main.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analiza eksploracyjna i test statystyczny"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### <b>Marta Szymańska</b> \n",
    "##### <b>Indeks: 151481</b>\n",
    "___"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Opis zbioru danych"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Muzykoterapia, czyli MT, polega na wykorzystaniu muzyki do poprawy stresu, nastroju i ogólnego stanu zdrowia psychicznego danej osoby. MT jest również uznawana za praktykę opartą na dowodach, wykorzystującą muzykę jako katalizator dla „szczęśliwych” hormonów, takich jak oksytocyna. MT wykorzystuje szeroką gamę różnych gatunków."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zbiór danych, który udało mi się znaleźć, ma na celu określenie, jakie korelacje istnieją między indywidualnym gustem muzycznym, a zgłaszanym przez badanych zdrowiem psychicznym. W idealnym przypadku odkrycia te mogłyby przyczynić się do bardziej świadomego zastosowania MT lub po prostu dostarczyć interesujących widoków na temat umysłu."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zestaw danych, który wykorzystałam, pochodzi z platformy internetowej kaggle.com: https://www.kaggle.com/datasets/catherinerasgaitis/mxmh-survey-results.\n",
    "<br>\n",
    "Wybrane dane obejmują próbę 736 badanych osób. Respondenci nie byli ograniczeni wiekiem ani lokalizacją. Ankieta była przeprowadzana wśród różnych osób, szerzona głównie poprzez platformy takie jak Discord, Reddit i inne social media. Plakaty i „wizytówki” były również używane do reklamowania formularza w bibliotekach, parkach i innych miejscach publicznych. \n",
    "<br>\n",
    "<b>Blok 1</b>: Gatunki muzyczne <br>\n",
    "Ankietowani oceniają, jak często słuchają 16 gatunków muzycznych, gdzie mogą wybrać:\n",
    "- Nigdy\n",
    "- Rzadko\n",
    "- Czasami\n",
    "- Bardzo często <br>\n",
    "\n",
    "<b>Blok 2</b>: Zdrowie psychiczne <br>\n",
    "Respondenci oceniają lęk, depresję, bezsenność i zaburzenia obsesyjno-kompulsyjne w skali od 0 do 10, gdzie: <br>\n",
    "0 - nie doświadczam tego. <br>\n",
    "10 - Doświadczam tego regularnie, stale/lub do skrajności. <br>\n",
    "<br>\n",
    "Baza zawiera 33 atrubuty, tj.:\n",
    "Nazwa atrybutu - Rodzaj danych \n",
    "- <b>Timestamp</b> - Jakościowe <br>       \n",
    "- <b>Age</b> - Ilościowe<br> \n",
    "- <b>Primary streaming service</b> - Jakościowe<br> \n",
    "- <b>Hours per day</b> - Ilościowe<br> \n",
    "- <b>While working</b> - Jakościowe<br> \n",
    "- <b>Instrumentalist</b> - Jakościowe<br> \n",
    "- <b>Composer</b> - Jakościowe<br> \n",
    "- <b>Fav genre</b> - Jakościowe<br> \n",
    "- <b>Exploratory</b> - Jakościowe<br> \n",
    "- <b>Foreign languages</b> - Jakościowe<br> \n",
    "- <b>BPM</b> - Ilościowe<br> \n",
    "- <b>Frequency [Classical]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Country]</b> - Jakościowe<br> \n",
    "- <b>Frequency [EDM]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Folk]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Gospel]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Hip hop]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Jazz]</b> - Jakościowe<br> \n",
    "- <b>Frequency [K pop]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Latin]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Lofi]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Metal]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Pop]</b> - Jakościowe<br> \n",
    "- <b>Frequency [R&B]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Rap]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Rock]</b> - Jakościowe<br> \n",
    "- <b>Frequency [Video game music]</b> - Jakościowe<br> \n",
    "- <b>Anxiety</b> - Ilościowe<br> \n",
    "- <b>Depression</b> - Ilościowe<br> \n",
    "- <b>Insomnia</b> - Ilościowe<br> \n",
    "- <b>OCD</b> - Ilościowe<br> \n",
    "- <b>Music effects</b> - Jakościowe<br> \n",
    "- <b>Permissions</b> - Jakościowe<br> \n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analiza eksploracyjna"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wczytanie danych:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "dirtyData <- read.csv('mxmh_survey_results.csv')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Przed przystąpieniem do analizy należy wyczyszcić dane. W tym przypadku zostały usunięte wszystkie wiersze, w których brakowało wartości numerycznych oraz niektórych jakościowych. Z tego powodu liczba osób zmniejszyła się."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 33</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Timestamp</th><th scope=col>Age</th><th scope=col>Primary.streaming.service</th><th scope=col>Hours.per.day</th><th scope=col>While.working</th><th scope=col>Instrumentalist</th><th scope=col>Composer</th><th scope=col>Fav.genre</th><th scope=col>Exploratory</th><th scope=col>Foreign.languages</th><th scope=col>⋯</th><th scope=col>Frequency..R.B.</th><th scope=col>Frequency..Rap.</th><th scope=col>Frequency..Rock.</th><th scope=col>Frequency..Video.game.music.</th><th scope=col>Anxiety</th><th scope=col>Depression</th><th scope=col>Insomnia</th><th scope=col>OCD</th><th scope=col>Music.effects</th><th scope=col>Permissions</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>⋯</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>3</th><td>8/27/2022 21:28:18</td><td>18</td><td>Spotify      </td><td>4.0</td><td>No </td><td>No </td><td>No </td><td>Video game music</td><td>No </td><td>Yes</td><td>⋯</td><td>Never          </td><td>Rarely         </td><td>Rarely         </td><td>Very frequently</td><td>7</td><td>7</td><td>10</td><td>2</td><td>No effect</td><td>I understand.</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>8/27/2022 21:40:40</td><td>61</td><td>YouTube Music</td><td>2.5</td><td>Yes</td><td>No </td><td>Yes</td><td>Jazz            </td><td>Yes</td><td>Yes</td><td>⋯</td><td>Sometimes      </td><td>Never          </td><td>Never          </td><td>Never          </td><td>9</td><td>7</td><td> 3</td><td>3</td><td>Improve  </td><td>I understand.</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>8/27/2022 21:54:47</td><td>18</td><td><span style=white-space:pre-wrap>Spotify      </span></td><td>4.0</td><td>Yes</td><td>No </td><td>No </td><td><span style=white-space:pre-wrap>R&amp;B             </span></td><td>Yes</td><td>No </td><td>⋯</td><td>Very frequently</td><td>Very frequently</td><td><span style=white-space:pre-wrap>Never          </span></td><td><span style=white-space:pre-wrap>Rarely         </span></td><td>7</td><td>2</td><td> 5</td><td>9</td><td><span style=white-space:pre-wrap>Improve  </span></td><td>I understand.</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>8/27/2022 21:56:50</td><td>18</td><td>Spotify      </td><td>5.0</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Jazz            </td><td>Yes</td><td>Yes</td><td>⋯</td><td>Very frequently</td><td>Very frequently</td><td>Very frequently</td><td>Never          </td><td>8</td><td>8</td><td> 7</td><td>7</td><td>Improve  </td><td>I understand.</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>8/27/2022 22:00:29</td><td>18</td><td>YouTube Music</td><td>3.0</td><td>Yes</td><td>Yes</td><td>No </td><td>Video game music</td><td>Yes</td><td>Yes</td><td>⋯</td><td>Rarely         </td><td>Never          </td><td>Never          </td><td>Sometimes      </td><td>4</td><td>8</td><td> 6</td><td>0</td><td>Improve  </td><td>I understand.</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>8/27/2022 22:18:59</td><td>21</td><td>Spotify      </td><td>1.0</td><td>Yes</td><td>No </td><td>No </td><td>K pop           </td><td>Yes</td><td>Yes</td><td>⋯</td><td>Sometimes      </td><td>Rarely         </td><td>Never          </td><td>Rarely         </td><td>5</td><td>3</td><td> 5</td><td>3</td><td>Improve  </td><td>I understand.</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 33\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & Timestamp & Age & Primary.streaming.service & Hours.per.day & While.working & Instrumentalist & Composer & Fav.genre & Exploratory & Foreign.languages & ⋯ & Frequency..R.B. & Frequency..Rap. & Frequency..Rock. & Frequency..Video.game.music. & Anxiety & Depression & Insomnia & OCD & Music.effects & Permissions\\\\\n",
       "  & <chr> & <int> & <chr> & <dbl> & <chr> & <chr> & <chr> & <chr> & <chr> & <chr> & ⋯ & <chr> & <chr> & <chr> & <chr> & <dbl> & <dbl> & <dbl> & <dbl> & <chr> & <chr>\\\\\n",
       "\\hline\n",
       "\t3 & 8/27/2022 21:28:18 & 18 & Spotify       & 4.0 & No  & No  & No  & Video game music & No  & Yes & ⋯ & Never           & Rarely          & Rarely          & Very frequently & 7 & 7 & 10 & 2 & No effect & I understand.\\\\\n",
