) %>% \n",
    "                    group_by(version) %>% summarise(mean = mean(retention_1))\n",
    "    \n",
    "    boot_1d_30[i] = boot_mean[1,2]$mean # считаем средние и записываем их в вектора\n",
    "    boot_1d_40[i] = boot_mean[2,2]$mean    \n",
    "}\n",
    "\n",
    "# строим общую табличку и смотрим на неё\n",
    "# в колонка таблицы лежат сбутстрапированные распределения для долей вернувшихся в игру с воротами \n",
    "# на разных уровнях\n",
    "plot_df = data.frame(gate_30_mean = boot_1d_30, gate_40_mean = boot_1d_40)\n",
    "head(plot_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GBBDDMqUd5UYT0f9Osrk159WfKqCxpP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ysX/88Yd069ZN3nzzTSldrZrcoxE2qlx8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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(plot_df)+ \n",
    "    geom_density(aes(x=gate_30_mean, y=..density.., fill='gate_30'),alpha=0.4) +\n",
    "    geom_density(aes(x=gate_40_mean, y=..density.., fill='gate_40'),alpha=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Смотрим на разницу поближе\n",
    "<p>Эти два распределения представляют собой оценку распределений 1-day retention для наших двух АБ-групп. Даже просто визуально понятно, что какое-то доказательство различия двух групп у нас есть. Посмотрим теперь подробнее на разницу в ретеншене у двух групп.</p>\n",
    "<p>(<em>Чтобы посчиталось быстрее число  итераций мы выбрали достаточно небольшим - всего 500 раз считаем средние по выборкам. В боевых условиях число было бы больше, например, 10 тысяч итераций. </em>)</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IpFisQ8bIrtFiLZyvLhwyi18JHmlOPs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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_df['diff'] = (plot_df$gate_30_mean - plot_df$gate_40_mean)/plot_df$gate_40_mean*100\n",
    "\n",
    "ggplot(plot_df)+ \n",
    "     geom_density(aes(x=diff, y=..density.., fill='diff'),alpha=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9. Вероятность разницы\n",
    "<p><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/ziggy_smiling.png\" style=\"width:200px; float:left\"> </p>\n",
    "<p>Из этого графика мы видим, что наиболее вероятная разница составляет примерно 1%-2%, а большая часть распределения находится справа от нуля, то есть вариант с воротами на 30 уровне пока выигрывает. Но какова вероятность того, что эта разница больше 0%? Посчитаем и её тоже.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.956"
      ],
      "text/latex": [
       "0.956"
      ],
      "text/markdown": [
       "0.956"
      ],
      "text/plain": [
       "[1] 0.956"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(plot_df$diff > 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10. 7-day retention по АБ-группам\n",
    "<p>Бутстрап-анализ свидетельствует о высокой вероятности того, что удержание первого дня лучше в группе с воротами на 30-м уровне, чем на 40-м. Однако, так как игроки успели пожить в игре всего один день, вполне возможно, что их большинство еще даже не дошли даже до 30-го уровня. А значит, многие игроки не будут затронуты нашим изменением и сильного эффекта мы не увидим.</p>\n",
    "<p>Однако спустя неделю после установки, уже больше игроков пройдут 40 уровней, поэтому имеет смысл посмотреть на удержание седьмого дня. Т.е., какой процент людей, установивших игру, снова показался в игре через 7 дней.</p>\n",
    "<p>Начнем с рассчета 7-day retention для двух АБ-групп.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>version</th><th scope=col>mean(retention_7)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>gate_30  </td><td>0.1902013</td></tr>\n",
       "\t<tr><td>gate_40  </td><td>0.1820000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " version & mean(retention\\_7)\\\\\n",
       "\\hline\n",
       "\t gate\\_30 & 0.1902013\\\\\n",
       "\t gate\\_40 & 0.1820000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "version | mean(retention_7) | \n",
       "|---|---|\n",
       "| gate_30   | 0.1902013 | \n",
       "| gate_40   | 0.1820000 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  version mean(retention_7)\n",
       "1 gate_30 0.1902013        \n",
       "2 gate_40 0.1820000        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df %>% group_by(version) %>% summarise(mean(retention_7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11. Снова бутстрапим разницу \n",