       "\t4 & 8/27/2022 21:40:40 & 61 & YouTube Music & 2.5 & Yes & No  & Yes & Jazz             & Yes & Yes & ⋯ & Sometimes       & Never           & Never           & Never           & 9 & 7 &  3 & 3 & Improve   & I understand.\\\\\n",
       "\t5 & 8/27/2022 21:54:47 & 18 & Spotify       & 4.0 & Yes & No  & No  & R\\&B              & Yes & No  & ⋯ & Very frequently & Very frequently & Never           & Rarely          & 7 & 2 &  5 & 9 & Improve   & I understand.\\\\\n",
       "\t6 & 8/27/2022 21:56:50 & 18 & Spotify       & 5.0 & Yes & Yes & Yes & Jazz             & Yes & Yes & ⋯ & Very frequently & Very frequently & Very frequently & Never           & 8 & 8 &  7 & 7 & Improve   & I understand.\\\\\n",
       "\t7 & 8/27/2022 22:00:29 & 18 & YouTube Music & 3.0 & Yes & Yes & No  & Video game music & Yes & Yes & ⋯ & Rarely          & Never           & Never           & Sometimes       & 4 & 8 &  6 & 0 & Improve   & I understand.\\\\\n",
       "\t8 & 8/27/2022 22:18:59 & 21 & Spotify       & 1.0 & Yes & No  & No  & K pop            & Yes & Yes & ⋯ & Sometimes       & Rarely          & Never           & Rarely          & 5 & 3 &  5 & 3 & Improve   & I understand.\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 33\n",
       "\n",
       "| <!--/--> | Timestamp &lt;chr&gt; | Age &lt;int&gt; | Primary.streaming.service &lt;chr&gt; | Hours.per.day &lt;dbl&gt; | While.working &lt;chr&gt; | Instrumentalist &lt;chr&gt; | Composer &lt;chr&gt; | Fav.genre &lt;chr&gt; | Exploratory &lt;chr&gt; | Foreign.languages &lt;chr&gt; | ⋯ ⋯ | Frequency..R.B. &lt;chr&gt; | Frequency..Rap. &lt;chr&gt; | Frequency..Rock. &lt;chr&gt; | Frequency..Video.game.music. &lt;chr&gt; | Anxiety &lt;dbl&gt; | Depression &lt;dbl&gt; | Insomnia &lt;dbl&gt; | OCD &lt;dbl&gt; | Music.effects &lt;chr&gt; | Permissions &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 3 | 8/27/2022 21:28:18 | 18 | Spotify       | 4.0 | No  | No  | No  | Video game music | No  | Yes | ⋯ | Never           | Rarely          | Rarely          | Very frequently | 7 | 7 | 10 | 2 | No effect | I understand. |\n",
       "| 4 | 8/27/2022 21:40:40 | 61 | YouTube Music | 2.5 | Yes | No  | Yes | Jazz             | Yes | Yes | ⋯ | Sometimes       | Never           | Never           | Never           | 9 | 7 |  3 | 3 | Improve   | I understand. |\n",
       "| 5 | 8/27/2022 21:54:47 | 18 | Spotify       | 4.0 | Yes | No  | No  | R&amp;B              | Yes | No  | ⋯ | Very frequently | Very frequently | Never           | Rarely          | 7 | 2 |  5 | 9 | Improve   | I understand. |\n",
       "| 6 | 8/27/2022 21:56:50 | 18 | Spotify       | 5.0 | Yes | Yes | Yes | Jazz             | Yes | Yes | ⋯ | Very frequently | Very frequently | Very frequently | Never           | 8 | 8 |  7 | 7 | Improve   | I understand. |\n",
       "| 7 | 8/27/2022 22:00:29 | 18 | YouTube Music | 3.0 | Yes | Yes | No  | Video game music | Yes | Yes | ⋯ | Rarely          | Never           | Never           | Sometimes       | 4 | 8 |  6 | 0 | Improve   | I understand. |\n",
       "| 8 | 8/27/2022 22:18:59 | 21 | Spotify       | 1.0 | Yes | No  | No  | K pop            | Yes | Yes | ⋯ | Sometimes       | Rarely          | Never           | Rarely          | 5 | 3 |  5 | 3 | Improve   | I understand. |\n",
       "\n"
      ],
      "text/plain": [
       "  Timestamp          Age Primary.streaming.service Hours.per.day While.working\n",
       "3 8/27/2022 21:28:18 18  Spotify                   4.0           No           \n",
       "4 8/27/2022 21:40:40 61  YouTube Music             2.5           Yes          \n",
       "5 8/27/2022 21:54:47 18  Spotify                   4.0           Yes          \n",
       "6 8/27/2022 21:56:50 18  Spotify                   5.0           Yes          \n",
       "7 8/27/2022 22:00:29 18  YouTube Music             3.0           Yes          \n",
       "8 8/27/2022 22:18:59 21  Spotify                   1.0           Yes          \n",
       "  Instrumentalist Composer Fav.genre        Exploratory Foreign.languages ⋯\n",
       "3 No              No       Video game music No          Yes               ⋯\n",
       "4 No              Yes      Jazz             Yes         Yes               ⋯\n",
       "5 No              No       R&B              Yes         No                ⋯\n",
       "6 Yes             Yes      Jazz             Yes         Yes               ⋯\n",
       "7 Yes             No       Video game music Yes         Yes               ⋯\n",
       "8 No              No       K pop            Yes         Yes               ⋯\n",
       "  Frequency..R.B. Frequency..Rap. Frequency..Rock. Frequency..Video.game.music.\n",
       "3 Never           Rarely          Rarely           Very frequently             \n",
       "4 Sometimes       Never           Never            Never                       \n",
       "5 Very frequently Very frequently Never            Rarely                      \n",
       "6 Very frequently Very frequently Very frequently  Never                       \n",
       "7 Rarely          Never           Never            Sometimes                   \n",
       "8 Sometimes       Rarely          Never            Rarely                      \n",
       "  Anxiety Depression Insomnia OCD Music.effects Permissions  \n",
       "3 7       7          10       2   No effect     I understand.\n",
       "4 9       7           3       3   Improve       I understand.\n",
       "5 7       2           5       9   Improve       I understand.\n",
       "6 8       8           7       7   Improve       I understand.\n",
       "7 4       8           6       0   Improve       I understand.\n",
       "8 5       3           5       3   Improve       I understand."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data <- subset(dirtyData,(!is.na(dirtyData[\"Age\"]) & !is.na(dirtyData[\"Anxiety\"])) & !is.na(dirtyData[\"Depression\"]) & !is.na(dirtyData[\"Insomnia\"]) & !is.na(dirtyData[\"OCD\"]) & !is.na(dirtyData[\"Hours.per.day\"]) & !is.na(dirtyData[\"BPM\"]))\n",
    "data <- data[-which(data$While.working == \"\"), ]\n",
    "data <- data[-which(data$Instrumentalist == \"\"), ]\n",
    "data <- data[-which(data$Music.effects == \"\"), ]\n",
    "data <- data[-which(data$Foreign.languages == \"\"), ]\n",
    "head(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Struktura danych:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 695,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t619 obs. of  33 variables:\n",
      " $ Timestamp                   : chr  \"8/27/2022 21:28:18\" \"8/27/2022 21:40:40\" \"8/27/2022 21:54:47\" \"8/27/2022 21:56:50\" ...\n",
      " $ Age                         : int  18 61 18 18 18 21 19 18 19 19 ...\n",
      " $ Primary.streaming.service   : chr  \"Spotify\" \"YouTube Music\" \"Spotify\" \"Spotify\" ...\n",
      " $ Hours.per.day               : num  4 2.5 4 5 3 1 6 1 8 2 ...\n",
      " $ While.working               : chr  \"No\" \"Yes\" \"Yes\" \"Yes\" ...\n",
      " $ Instrumentalist             : chr  \"No\" \"No\" \"No\" \"Yes\" ...\n",
      " $ Composer                    : chr  \"No\" \"Yes\" \"No\" \"Yes\" ...\n",
      " $ Fav.genre                   : chr  \"Video game music\" \"Jazz\" \"R&B\" \"Jazz\" ...\n",
      " $ Exploratory                 : chr  \"No\" \"Yes\" \"Yes\" \"Yes\" ...\n",
      " $ Foreign.languages           : chr  \"Yes\" \"Yes\" \"No\" \"Yes\" ...\n",
      " $ BPM                         : int  132 84 107 86 66 95 94 155 125 88 ...\n",
      " $ Frequency..Classical.       : chr  \"Never\" \"Sometimes\" \"Never\" \"Rarely\" ...\n",
      " $ Frequency..Country.         : chr  \"Never\" \"Never\" \"Never\" \"Sometimes\" ...\n",
      " $ Frequency..EDM.             : chr  \"Very frequently\" \"Never\" \"Rarely\" \"Never\" ...\n",
      " $ Frequency..Folk.            : chr  \"Never\" \"Rarely\" \"Never\" \"Never\" ...\n",
      " $ Frequency..Gospel.          : chr  \"Never\" \"Sometimes\" \"Rarely\" \"Never\" ...\n",
      " $ Frequency..Hip.hop.         : chr  \"Rarely\" \"Never\" \"Very frequently\" \"Sometimes\" ...\n",
      " $ Frequency..Jazz.            : chr  \"Rarely\" \"Very frequently\" \"Never\" \"Very frequently\" ...\n",
      " $ Frequency..K.pop.           : chr  \"Very frequently\" \"Sometimes\" \"Very frequently\" \"Very frequently\" ...\n",
      " $ Frequency..Latin.           : chr  \"Never\" \"Very frequently\" \"Sometimes\" \"Rarely\" ...\n",
      " $ Frequency..Lofi.            : chr  \"Sometimes\" \"Sometimes\" \"Sometimes\" \"Very frequently\" ...\n",
      " $ Frequency..Metal.           : chr  \"Sometimes\" \"Never\" \"Never\" \"Rarely\" ...\n",
      " $ Frequency..Pop.             : chr  \"Rarely\" \"Sometimes\" \"Sometimes\" \"Very frequently\" ...\n",
      " $ Frequency..R.B.             : chr  \"Never\" \"Sometimes\" \"Very frequently\" \"Very frequently\" ...\n",
      " $ Frequency..Rap.             : chr  \"Rarely\" \"Never\" \"Very frequently\" \"Very frequently\" ...\n",
      " $ Frequency..Rock.            : chr  \"Rarely\" \"Never\" \"Never\" \"Very frequently\" ...\n",
      " $ Frequency..Video.game.music.: chr  \"Very frequently\" \"Never\" \"Rarely\" \"Never\" ...\n",
      " $ Anxiety                     : num  7 9 7 8 4 5 2 2 1 2 ...\n",
      " $ Depression                  : num  7 7 2 8 8 3 0 2 0 1 ...\n",
      " $ Insomnia                    : num  10 3 5 7 6 5 0 5 0 2 ...\n",
      " $ OCD                         : num  2 3 9 7 0 3 0 1 1 0 ...\n",
      " $ Music.effects               : chr  \"No effect\" \"Improve\" \"Improve\" \"Improve\" ...\n",
      " $ Permissions                 : chr  \"I understand.\" \"I understand.\" \"I understand.\" \"I understand.\" ...\n"
     ]
    }
   ],
   "source": [
    "str(data)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zbiór danych jest dość bogaty pod względem różnyh cech, co utrudnia pełne zrozumienie treści. Z tego powodu wybrane kolumny zostały poddane analizie osobno. Dane zostaną przedstawione czytelnie i w sposób wizualny."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Szereg rozdzielczy przedziałowy"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wyliczenie rozstępu badanej cechy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 696,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Rozstęp [w latach]:  79'</span>"
      ],
      "text/latex": [
       "'Rozstęp {[}w latach{]}:  79'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Rozstęp [w latach]:  79'</span>"
      ],
      "text/plain": [
       "[1] \"Rozstęp [w latach]:  79\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R <- max(data$Age)-min(data$Age)\n",
    "paste(\"Rozstęp [w latach]: \",R)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Decyzja o liczbie przedziałów k, korzystajać ze wzorów kilku popularnych heurystyk:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 697,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 4 × 1 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>liczba klas</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>sqrt(n)</th><td>24.87971</td></tr>\n",
       "\t<tr><th scope=row>1+3.322log(n)</th><td>22.35417</td></tr>\n",
       "\t<tr><th scope=row>5log(n)</th><td>32.14053</td></tr>\n",
       "\t<tr><th scope=row>(age_max-age_min)/h</th><td>28.33637</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 4 × 1 of type dbl\n",
       "\\begin{tabular}{r|l}\n",
       "  & liczba klas\\\\\n",
       "\\hline\n",
       "\tsqrt(n) & 24.87971\\\\\n",
       "\t1+3.322log(n) & 22.35417\\\\\n",
       "\t5log(n) & 32.14053\\\\\n",
       "\t(age\\_max-age\\_min)/h & 28.33637\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 4 × 1 of type dbl\n",
       "\n",
       "| <!--/--> | liczba klas |\n",
       "|---|---|\n",
       "| sqrt(n) | 24.87971 |\n",
       "| 1+3.322log(n) | 22.35417 |\n",
       "| 5log(n) | 32.14053 |\n",
       "| (age_max-age_min)/h | 28.33637 |\n",
       "\n"
      ],
      "text/plain": [
       "                    liczba klas\n",
       "sqrt(n)             24.87971   \n",
       "1+3.322log(n)       22.35417   \n",
       "5log(n)             32.14053   \n",
       "(age_max-age_min)/h 28.33637   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n <- length(data$Age)\n",
    "k1 <- sqrt(n)\n",
    "k2 <- 1+3.322*log(n)\n",
    "k3 <- 5*log(n)\n",
    "k4 <- R/(2.64*n^(-1/3)*IQR(data$Age)) # IQR - rozst˛ep mi˛edzykwartylowy\n",
    "l_klas <- matrix(c(k1,k2,k3,k4),dimnames = list(c(\"sqrt(n)\", \"1+3.322log(n)\",\"5log(n)\", \"(age_max-age_min)/h\"),c(\"liczba klas\")))\n",
    "l_klas"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wyliczone liczności przedziałów są zbliżone do siebie. Dwie z nich są prawie równe, zatem jako k zostaje przyjęta zaokrąglona wartość jednej z nich. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 698,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "k <- round(k1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wyliczenie szerokości przedziałów:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 699,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 2 × 1 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>rozpiętość przedziału</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>2.64*n^(-1/3)*IQR</th><td>2.787937</td></tr>\n",
       "\t<tr><th scope=row>(age_max-age_min)/k</th><td>3.160000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 1 of type dbl\n",
       "\\begin{tabular}{r|l}\n",
       "  & rozpiętość przedziału\\\\\n",
       "\\hline\n",
       "\t2.64*n\\textasciicircum{}(-1/3)*IQR & 2.787937\\\\\n",
       "\t(age\\_max-age\\_min)/k & 3.160000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 1 of type dbl\n",
       "\n",
       "| <!--/--> | rozpiętość przedziału |\n",
       "|---|---|\n",
       "| 2.64*n^(-1/3)*IQR | 2.787937 |\n",
       "| (age_max-age_min)/k | 3.160000 |\n",
       "\n"
      ],
      "text/plain": [
       "                    rozpiętość przedziału\n",
       "2.64*n^(-1/3)*IQR   2.787937             \n",
       "(age_max-age_min)/k 3.160000             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h1 <- 2.64*n^(-1/3)*IQR(data$Age)\n",
    "h2 <- R/k\n",
    "span_of_range <- matrix(c(h1,h2),dimnames = list(c(\"2.64*n^(-1/3)*IQR\", \"(age_max-age_min)/k\"),c(\"rozpiętość przedziału\")))\n",
    "span_of_range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 700,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "h <- ceiling(h1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utworzenie szeregu rozdzielczego przedziałowego. Przedziały są lewostronnie otwarte i prawostronnie zamknięte. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 701,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'age_min:  10'</span>"
      ],
      "text/latex": [
       "'age\\_min:  10'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'age_min:  10'</span>"
      ],
      "text/plain": [
       "[1] \"age_min:  10\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "paste(\"age_min: \", min(data$Age))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 702,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'Początek pierwszego przedziału:  9'</span>"
      ],
      "text/latex": [
       "'Początek pierwszego przedziału:  9'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'Początek pierwszego przedziału:  9'</span>"
      ],
      "text/plain": [
       "[1] \"Początek pierwszego przedziału:  9\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "beginning <- min(data$Age) - 1\n",
    "paste(\"Początek pierwszego przedziału: \", beginning)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zliczenie obserwacji w poszczególnych przedziałach:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 703,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 25 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>nr.klasy</th><th scope=col>początek.klasy</th><th scope=col>koniec.klasy</th><th scope=col>srodek.klasy</th><th scope=col>liczebnosc.klasy</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td> 9</td><td>12</td><td>10.5</td><td>  2</td></tr>\n",
       "\t<tr><td> 2</td><td>12</td><td>15</td><td>13.5</td><td> 42</td></tr>\n",
       "\t<tr><td> 3</td><td>15</td><td>18</td><td>16.5</td><td>162</td></tr>\n",
       "\t<tr><td> 4</td><td>18</td><td>21</td><td>19.5</td><td>134</td></tr>\n",
       "\t<tr><td> 5</td><td>21</td><td>24</td><td>22.5</td><td> 80</td></tr>\n",
       "\t<tr><td> 6</td><td>24</td><td>27</td><td>25.5</td><td> 50</td></tr>\n",
       "\t<tr><td> 7</td><td>27</td><td>30</td><td>28.5</td><td> 31</td></tr>\n",
       "\t<tr><td> 8</td><td>30</td><td>33</td><td>31.5</td><td> 28</td></tr>\n",
       "\t<tr><td> 9</td><td>33</td><td>36</td><td>34.5</td><td> 19</td></tr>\n",
       "\t<tr><td>10</td><td>36</td><td>39</td><td>37.5</td><td> 10</td></tr>\n",
       "\t<tr><td>11</td><td>39</td><td>42</td><td>40.5</td><td> 13</td></tr>\n",
       "\t<tr><td>12</td><td>42</td><td>45</td><td>43.5</td><td>  6</td></tr>\n",
       "\t<tr><td>13</td><td>45</td><td>48</td><td>46.5</td><td>  2</td></tr>\n",
       "\t<tr><td>14</td><td>48</td><td>51</td><td>49.5</td><td>  7</td></tr>\n",
       "\t<tr><td>15</td><td>51</td><td>54</td><td>52.5</td><td>  3</td></tr>\n",
       "\t<tr><td>16</td><td>54</td><td>57</td><td>55.5</td><td>  7</td></tr>\n",