    "<p>Как и с 1-day retention, мы видим, что 7-day retention немного ниже (18.2%), когда ворота находятся на 40-м уровне, чем на 30-м (19.0%). Эта разница также выше, чем для удержания первого дня, скорее всего из-за того, что игроки имели больше времени на то, чтобы столкнуться с первыми воротами. Мы также видим, что удержание 7-го дня в целом ниже, чем удержание 1-го - спустя неделю намного меньше людей всё ещё заходит в игру.<p>Но как и раньше, давайте применим бутстрап анализ и выясним, насколько уверены мы должны быть в разнице между двумя АБ-группами.</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>gate_30_mean</th><th scope=col>gate_40_mean</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0.1898322</td><td>0.1799632</td></tr>\n",
       "\t<tr><td>0.1898799</td><td>0.1842500</td></tr>\n",
       "\t<tr><td>0.1943012</td><td>0.1824568</td></tr>\n",
       "\t<tr><td>0.1902426</td><td>0.1808297</td></tr>\n",
       "\t<tr><td>0.1891226</td><td>0.1828430</td></tr>\n",
       "\t<tr><td>0.1900943</td><td>0.1822900</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       " gate\\_30\\_mean & gate\\_40\\_mean\\\\\n",
       "\\hline\n",
       "\t 0.1898322 & 0.1799632\\\\\n",
       "\t 0.1898799 & 0.1842500\\\\\n",
       "\t 0.1943012 & 0.1824568\\\\\n",
       "\t 0.1902426 & 0.1808297\\\\\n",
       "\t 0.1891226 & 0.1828430\\\\\n",
       "\t 0.1900943 & 0.1822900\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "gate_30_mean | gate_40_mean | \n",
       "|---|---|---|---|---|---|\n",
       "| 0.1898322 | 0.1799632 | \n",
       "| 0.1898799 | 0.1842500 | \n",
       "| 0.1943012 | 0.1824568 | \n",
       "| 0.1902426 | 0.1808297 | \n",
       "| 0.1891226 | 0.1828430 | \n",
       "| 0.1900943 | 0.1822900 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  gate_30_mean gate_40_mean\n",
       "1 0.1898322    0.1799632   \n",
       "2 0.1898799    0.1842500   \n",
       "3 0.1943012    0.1824568   \n",
       "4 0.1902426    0.1808297   \n",
       "5 0.1891226    0.1828430   \n",
       "6 0.1900943    0.1822900   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "boot_7d_30 = rep(0, iterations)\n",
    "boot_7d_40 = rep(0, iterations)\n",
    "\n",
    "for(i in 1:iterations){\n",
    "    boot_mean = sample_n(df, size = dim(df)[1], replace=TRUE)%>% group_by(version) %>% summarise(mean = mean(retention_7))\n",
    "    boot_7d_30[i] = boot_mean[1,2]$mean\n",
    "    boot_7d_40[i] = boot_mean[2,2]$mean    \n",
    "}\n",
    "\n",
    "plot_df7 = data.frame(gate_30_mean = boot_7d_30, gate_40_mean = boot_7d_40)\n",
    "head(plot_df7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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y2AllkKF2rn6NKlSx44Ig9BAQpQgAIWAQbQFgk+UoACNgIrVqyAdCDsULsWpAkH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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_df7['diff'] = (plot_df7$gate_30_mean - plot_df7$gate_40_mean)/plot_df7$gate_40_mean*100\n",
    "\n",
    "ggplot(plot_df7)+ \n",
    "     geom_density(aes(x=diff, y=..density.., fill='diff'),alpha=0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "1"
      ],
      "text/latex": [
       "1"
      ],
      "text/markdown": [
       "1"
      ],
      "text/plain": [
       "[1] 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(plot_df7$diff > 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.  Выводы\n",
    "<p>Итак, результаты бутстрапа говорят нам о том, что есть значительное доказательство превышения 7-day retentino в группе с воротами на 30-м уровне над группой с воротами на 40-м. Значит, если мы хотим держать ретеншн на высоком уровне и иметь большее число игроков, нам <strong>не нужно</strong> сдвигать ворота с 30-го на 40-й уровень.\n",
    "<p><img src=\"https://s3.amazonaws.com/assets.datacamp.com/production/project_184/img/cookie_yellow.png\" style=\"width:100px; float:center\"> </p>\n",
    "<p>Так почему же ретеншн выше, когда ворота расположены раньше? Логично было бы ожидать обратной ситуации - чем позже ставится препятствие, тем дольше игроки будут взаимодействовать с игрой. Однако это не то, что мы видим в данных. Теория гедонистической адаптации может помочь с объяснением. Если вкратце, гедонистическая адаптация - это тенденция получать всё меньше и меньше удовольствия от деятельности, если она продолжается длительное время. Заставляя игроков сделать паузу, когда они достигают 30-го уровня, мы продлеваем им удовольствие от игры, в результате чего они хотят в неё возвращаться. И напротив, сдвигая ворота к 40-му уровню мы даем игрокам возможность наиграться и просто заскучать.</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 13. Z-тест\n",