       "\t<tr><td>17</td><td>57</td><td>60</td><td>58.5</td><td>  8</td></tr>\n",
       "\t<tr><td>18</td><td>60</td><td>63</td><td>61.5</td><td>  4</td></tr>\n",
       "\t<tr><td>19</td><td>63</td><td>66</td><td>64.5</td><td>  2</td></tr>\n",
       "\t<tr><td>20</td><td>66</td><td>69</td><td>67.5</td><td>  3</td></tr>\n",
       "\t<tr><td>21</td><td>69</td><td>72</td><td>70.5</td><td>  2</td></tr>\n",
       "\t<tr><td>22</td><td>72</td><td>75</td><td>73.5</td><td>  2</td></tr>\n",
       "\t<tr><td>23</td><td>75</td><td>78</td><td>76.5</td><td>  0</td></tr>\n",
       "\t<tr><td>24</td><td>78</td><td>81</td><td>79.5</td><td>  1</td></tr>\n",
       "\t<tr><td>25</td><td>81</td><td>84</td><td>82.5</td><td>  0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 25 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " nr.klasy & początek.klasy & koniec.klasy & srodek.klasy & liczebnosc.klasy\\\\\n",
       " <int> & <dbl> & <dbl> & <dbl> & <int>\\\\\n",
       "\\hline\n",
       "\t  1 &  9 & 12 & 10.5 &   2\\\\\n",
       "\t  2 & 12 & 15 & 13.5 &  42\\\\\n",
       "\t  3 & 15 & 18 & 16.5 & 162\\\\\n",
       "\t  4 & 18 & 21 & 19.5 & 134\\\\\n",
       "\t  5 & 21 & 24 & 22.5 &  80\\\\\n",
       "\t  6 & 24 & 27 & 25.5 &  50\\\\\n",
       "\t  7 & 27 & 30 & 28.5 &  31\\\\\n",
       "\t  8 & 30 & 33 & 31.5 &  28\\\\\n",
       "\t  9 & 33 & 36 & 34.5 &  19\\\\\n",
       "\t 10 & 36 & 39 & 37.5 &  10\\\\\n",
       "\t 11 & 39 & 42 & 40.5 &  13\\\\\n",
       "\t 12 & 42 & 45 & 43.5 &   6\\\\\n",
       "\t 13 & 45 & 48 & 46.5 &   2\\\\\n",
       "\t 14 & 48 & 51 & 49.5 &   7\\\\\n",
       "\t 15 & 51 & 54 & 52.5 &   3\\\\\n",
       "\t 16 & 54 & 57 & 55.5 &   7\\\\\n",
       "\t 17 & 57 & 60 & 58.5 &   8\\\\\n",
       "\t 18 & 60 & 63 & 61.5 &   4\\\\\n",
       "\t 19 & 63 & 66 & 64.5 &   2\\\\\n",
       "\t 20 & 66 & 69 & 67.5 &   3\\\\\n",
       "\t 21 & 69 & 72 & 70.5 &   2\\\\\n",
       "\t 22 & 72 & 75 & 73.5 &   2\\\\\n",
       "\t 23 & 75 & 78 & 76.5 &   0\\\\\n",
       "\t 24 & 78 & 81 & 79.5 &   1\\\\\n",
       "\t 25 & 81 & 84 & 82.5 &   0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 25 × 5\n",
       "\n",
       "| nr.klasy &lt;int&gt; | początek.klasy &lt;dbl&gt; | koniec.klasy &lt;dbl&gt; | srodek.klasy &lt;dbl&gt; | liczebnosc.klasy &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "|  1 |  9 | 12 | 10.5 |   2 |\n",
       "|  2 | 12 | 15 | 13.5 |  42 |\n",
       "|  3 | 15 | 18 | 16.5 | 162 |\n",
       "|  4 | 18 | 21 | 19.5 | 134 |\n",
       "|  5 | 21 | 24 | 22.5 |  80 |\n",
       "|  6 | 24 | 27 | 25.5 |  50 |\n",
       "|  7 | 27 | 30 | 28.5 |  31 |\n",
       "|  8 | 30 | 33 | 31.5 |  28 |\n",
       "|  9 | 33 | 36 | 34.5 |  19 |\n",
       "| 10 | 36 | 39 | 37.5 |  10 |\n",
       "| 11 | 39 | 42 | 40.5 |  13 |\n",
       "| 12 | 42 | 45 | 43.5 |   6 |\n",
       "| 13 | 45 | 48 | 46.5 |   2 |\n",
       "| 14 | 48 | 51 | 49.5 |   7 |\n",
       "| 15 | 51 | 54 | 52.5 |   3 |\n",
       "| 16 | 54 | 57 | 55.5 |   7 |\n",
       "| 17 | 57 | 60 | 58.5 |   8 |\n",
       "| 18 | 60 | 63 | 61.5 |   4 |\n",
       "| 19 | 63 | 66 | 64.5 |   2 |\n",
       "| 20 | 66 | 69 | 67.5 |   3 |\n",
       "| 21 | 69 | 72 | 70.5 |   2 |\n",
       "| 22 | 72 | 75 | 73.5 |   2 |\n",
       "| 23 | 75 | 78 | 76.5 |   0 |\n",
       "| 24 | 78 | 81 | 79.5 |   1 |\n",
       "| 25 | 81 | 84 | 82.5 |   0 |\n",
       "\n"
      ],
      "text/plain": [
       "   nr.klasy początek.klasy koniec.klasy srodek.klasy liczebnosc.klasy\n",
       "1   1        9             12           10.5           2             \n",
       "2   2       12             15           13.5          42             \n",
       "3   3       15             18           16.5         162             \n",
       "4   4       18             21           19.5         134             \n",
       "5   5       21             24           22.5          80             \n",
       "6   6       24             27           25.5          50             \n",
       "7   7       27             30           28.5          31             \n",
       "8   8       30             33           31.5          28             \n",
       "9   9       33             36           34.5          19             \n",
       "10 10       36             39           37.5          10             \n",
       "11 11       39             42           40.5          13             \n",
       "12 12       42             45           43.5           6             \n",
       "13 13       45             48           46.5           2             \n",
       "14 14       48             51           49.5           7             \n",
       "15 15       51             54           52.5           3             \n",
       "16 16       54             57           55.5           7             \n",
       "17 17       57             60           58.5           8             \n",
       "18 18       60             63           61.5           4             \n",
       "19 19       63             66           64.5           2             \n",
       "20 20       66             69           67.5           3             \n",
       "21 21       69             72           70.5           2             \n",
       "22 22       72             75           73.5           2             \n",
       "23 23       75             78           76.5           0             \n",
       "24 24       78             81           79.5           1             \n",
       "25 25       81             84           82.5           0             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "inclusive_series <- data.frame(nr.klasy = seq(1, k))\n",
    "inclusive_series$początek.klasy <- beginning + (inclusive_series$nr.klasy - 1)*h\n",
    "inclusive_series$koniec.klasy <- beginning + (inclusive_series$nr.klasy - 1)*h + h\n",
    "inclusive_series$srodek.klasy <- (inclusive_series$początek.klasy+inclusive_series$koniec.klasy)/2 \n",
    "inclusive_series$liczebnosc.klasy <- NA\n",
    "\n",
    "for (i in 1:k) {\n",
    "  inclusive_series$liczebnosc.klasy[i] <- \n",
    "    sum(data$Age > inclusive_series$początek.klasy[i] & data$Age <= inclusive_series$koniec.klasy[i])\n",
    "}\n",
    "\n",
    "inclusive_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 704,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pS5Dw+wgSIDD9xr4or/9/ivjDPmCZ6Tf2Fe2/hZNeI0SQ8Ptmv2iMKxuAZaafaze8I/EpQsAi/izPXLuPxKcIAUvdfvZ3LQvXxRoECeZNZ/mx/RShPGQXKxAkmMeVDYAAQQIE+KIxQIAvGgME+KIxQIAvGgME+KIxQIAvGgME+KIxQIAvGgME+KIxQIArGwABf5an2qu+57pYhSDBvNm/kA3XxSoECeZdH/4O3MUqBAnm+bO8SpNT4C5WIUgwj2/sAwQIEiDA4W9AgCABAmE+E3K2i9UIEsybBilInAgSfh9BAgQIEiBAkAABggQIECRA4BKkIF976XexGkGCeQQJEODKBkCAIAEC62f5ad996FCa/fFHTAQJv2/tLK9ib4/q8cd3EST8vrWzPHPRsfvq5jKPHn9XJkHC71s7y4dvQG8ULgrRxYggwby1s3xyhPzx4XKChN/HOxIg8MI+Ut59rx/7SMD6WZ54R+3ih5+HR5Dw+144j5S155GidM95JGweVzYAAgQJEOASIUCAS4QAAS4RAgQ4IQsIBLpESPrntgQJ5vGOBAhwiRAgwCVCgACXCAECXNkACBAkQIAgAQIECRAgSIDA+isbnr54gSDh962d5QeCBFysnuVF9PiPJwRdDAgSzFs/y4vHFwYpuugRJJj3wiw/eNetBuqiQ5BgHkftAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAhsMkjPUqw9tmGTQXq2nWLtsQ0EiSBBgCARJAgQJIIEAYJEkCBAkAgSBAgSQYIAQSJIECBIBAkCBIkgQYAgESQIECSCBAGCRJAgQJAIEgQIEkGCAEEiSBAgSAQJAgSJIEGAIBEkCBAkggQBgkSQILB+lp/2qWuk2SlUFz2CBPPWzvIqdhdJkC5GBAnmrZ3lmYuORXurzCOXhehiRJBg3tpZHrlivF24KEQXI4IE89bOcufu/SDrYkSQYB7vSAQJAi/sI+Vle4t9JGD9LE+8o3ZxFaSLAUGCeS+cR8ra80hRuuc8EjaPKxsIEgQCBcn5Xl0YQYJ5L87yQ+xcmgftgiDhC7x2Hqk/4vDwoB1Bwga8FKTMZdX5XGbuEKKLEUGCeS8FKXLtce/KxSG6GBEkmPdSkIbjCFwihK17KUi7IUhcIoSNWx+kdH/I3bG+WWVcIoStWx+k8RyRcxGXCGHjVs/yojgc0rQ95JA9zBFBwgZwiRBBggBBIkgQIEgECQKfDNK/ZxEkWPfRIH0qIM+2Cz82+BUE6UG78GODX0GQHrQLPzb4FQTpQbvwY4NfQZAetAs/NvgVBOlBu/Bjg19BkB60Cz82+BUE6UG78GODX0GQHrR7VvgxhHUESdAu/BjCOoIkaBd+DGEdQRK0Cz+GsI4gCdqFH0NYR5AE7cKPIawjSIJ24ccQ1hEkQbvwYwjrCJKgXfgxhHUESdAu/BjCOoIkaBd+DGEdQRK0Cz+GsI4gCdqFH0NYR5AE7cKPIawjSIJ24ccQ1hEkQbvwYwjrCJKgXfgxhHUESdAu/BjCOoIkaBd+DGEdQRK0Cz+GsI4gCdqFH0NYR5AE7cKPIawjSIJ24ccQ1hEkQbvwYwjrCJKgXfgxhHUESdAu/BjCOoIkaBd+DGEdQRK0Cz+GsI4gCdqFH0NYR5AE7cKPIawjSIJ24ccQ1hEkQbvwYwjrCJKgXfgxhHUESdAu/BjCOoIkaBd+DGEdQRK0Cz+GsI4gCdqFH0NYR5AE7cKPIawjSIJ24ccQ1hEkQbvwYwjrCJKgXfgxhHUESdDuWeHHGp9CkN7YLvxY41MI0hvbhR9rfApBemO78GONTyFIb2wXfqzxKQTpje3CjzU+hSC9sV34scanEKQ3tgs/1vgUgvTGduHHGp9CkN7YLvxY41MI0hvbhR9rfApBemO78GONTyFIb2wXfqzxKQTpje3CjzU+hSC9sV34scanEKQ3tgs/1vgUgvTGduHHGp9CkN7YLvxY41MI0hvbfegvafkL3jcgSAbbiZ8A3jHfgCAZbCd+AgjSGxAkg+3ETwBBegOCZLCd+AkgSG9AkAy2Ez8BBOkNCJLBduIngCC9AUEy2E78BBCkNyBIBtuJnwCC9AYEyWA78RNAkN6AIBlsJ34CCNIbECSD7cRPAEF6A4JksJ34CSBIb0CQDLYTX2RKkN6AIH1xuyefAIL0BgTpi9s9+QQQpDcgSF/c7skngCC9AUH64nZPPgEE6Q0I0he3e/IJ+NRBjk0hSF/c7sknwPrh+Z9AkL643bPU/YafM9+HINFucbvwc+b7ECTaLW7HvtQtgkS7YO3Czy07CBLtgrXb0jsXQaLdx9uFn4PhESTafbxd+DkY3vognfapa6TZaWUX5p9g2r2n3eo5aMjaIFWxu0jWdWH+Cabde9qtnIOmrA1S5qJj0d4q88hlq7ow/wTT7j3txAclPnKQY22QIleMtwsXrerC/BNMO1vtnpybH3knXBsk5+790P/Gc28ZT79yACGsnPvzgVj5uAXvSMDve2EfKS/bW3/uIwG/b/Xh78TbdosrZUnA93nhPFLWnkeK0v0f55GA3/eGKxuA30eQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAAGCBAgQJECAIAECBAkQIEiAAEECBAgSIECQAIFfCpLDb/v0BHvEdHELWV8X6nuN6fpMF7eQ9XWhvteYrs90cQtZXxfqe43p+kwXt5D1daG+15iuz3RxC1lfF+p7jen6TBe3kPV1ob7XmK7PdHELWV8X6nuN6fpMF7eQ9XWhvteYrs90cQtZXxfqe43p+kwXt5D1daG+15iuz3RxC1lfF+p7jen6TBe3kPV1ob7XmK7PdHHAtyBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAr8QpEPsoqxqb2bReNOUUz/OJusrds7tyvamxfoqryiL9XV+IEhZ+00FUTO8SXsz/nRFN6qoG2eT9eW2x6+MuvqapFusr/f9QSrcrp4DB7drXvej4lxE7vTpmq6l3VeS2KwvqouqUpcZrW/XVFa/Wlp+fs+/EKS0W4VmqmYur28d3f6zFd049t/tY7K+YztRKxcZrc/Zf34b3x+kXjPQqWve/wuXfrqYqdIl3WwwWd/OFcNNk/X1W8VN0E3W1/uVIFUumbx4WZK4sivJZH2xO++jdvPYZn37ftNub7S+nsWa1jg07/o2B3rvjmfDQXIubXfmz0brOx+aow3R4Wy1vo7FmlYoo+bt3uRAt1sipoPUHGzY2X3F37eH6pr9Ipv1dSzWtFwVJc0/Jgc6bg4smw5Ss49UNgeVTdZ3aDbt6qAfjNbXs1jTckl3aiEyONC79khTV5LF+vzZabK+2DW7b1UTdJP19SzWtFQZJ915+e6oTmnqqI7/5fYW6/NPH5iszxmvr/cDQcpd0t/at6/+eXuYxwo/SBbr64sqm0E0WV/3NtSe5zJZX+/7g1SOOTJ85tvwlQ313lHV7IMcjdaXuebiuszslRe97w/S7vKKX29PN5I/H/N2/faJyfr2l6JM1pcYr6/z/UHyNp36C4U/XdGMPkg268uToSib9V2Ksllf6/uDBBhAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiBAkAABggQIECRAgCABAgQJECBIgABBAgQIEiCwgSB13+cX7conW9/74anvpV/+CIn8topp16Xb3X3wwyLv3vn8ql23zOebLVqmOd9b+dOGr8aMnkrSVwYpvurmNkj76P6j3xyk62JXLdOc7638ad2zUyXPfav8o+dy+fP8ppkx1830d/GDbwJfF6TnPf/iQpAsG74I2T14Ub5pvfg+1SNW+TtISx+9YjHPLoIgfanh2em2d6rYpWfvi9APsYsOXYMsqt+0ulb93W2LPHX9V2k7V7i4bVr1/566XY/ctdv9O3fqOhsX2v2YuX33y/gw85BJDZcH9Q+NXFKez/MV54lzSd7f2fxTpi7aj6v6TNd9T9nwZeGXlfXGYzIEfh+T5o+W77UcVuOqp34tm0r2fz+n9mwnSO07knP105d50zJt/02aBklzK70J0r673c2BKO1mx9H1z3bULnzXbTbWPbSdXRba/pi1N5Phl9cP8WvwCm7/3z4oqs6zFR+6Xx0uQYqaG3svSH913feXDov0VtYbj+kQeH34zedG47I+l5Z9sTc9dWuZdmv0fTYTpDLpnsWkGn6/q6dO3vxc7z7lTTai4lxE49ZFc3c3IY/Nna5dUpR3L7o71x+52Df3Nnecu3Q17byFNj92k3lY/PHmIV5zv+Dm/8fmrt04Ua8qjlzRNIkvj6jvOgw/P9P10N9wv7+y3nhMhmDax3jH7Ghc1meyiO6XXk/DWl6W/nU2EaT+qF37kjfudCfNJEtdk6uq3to7d+81+TAr2rsvU6S5VdbbNee4fcT4XJdNs1P9Qlo0DynP3XvGuNB2W6V9r0nboNQxuHmI1/zS17lf0snbubuu2I3ZGx5xOl9C9EzXw6O7+6cFXI1H/9tpH37vc6Nxfb8XpOue+g2G01WDr/GNNS/kn0e6PEdJv+k1bjL1d/X/JJcts3OZ75PmVvvqfGheaE/jq23dsKonbFH/ohyiN1lo0mfXW/zNQy77P14JN4ewbyrO6i2hopg+wg/S3137/V2t7MPfXmob75gdjfODBd/+YroeX+Yba17o5hWwkXSbaPeCNN59HvYwhiC1r5z78dW2fsnen6P4HMfdds1NkOp9itjrudv0u3rIU0G6rfi8b/ZXmtNj80H6u+vJoExX9uFvx9qSaeUPln+z4JtfnKfr8WW+seaFZoJURv1+h3efN3Emd+9cfMjLftPu3LwP5M1EuTwuPtWts+ZwYHUz/ev3hML1Ow6XXm4fMlPwdElzFdfyLPb3kfzHPdP1zZpfVvbhb4c+vDtmR+N8fxG3PZ2n6/FlvrHmhW6DNM7KfvfBu9kcv77cPU5m7xkvXFI47wht5nb1I/P6/7u+STo9brBv93FSb0dk+hCvuVfkqdsS6/ceZiu+qvEmSH93PSzhNNzvrexlPG6GYNLHeRKk+eXfWUT/i8TbR7p+wr7GN9a80G2QxlnZHZqq93vSZiINR6kud/ev7OfC35iP600m72qjeqp17yvtxGuaeAttHxE3ubscOrt+iNe8E7tDc1zONb9Mmn2ObL7iuDvw1b4jXXYAJ5P8j66Htezuzycrm/tH7a6GwHvXG+6YHY07o9gVO/5iXEuCZNptkLz9jG5Lvb0Mrz2FsXPOu7tpkfU/nIZH5256fLbduKoXFI0dXBbav4c1c2s8mXP9EL+GVnt+KL0sKarmKz6OhcVu+no+BumvrvtB2bU9nicrexmP2yEYlu83nxuNy6B7Lbti/Yd655Gun7Cv8Y01L/QwSM1Jf9dfGL7vz+RPg1RvzbvkdNnwqTdC3OTc+759t9j3ZyHbJuNCux/37SQ9RO3lBTcPmdQwFLLrH9ocmSvvVdxe2dDMxFN8J0h/dt0/Yrye4LKyl/G4HYJx+X7zR8v3W3bFTh7aryVB2pTcuef+IgMbQpAWS77yEhaERZAWcv5VcUCPIC0U+TsEQI8gAQIECRAgSIAAQQIECBIgQJAAAYIECBAkQIAgAQIECRAgSIAAQQIECBIgQJAAAYIECBAkQIAgAQIECRAgSIAAQQIECBIgQJAAAYIECBAkQIAgAQIECRAgSIDA/9PJUD15qLUzAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Liczba uczestników badania\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(\"plotly\")\n",
    "histogram <- hist(data$Age, main=\"Liczba uczestników badania\", xlab=\"Przedziały wiekowe uczestników badania w latach\", breaks=k, col=\"#57af9b\", border=\"#7A3E3E\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Szereg rozdzielczy punktowy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 705,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Frequency Classical\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PmJMR0qyHCLJ6xpyMkGY9RJDVM+ZkhDTrIYKsnjEnI6RZDxFk9Yw5GSHNeoggq2fMyQhp1kMEWT1jTkZIsx4iyOoZczJCmvUQQVbPmJMR0qyHCLJ6xpyMkGY9RJDVM+ZkhDTrIYKsnjEnI6RZDxFk9Yw5GSHNeoggq2fMyQhp1kMEWT1jTkZIsx4iyOoZczJCmmC/qVKnqveZhwiyesacjJDedizTxSrvEEFWz5iTEdLb6lT8NP2lw65IddYhgqyeMScjpLcVqTlfblKRdYggq2fMyQjp/d+Xnn3w/iGCrJ4xJyOkt3GL9BHxx/xWisdIu0N/icdIM4o/5rfKfvp7NXrWrjxmHSLI6hlzMkKaYF/3ryMV1YbXkWYTf8xvxTsbRPxraJAxvxUhifjX0CBjfiveIiTiX0ODjPmteIuQiH8NDTLmt+ItQiL+NTTImN+KF2RF/GtokDG/ldNbhNLYs68RZPWMORkhvY1bpI+IP+a34i1CIv41NMiY34q3CIn419AgY34r3iIk4l9Dg4z5rXhng4h/DQ0y5rciJBH/GhpkzG9FSCL+NTTImN+KkET8a2iQMb8VIYn419AgY36r/Hc2vPXmhZeHCLJ6xpyMkN62JaRPiD/mt8q+a9cUr//HE28cIsjqGXMyQpqgef3GoDcOEWT1jDkZIU2xHb1vNesQQVbPmJMR0qyHCLJ6xpyMkGY9RJDVM+ZkhDTrIYKsnjEnI6RZDxFk9Yw5GSHNeoggq2fMyQhp1kMEWT1jTkZIsx4iyOoZczJCmvUQQVbPmJMR0qyHCLJ6xpyMkGY9RJDVM+ZkhDTrIYKsnjEnI6RZDxFk9Yw5GSHNeoggq2fMyQhp1kMEWT1jTkZIsx4iyOoZczJCmvUQQVbPmJMR0qyHCLJ6xpyMkGY9RJDVM+ZkhDTrIYKsnjEnI6RZDxFk9Yw5GSHNeoggq2fMyQhp1kMEWT1jTvZqzAV559r7LkISX3AN/fRsIzHGJCQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmpYWEtN9UqVPV+8xDLOicBlk9Y1paREjHMl2s8g6xoHMaZPWMaWkRIdWp+Gn6S4ddkeqsQyzonAZZPWNaWkRIRWrOl5tUZB1iQec0yOoZ09IiQkrp2QfvH2JB5zTI6hnT0iJC4hbpIxjT0CJCah8j7Q79JR4jzYgxDS0ipN/V6Fm78ph1iAWd0yCrZ0xLywjpd1/3ryMV1YbXkWbDmIYWEpL+EAs6p0FWz5iWIoSUxp590oLOaZDVM6alJYW0LVOqdpmHWNA5DbJ6xrS0iJDkdmZ4xuHlk3aEZIgxDS0npDrVx9/fQ522WYdY0DkNsnrGtLSckIrUP+99TGXWIRZ0ToOsnjEtLSek0/MIvEVoLoxpaDkhrU8h8RahmTCmoYWEVG22u/TTXjzWvEVoLoxpaCEhnV8jSqngLUIzYUxDiwjpt2m226rqn3KoX3ZESIYY09AyQjI4xILOaZDVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlgjJQYzVM6YlQnIQY/WMaYmQHMRYPWNaIiQHMVbPmJYIyUGM1TOmJUJyEGP1jGmJkBzEWD1jWiIkBzFWz5iWCMlBjNUzpiVCchBj9YxpiZAcxFg9Y1oiJAcxVs+YlhYS0n5TpU5V7zMPsaBzGmT1jGlpESEdy3SxyjvEgs5pkNUzpqVFhFSn4qfpLx12RaqzDrGgcxpk9YxpaREhFak5X25SkXWIBZ3TIKtnTEuLCCmlZx8MPzPy7Gv8tyTPv9VPT3aFMQ09n3K6GW6RgO+neIy0O/SX/vkYCfh+2U9/r0b33cqj5UhAPIrXker+daSi2vzjdSTg+83wzgbg+xESYICQAAOEBBggJMAAIQEGCAkwQEiAAUICDBASYICQAAOEBBggJMAAIQEGCAkwQEiAAUICDBASYICQAAOEBBggJMAAIQEGCAkwQEiAAUICDBASYICQAAOEBBggJMAAIQEGwoSU0u504bODvHL6V97//Q/dzPddHOuynWg74Xf0J9ppwH0qz5fL00pf+ue/oPomz+/qN1RIxenCZwd55bz0f5Y023dxLGSi4u1/DK7sR/MasDifm8N7/2KqUUi+31WokNJmuPDhSV4YZqvT6s3P9LdOq0N7pV29/8+T+o62OQ9SvzeS0TiJkERKZTrIhU+P8txptn/PONt3kVJ/U3R8/4C+ox3Pt0OF7PNfCMlWSk2q5EL3322Zim23FrnLXXZXl+Hn+itPKZ88+5DjH3dVe4+qvhpoPOIw+nH0qMFxJNEevxyO3942FJvudmG4YTiNNtyNGv7/ySe139yqfeT1zmOcW6vhkdFebrZvlnZ/UkbfwP1pbEcr2nsqp4Fvrh3dh4eq/w7O35XXaQ8UUnsvZf87nKpKHtR3a+n+WDt0F88/135KlT7yL61f3bXbyF37ejTQeMT2g/7Rws9wl9VJndaXP/hXo+P34+1WpxHPo12F9OyTfrfyzU15DmOwS+v+x3Uf1O3S7k/KVUi3p1G+o81NSOMv2j9E3Iy+K6fTHikk+UOkOx+7tDr+Hrs/2+R8bNpLl59rP2X1mX9n/fzAuOk/+On2lX7PA12NeLpGrd+7h5OtvaqVtTzA/0lF89sU3Vz9RNvhv8XtaL+nkJ5+UtF9iz9Zf6oXcp3rD3O3tPuTMnqu4f40nr6jq5Buv+i2G/P8y06nPVJI7RnZyoWqv+N/7G7m+12WNz/372fNvIaUPwub67lPA12NONwf/fW9Z9farbsn7eSP/+6/O7ndkVv3w+/9GR2F9OKTcu7W9eou5DYBuYm7XdrdSbkK6fY0nr6jq5Duvuj1L/uc9lAh9edAzsr57HZ/shy6pYx+7mPPR8iQxek6dthtVsM1YPjlqxG33a3p3veendhv+medz2NcP6K4OaPjn3z6Se2jpqppHh7sX5r+TtdquNW+XdrdSbm6azf8cPubbsd++b34nPZYIe3bm+WbU9WdkVquJQsJaZ+Gew2r0R+lwy9fjdg/gbVxvmc3aC53b0xC+t10Dz6KrNm7Pw6Hx/r3S7s7KeYh+Zz2WCG1t9rNbSlF2f3foxM+v9OQ/TOG61Rud4frkK4/s27vmJS+9+zOh3x6tbv6pUc/+fCTWru6zLt/1N0kbNLpycPbSW9PyqOQHv3M+9+Ly2kPFtIhlXIv+HIPvU79bfX45z4cUnN6suG3G3gU0u2I7Z2cxvmeXTU8sdb/MXx6RFHdN3J39h6FVN0+MMo70d2tkTxQebS025Nyn83oN8nF/XnY/Tvfi8tpDxZS/5zy8GRN+ydb9yd/e1XtlzL6uQ+HNNwkdQ90m6vHSHcjlunNVyWztdesbXt29qsuqKtn7S7z3pzRy5MLLz6plKck8/5cX6fTc+CPlnZzUu5DGv2m3eVZu7L9Do+ru+/l9Psu35XPaY8W0m9/0oaHH3IXvRzekHP5uU+HdOxvkurhnvrlUf7diLvk/pzdaYrLqy6n17Gu/3sZrezf1vgopNEn/Zy/twztt3260XiwtJuT8uDe32j7/bfX59O/slXdjHmZ/fJd+Zz2cCHt5MK2PTHDK40/p6Wcf+7TIbXr7W6S1t37wHdXf9rejHhM/s/ZNev2z57Vz3D84vLOhpv/nkfbl09DGp32/p0Nua8yFJf3q94v7eakPHrsO9r+tnuvQ/8Lm2J4Kurui3b/vXxXPqc9TEhfaZfmec4ulIyTMvFPTo/TTkiftMp5j823yzgpE0PyOO2E9DmnRy4YyTopk0LyOe2E9DnFR96hvnBZJ2VSSD6nnZAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwAAhAQYICTBASIABQgIMEBJggJAAA4QEGCAkwMD/AegOvAgHJ1iuAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Frequency EDM\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Frequency Classical\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Frequency Country\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "freq_Classical <- data.frame(opinion = c('Never', 'Rarely', 'Sometimes', 'Very Frequently'), number = matrix(table(data$Frequency..Classical.)))\n",
    "freq_Country<- data.frame(opinion = c('Never', 'Rarely', 'Sometimes', 'Very Frequently'), number = matrix(table(data$Frequency..Country.)))\n",
    "freq_EDM <- data.frame(opinion = c('Never', 'Rarely', 'Sometimes', 'Very Frequently'), number = matrix(table(data$Frequency..EDM.)))\n",
    "freq_Folk <- data.frame(opinion = c('Never', 'Rarely', 'Sometimes', 'Very Frequently'), number = matrix(table(data$Frequency..Folk.)))\n",
    "\n",
    "\n",
    "barplot(freq_Classical$number,names.arg=freq_Classical$opinion, main = \"Frequency Classical\", col=\"#6096B4\", border=\"#20262E\")\n",
    "barplot(freq_EDM$number,names.arg=freq_EDM$opinion, main = \"Frequency EDM\", col=\"#913175\", border=\"#20262E\")\n",
    "barplot(freq_Folk$number,names.arg=freq_Folk$opinion, main = \"Frequency Classical\", col=\"#CE7777\", border=\"#20262E\")\n",
    "barplot(freq_Country$number,names.arg=freq_Country$opinion, main = \"Frequency Country\", col=\"#658864\", border=\"#20262E\")\n",
    "\n",
    "\n",
    "# barplotsTogother"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wartości statystyk opisowych"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Miary położenia"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na zmienne zawierające dane pomiarowe lub liczności składają się z setek wartości. Podstawowym zadaniem w badaniach eksploracyjnych jest określenie tendencji centralnej. W przypadku podanych danych będziemy porównywać ze sobą dwie próbki - rozkład liczby godzin słuchania muzyki wśród osób, które jednocześnie preferują utwory w języku ojczystym lub zagranicznym. Dzięki temu porównamy liczbę godzin spędzonych z muzyką w trakcie dnia ze względu język, w jakim przeważnie jest słuchana."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 707,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "lang = list(foreign=c(),notforeign=c())\n",
    "for (i in 1:length(data$Foreign.languages)) {\n",
    "    if(grepl(\"Yes\",data$Foreign.languages[i])){\n",
    "        lang$foreign <- c(lang$foreign, data$Hours.per.day[i])\n",
    "    } else {\n",
    "        lang$notforeign <- c(lang$notforeign, data$Hours.per.day[i])\n",
    "    }\n",
    "}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wyliczenie trach miar: średniej, mediany i dominanty:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 708,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 2 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>film</th><th scope=col>dominanta</th><th scope=col>mediana</th><th scope=col>średnia</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Foreign music    </td><td>2</td><td>3</td><td>3.920487</td></tr>\n",
       "\t<tr><td>Not foreign music</td><td>1</td><td>2</td><td>3.416481</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 2 × 4\n",
       "\\begin{tabular}{llll}\n",
       " film & dominanta & mediana & średnia\\\\\n",
       " <chr> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Foreign music     & 2 & 3 & 3.920487\\\\\n",
       "\t Not foreign music & 1 & 2 & 3.416481\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 2 × 4\n",
       "\n",
       "| film &lt;chr&gt; | dominanta &lt;dbl&gt; | mediana &lt;dbl&gt; | średnia &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| Foreign music     | 2 | 3 | 3.920487 |\n",
       "| Not foreign music | 1 | 2 | 3.416481 |\n",
       "\n"
      ],
      "text/plain": [
       "  film              dominanta mediana średnia \n",
       "1 Foreign music     2         3       3.920487\n",
       "2 Not foreign music 1         2       3.416481"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mode <- function(x) {\n",
    "  ux <- unique(x)\n",
    "  ux[which.max(tabulate(match(x, ux)))]\n",
    "}\n",
    "\n",
    "miary_centr <- data.frame(film = c(\"Foreign music\",\"Not foreign music\"),\n",
    "                          dominanta = c(mode(lang$foreign),mode(lang$notforeign)),\n",
    "                          mediana = c(median(lang$foreign),median(lang$notforeign)),\n",
    "                          średnia = c(mean(lang$foreign),mean(lang$notforeign)))\n",
    "\n",
    "miary_centr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 709,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "   0.00    2.00    3.00    3.92    5.00   24.00 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  0.000   1.000   2.000   3.416   4.000  24.000 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lang$foreign)\n",
    "summary(lang$notforeign)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartości dominanty, mediany i średniej w obu zbiorach różnią się. W przypadku zagranicznej muzyki dominuje wartość 2 godzin, a środkowa wartość to 3 godziny. Wartości w drugim zbiorze są odpowiednio o 1 godzinę mniejsze. Średnie również nieznacznie się różnią. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mediana jest częściej używana w statystyce niż średnia arytmetyczna ze względu na większą odporność na wartości skrajne. Średnie są silnie narażone na działanie wartości skrajnych. W tym przypadku jednak ze względu na stosunkowo małe dane można oprzeć wnioski również na średniej (po szybkiej analizie nie znalazłam wartości odstających). Na podstawie tych trzech wartości można wywnioskować, że większą popularnością cieszą się utwory zagraniczne, w języku innym niż ojczysty wśród uczestników ankiety."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartości tych trzech miar wskazują skośność obserwowanego rozkładu. \n",
    "Dzięki zależności dominanta < mediana < średnia można stwierdzić, że mamy do czynienia z asymetrią prawostronną."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Miary rozproszenia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 710,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 2 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>lang</th><th scope=col>wariancja</th><th scope=col>odchylenie_st</th><th scope=col>skośność</th><th scope=col>kurtoza</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Foreign   </td><td> 8.368839</td><td>2.892895</td><td>2.020626</td><td>10.38592</td></tr>\n",
       "\t<tr><td>Notforeign</td><td>10.623677</td><td>3.259398</td><td>2.928448</td><td>15.66503</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 2 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " lang & wariancja & odchylenie\\_st & skośność & kurtoza\\\\\n",
       " <chr> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t Foreign    &  8.368839 & 2.892895 & 2.020626 & 10.38592\\\\\n",
       "\t Notforeign & 10.623677 & 3.259398 & 2.928448 & 15.66503\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 2 × 5\n",
       "\n",
       "| lang &lt;chr&gt; | wariancja &lt;dbl&gt; | odchylenie_st &lt;dbl&gt; | skośność &lt;dbl&gt; | kurtoza &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| Foreign    |  8.368839 | 2.892895 | 2.020626 | 10.38592 |\n",
       "| Notforeign | 10.623677 | 3.259398 | 2.928448 | 15.66503 |\n",
       "\n"
      ],
      "text/plain": [
       "  lang       wariancja odchylenie_st skośność kurtoza \n",
       "1 Foreign     8.368839 2.892895      2.020626 10.38592\n",
       "2 Notforeign 10.623677 3.259398      2.928448 15.66503"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "skośność <- function(x){\n",
    "    mean((x-mean(x))^3)/ (sqrt(mean((x-mean(x))^2)))^3\n",
    "}\n",
    "\n",
    "kurtoza <- function(x){\n",
    "    mean((x-mean(x))^4)/ (sqrt(mean((x-mean(x))^2)))^4\n",
    "}\n",
    "\n",
    "miary_rozpr <- data.frame(lang = c(\"Foreign\",\"Notforeign\"),\n",
    "                          wariancja = c(var(lang$foreign),var(lang$notforeign)),\n",
    "                          odchylenie_st = c(sd(lang$foreign),sd(lang$notforeign)),\n",
    "                          skośność = c(skośność(lang$foreign),skośność(lang$notforeign)),\n",
    "                          kurtoza = c(kurtoza(lang$foreign),kurtoza(lang$notforeign)))\n",
    "\n",
    "miary_rozpr"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na podstawie wartości wariancji i odchylenia standardowego można stwierdzić, że w obu próbkach występuje mała zmienność wyników oraz rozproszenia wokół średniej. Podobnie jak wcześniej wnioskowano, oba rozkłady są prawostronnie skośne, ponieważ miara skośności jest większa od 0. Dodatnie wartości kurtozy wskazują na większe skupienie wyników i bardziej wydłużony rozkład wartości. W obu przypadkach bardzo wysoka kurtoza oznacza, że odchylenia od średniej w wariancji wynikają głównie z rzadkich obserwacji."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tabela szeregu rozdzielczego:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 711,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Szereg rodzielczy dla badanych słuchających zagranicznej muzyki:'"
      ],
      "text/latex": [
       "'Szereg rodzielczy dla badanych słuchających zagranicznej muzyki:'"
      ],
      "text/markdown": [
       "'Szereg rodzielczy dla badanych słuchających zagranicznej muzyki:'"
      ],
      "text/plain": [