    "\n",
    "Бутсрап позволил нам посмотреть не просто на какие-то отдельные значения долей, он позволил нам намного большее, сымитировать распределение этих долей. Давайте попробуем воспользоваться здесь z-тестом для равенства долей. Будем проверять гипотезу о том, что 1-day retention с воротами на разных уровнях не отличаются друг от друга против альтернативы, что разичаются. Каких-то априорных мыслей о знаке отличия у нас не возникает, поэтому приходится рассматривать двустороннюю альтернативу."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>version</th><th scope=col>m</th><th scope=col>n</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>gate_30</td><td>20034  </td><td>44700  </td></tr>\n",
       "\t<tr><td>gate_40</td><td>20119  </td><td>45489  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " version & m & n\\\\\n",
       "\\hline\n",
       "\t gate\\_30 & 20034     & 44700    \\\\\n",
       "\t gate\\_40 & 20119     & 45489    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "version | m | n | \n",
       "|---|---|\n",
       "| gate_30 | 20034   | 44700   | \n",
       "| gate_40 | 20119   | 45489   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  version m     n    \n",
       "1 gate_30 20034 44700\n",
       "2 gate_40 20119 45489"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_ex = df %>% group_by(version) %>% summarise(m = sum(retention_1),n = n())\n",
    "df_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\t2-sample test for equality of proportions without continuity\n",
       "\tcorrection\n",
       "\n",
       "data:  df_ex$m out of df_ex$n\n",
       "X-squared = 3.183, df = 1, p-value = 0.07441\n",
       "alternative hypothesis: two.sided\n",
       "95 percent confidence interval:\n",
       " -0.0005820999  0.0123924394\n",
       "sample estimates:\n",
       "   prop 1    prop 2 \n",
       "0.4481879 0.4422827 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_res = prop.test(x = df_ex$m, n = df_ex$n, correct = FALSE)\n",
    "test_res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Видим, что гипотеза о равенстве показателей при воротах на разных уровнях не отвергается на $5\\%$ уровне значимости. В первый день критерий не может обнаружить различий. Стоит обратить внимание, что в этом примере мы находимся на границе. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>version</th><th scope=col>m</th><th scope=col>n</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>gate_30</td><td>8502   </td><td>44700  </td></tr>\n",
       "\t<tr><td>gate_40</td><td>8279   </td><td>45489  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " version & m & n\\\\\n",
       "\\hline\n",
       "\t gate\\_30 & 8502      & 44700    \\\\\n",
       "\t gate\\_40 & 8279      & 45489    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "version | m | n | \n",
       "|---|---|\n",
       "| gate_30 | 8502    | 44700   | \n",
       "| gate_40 | 8279    | 45489   | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  version m    n    \n",
       "1 gate_30 8502 44700\n",
       "2 gate_40 8279 45489"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_ex = df %>% group_by(version) %>% summarise(m = sum(retention_7),n = n())\n",
    "df_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\t2-sample test for equality of proportions without continuity\n",
       "\tcorrection\n",
       "\n",
       "data:  df_ex$m out of df_ex$n\n",
       "X-squared = 10.013, df = 1, p-value = 0.001554\n",
       "alternative hypothesis: two.sided\n",
       "95 percent confidence interval:\n",
       " 0.003121044 0.013281552\n",
       "sample estimates:\n",
       "   prop 1    prop 2 \n",
       "0.1902013 0.1820000 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_res = prop.test(x = df_ex$m, n = df_ex$n, correct = FALSE)\n",
    "test_res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "На $7$ день различия начинают быть более существенными и гипотеза о равенстве отвергается, причём довольно уверенно отвергается."
   ]
  }
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