       "[1] \"Szereg rodzielczy dla badanych słuchających zagranicznej muzyki:\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 12 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>nr.klasy</th><th scope=col>poczatek.klasy</th><th scope=col>koniec.klasy</th><th scope=col>srodek.klasy</th><th scope=col>liczebnosc.klasy</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td> 0</td><td> 2</td><td> 1</td><td>127</td></tr>\n",
       "\t<tr><td> 2</td><td> 2</td><td> 4</td><td> 3</td><td>114</td></tr>\n",
       "\t<tr><td> 3</td><td> 4</td><td> 6</td><td> 5</td><td> 61</td></tr>\n",
       "\t<tr><td> 4</td><td> 6</td><td> 8</td><td> 7</td><td> 21</td></tr>\n",
       "\t<tr><td> 5</td><td> 8</td><td>10</td><td> 9</td><td> 16</td></tr>\n",
       "\t<tr><td> 6</td><td>10</td><td>12</td><td>11</td><td>  7</td></tr>\n",
       "\t<tr><td> 7</td><td>12</td><td>14</td><td>13</td><td>  1</td></tr>\n",
       "\t<tr><td> 8</td><td>14</td><td>16</td><td>15</td><td>  1</td></tr>\n",
       "\t<tr><td> 9</td><td>16</td><td>18</td><td>17</td><td>  0</td></tr>\n",
       "\t<tr><td>10</td><td>18</td><td>20</td><td>19</td><td>  0</td></tr>\n",
       "\t<tr><td>11</td><td>20</td><td>22</td><td>21</td><td>  0</td></tr>\n",
       "\t<tr><td>12</td><td>22</td><td>24</td><td>23</td><td>  1</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 12 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " nr.klasy & poczatek.klasy & koniec.klasy & srodek.klasy & liczebnosc.klasy\\\\\n",
       " <int> & <dbl> & <dbl> & <dbl> & <int>\\\\\n",
       "\\hline\n",
       "\t  1 &  0 &  2 &  1 & 127\\\\\n",
       "\t  2 &  2 &  4 &  3 & 114\\\\\n",
       "\t  3 &  4 &  6 &  5 &  61\\\\\n",
       "\t  4 &  6 &  8 &  7 &  21\\\\\n",
       "\t  5 &  8 & 10 &  9 &  16\\\\\n",
       "\t  6 & 10 & 12 & 11 &   7\\\\\n",
       "\t  7 & 12 & 14 & 13 &   1\\\\\n",
       "\t  8 & 14 & 16 & 15 &   1\\\\\n",
       "\t  9 & 16 & 18 & 17 &   0\\\\\n",
       "\t 10 & 18 & 20 & 19 &   0\\\\\n",
       "\t 11 & 20 & 22 & 21 &   0\\\\\n",
       "\t 12 & 22 & 24 & 23 &   1\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 12 × 5\n",
       "\n",
       "| nr.klasy &lt;int&gt; | poczatek.klasy &lt;dbl&gt; | koniec.klasy &lt;dbl&gt; | srodek.klasy &lt;dbl&gt; | liczebnosc.klasy &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "|  1 |  0 |  2 |  1 | 127 |\n",
       "|  2 |  2 |  4 |  3 | 114 |\n",
       "|  3 |  4 |  6 |  5 |  61 |\n",
       "|  4 |  6 |  8 |  7 |  21 |\n",
       "|  5 |  8 | 10 |  9 |  16 |\n",
       "|  6 | 10 | 12 | 11 |   7 |\n",
       "|  7 | 12 | 14 | 13 |   1 |\n",
       "|  8 | 14 | 16 | 15 |   1 |\n",
       "|  9 | 16 | 18 | 17 |   0 |\n",
       "| 10 | 18 | 20 | 19 |   0 |\n",
       "| 11 | 20 | 22 | 21 |   0 |\n",
       "| 12 | 22 | 24 | 23 |   1 |\n",
       "\n"
      ],
      "text/plain": [
       "   nr.klasy poczatek.klasy koniec.klasy srodek.klasy liczebnosc.klasy\n",
       "1   1        0              2            1           127             \n",
       "2   2        2              4            3           114             \n",
       "3   3        4              6            5            61             \n",
       "4   4        6              8            7            21             \n",
       "5   5        8             10            9            16             \n",
       "6   6       10             12           11             7             \n",
       "7   7       12             14           13             1             \n",
       "8   8       14             16           15             1             \n",
       "9   9       16             18           17             0             \n",
       "10 10       18             20           19             0             \n",
       "11 11       20             22           21             0             \n",
       "12 12       22             24           23             1             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "'Szereg rodzielczy dla badanych nie słuchających zagranicznej muzyki:'"
      ],
      "text/latex": [
       "'Szereg rodzielczy dla badanych nie słuchających zagranicznej muzyki:'"
      ],
      "text/markdown": [
       "'Szereg rodzielczy dla badanych nie słuchających zagranicznej muzyki:'"
      ],
      "text/plain": [
       "[1] \"Szereg rodzielczy dla badanych nie słuchających zagranicznej muzyki:\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 12 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>nr.klasy</th><th scope=col>poczatek.klasy</th><th scope=col>koniec.klasy</th><th scope=col>srodek.klasy</th><th scope=col>liczebnosc.klasy</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 1</td><td> 0</td><td> 2</td><td> 1</td><td>138</td></tr>\n",
       "\t<tr><td> 2</td><td> 2</td><td> 4</td><td> 3</td><td> 72</td></tr>\n",
       "\t<tr><td> 3</td><td> 4</td><td> 6</td><td> 5</td><td> 27</td></tr>\n",
       "\t<tr><td> 4</td><td> 6</td><td> 8</td><td> 7</td><td> 20</td></tr>\n",
       "\t<tr><td> 5</td><td> 8</td><td>10</td><td> 9</td><td>  6</td></tr>\n",
       "\t<tr><td> 6</td><td>10</td><td>12</td><td>11</td><td>  2</td></tr>\n",
       "\t<tr><td> 7</td><td>12</td><td>14</td><td>13</td><td>  0</td></tr>\n",
       "\t<tr><td> 8</td><td>14</td><td>16</td><td>15</td><td>  2</td></tr>\n",
       "\t<tr><td> 9</td><td>16</td><td>18</td><td>17</td><td>  1</td></tr>\n",
       "\t<tr><td>10</td><td>18</td><td>20</td><td>19</td><td>  0</td></tr>\n",
       "\t<tr><td>11</td><td>20</td><td>22</td><td>21</td><td>  0</td></tr>\n",
       "\t<tr><td>12</td><td>22</td><td>24</td><td>23</td><td>  2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 12 × 5\n",
       "\\begin{tabular}{lllll}\n",
       " nr.klasy & poczatek.klasy & koniec.klasy & srodek.klasy & liczebnosc.klasy\\\\\n",
       " <int> & <dbl> & <dbl> & <dbl> & <int>\\\\\n",
       "\\hline\n",
       "\t  1 &  0 &  2 &  1 & 138\\\\\n",
       "\t  2 &  2 &  4 &  3 &  72\\\\\n",
       "\t  3 &  4 &  6 &  5 &  27\\\\\n",
       "\t  4 &  6 &  8 &  7 &  20\\\\\n",
       "\t  5 &  8 & 10 &  9 &   6\\\\\n",
       "\t  6 & 10 & 12 & 11 &   2\\\\\n",
       "\t  7 & 12 & 14 & 13 &   0\\\\\n",
       "\t  8 & 14 & 16 & 15 &   2\\\\\n",
       "\t  9 & 16 & 18 & 17 &   1\\\\\n",
       "\t 10 & 18 & 20 & 19 &   0\\\\\n",
       "\t 11 & 20 & 22 & 21 &   0\\\\\n",
       "\t 12 & 22 & 24 & 23 &   2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 12 × 5\n",
       "\n",
       "| nr.klasy &lt;int&gt; | poczatek.klasy &lt;dbl&gt; | koniec.klasy &lt;dbl&gt; | srodek.klasy &lt;dbl&gt; | liczebnosc.klasy &lt;int&gt; |\n",
       "|---|---|---|---|---|\n",
       "|  1 |  0 |  2 |  1 | 138 |\n",
       "|  2 |  2 |  4 |  3 |  72 |\n",
       "|  3 |  4 |  6 |  5 |  27 |\n",
       "|  4 |  6 |  8 |  7 |  20 |\n",
       "|  5 |  8 | 10 |  9 |   6 |\n",
       "|  6 | 10 | 12 | 11 |   2 |\n",
       "|  7 | 12 | 14 | 13 |   0 |\n",
       "|  8 | 14 | 16 | 15 |   2 |\n",
       "|  9 | 16 | 18 | 17 |   1 |\n",
       "| 10 | 18 | 20 | 19 |   0 |\n",
       "| 11 | 20 | 22 | 21 |   0 |\n",
       "| 12 | 22 | 24 | 23 |   2 |\n",
       "\n"
      ],
      "text/plain": [
       "   nr.klasy poczatek.klasy koniec.klasy srodek.klasy liczebnosc.klasy\n",
       "1   1        0              2            1           138             \n",
       "2   2        2              4            3            72             \n",
       "3   3        4              6            5            27             \n",
       "4   4        6              8            7            20             \n",
       "5   5        8             10            9             6             \n",
       "6   6       10             12           11             2             \n",
       "7   7       12             14           13             0             \n",
       "8   8       14             16           15             2             \n",
       "9   9       16             18           17             1             \n",
       "10 10       18             20           19             0             \n",
       "11 11       20             22           21             0             \n",
       "12 12       22             24           23             2             "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_foreign <- hist(lang$foreign, plot=\"FALSE\") \n",
    "freq_tab_foreign <- data.frame(nr.klasy = seq(1, length(res_foreign$counts)),\n",
    "                           poczatek.klasy  = head(res_foreign$breaks,-1),\n",
    "                           koniec.klasy    = tail(res_foreign$breaks,-1),\n",
    "                           srodek.klasy    = res_foreign$mids,\n",
    "                           liczebnosc.klasy= res_foreign$counts)\n",
    "\n",
    "res_notforeign <- hist(lang$notforeign, plot=\"FALSE\") \n",
    "freq_tab_notforeign <- data.frame(nr.klasy = seq(1, length(res_notforeign$counts)),\n",
    "                              poczatek.klasy  = head(res_notforeign$breaks,-1),\n",
    "                              koniec.klasy    = tail(res_notforeign$breaks,-1),\n",
    "                              srodek.klasy    = res_notforeign$mids,\n",
    "                              liczebnosc.klasy= res_notforeign$counts)\n",
    "\n",
    "paste(\"Szereg rodzielczy dla badanych słuchających zagranicznej muzyki:\")\n",
    "freq_tab_foreign\n",
    "paste(\"Szereg rodzielczy dla badanych nie słuchających zagranicznej muzyki:\")\n",
    "freq_tab_notforeign"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wizualizacja danych: <br>\n",
    "Dominanta - kolor czerwony. <br>\n",
    "Mediana - kolor niebieski. <br>\n",
    "Średnia dla próby - kolor fioletowy. <br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 712,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Muzyka w języku ojczystym\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow=c(2,1))\n",
    "barplot(table(lang$foreign), main=paste(\"Muzyka w języku zagranicznym\"))\n",
    "abline(v=mean(lang$foreign), col=\"purple\")\n",
    "abline(v=mode(lang$foreign), col=\"red\")\n",
    "abline(v=median(lang$foreign), col=\"blue\")\n",
    "barplot(table(lang$notforeign), main=paste(\"Muzyka w języku ojczystym\"))\n",
    "abline(v=mean(lang$notforeign), col=\"purple\")\n",
    "abline(v=mode(lang$notforeign), col=\"red\")\n",
    "abline(v=median(lang$notforeign), col=\"blue\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Korelacja i regresja"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sprawdźmy, czy istnieje zależność między ocenami stanów depresji oraz lęku, które deklarują nasi badani."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 713,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.530473185769991"
      ],
      "text/latex": [
       "0.530473185769991"
      ],
      "text/markdown": [
       "0.530473185769991"
      ],
      "text/plain": [
       "[1] 0.5304732"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title \"Ocena samopoczucia\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data$Depression ~ data$Anxiety, col=\"red\", main = \"Ocena samopoczucia\", xlab = \"Depression\", ylab = \"Anxiety\")\n",
    "abline(model, col=\"blue\")\n",
    "cor(data$Depression, data$Anxiety)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 714,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = data$Depression ~ data$Anxiety, data = data)\n",
       "\n",
       "Coefficients:\n",
       " (Intercept)  data$Anxiety  \n",
       "      1.5164        0.5754  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model <- lm(data$Depression ~ data$Anxiety, data)\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 715,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>kowariancja</th><th scope=col>korelacja</th><th scope=col>korelacja_kwadrat</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>4.40187</td><td>0.5304732</td><td>0.2814018</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 3\n",
       "\\begin{tabular}{lll}\n",
       " kowariancja & korelacja & korelacja\\_kwadrat\\\\\n",
       " <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 4.40187 & 0.5304732 & 0.2814018\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 3\n",
       "\n",
       "| kowariancja &lt;dbl&gt; | korelacja &lt;dbl&gt; | korelacja_kwadrat &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 4.40187 | 0.5304732 | 0.2814018 |\n",
       "\n"
      ],
      "text/plain": [
       "  kowariancja korelacja korelacja_kwadrat\n",
       "1 4.40187     0.5304732 0.2814018        "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "measure <- data.frame(kowariancja = cov(data$Depression,data$Anxiety),\n",
    "                          korelacja = cor(data$Depression,data$Anxiety),\n",
    "                          korelacja_kwadrat = cor(data$Depression,data$Anxiety)^2)\n",
    "\n",
    "measure"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Otrzymane wartości współczynnika korelacji podniesionego do kwadratu wskazują na średnią korelację pomiędzy ocenami stanów depresji oraz lęku wśród badanych. Kierunek tej zależności jest pozytywny, co widać na wykresie."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Najważniejsze wnioski i obserwacje"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Skonstrułowane na podstawie szeregów rozdzielczych dla rozkładów wieku uczestników badania oraz ocen częstotliwości słuchania danych gatunków muzycznych histogramy pokazują, że pierwszy z nich ma rozkład unimodalny, dwuwierzchołkowy, a pozostałe wymienione - głównie unimodalne, wielowierzchołkowe.\n",
    "2. W pierwszym histogramie największy peak znajduje się dla przedziału wiekowego (15, 18> lat, kolejny dla (19,21> lat. Natomiast wraz ze zwiększającymi się wartościami na osi x - liczba osób spada. W ostatniej klasie liczba ta wynosi 0.\n",
    "3. W przypadku szeregów punktowych wśród badanych atrybutów jedynie rozkład częstotliwości słuchania muzyki klasycznej jest dwustronnie symetryczny. W przypadku pozostałych trzech rozkładów - są one asymetryczne prawostronnie.\n",
    "4. Oba rozkłady dotyczące słuchania muzyki w języku ojczystym, bądź zagranicznym są prawostronne.\n",
    "5. Dodatnie wartości kurtozy w obu rozkładach wskazują na większe skupienie wyników i bardziej wydłużony rozkład wartości.\n",
    "6. Współczynnik korelacji świadczy o dość słabej, ale istniejącej zależności pomiedzy badanymi cechami: oceną samopoczucia w kwestii depresji oraz lęków. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Testy statystyczne"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test T"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wylosujmy próbę 100 osób z bazy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 716,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "sampleT <- data[sample(nrow(data), 100), ]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "W tym teście skupimy się na rozkładzie liczby beatów na minutę. Należy obliczyć średnią oraz odchylenie standardowe w naszej próbie, natomiast σ populacji jest nam nieznane. Zakładam, że dane pochodzą z rozkładu normalnego."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 717,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>średnia</th><th scope=col>odch_st</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>124.03</td><td>35.39059</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 2\n",
       "\\begin{tabular}{ll}\n",
       " średnia & odch\\_st\\\\\n",
       " <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 124.03 & 35.39059\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 2\n",
       "\n",
       "| średnia &lt;dbl&gt; | odch_st &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| 124.03 | 35.39059 |\n",
       "\n"
      ],
      "text/plain": [
       "  średnia odch_st \n",
       "1 124.03  35.39059"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length_music <- data.frame(średnia = mean(sampleT$BPM),odch_st = sd(sampleT$BPM))\n",
    "length_music"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sprawdzając średnią liczbę uderzeń w próbie i odchylenie standardowe można sformułować pytanie, czy średnio w całej populacji są to 124 uderzenia na minutę w słuchanych utworach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 718,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Liczba beatów na minutę\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(sampleT$BPM, main=\"Liczba beatów na minutę\", xlab=\"bpm\", col=\"#99627A\", border=\"#E57C23\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Warunki testu T są spełnione. Hipotezy do testu dwustronnego:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "H0: µ = 124 <br>\n",
    "H1: µ != 124"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 719,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "alpha = 0.01"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zbiór krytyczny:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 720,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.62640545728083"
      ],
      "text/latex": [
       "2.62640545728083"
      ],
      "text/markdown": [
       "2.62640545728083"
      ],
      "text/plain": [
       "[1] 2.626405"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_t <- length(sampleT$BPM) - 1\n",
    "qt(1 - (alpha / 2), df_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 721,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Zbiór krytyczny: (-∞,- 2.63 ) ∪ ( 2.63 ,+∞)'"
      ],
      "text/latex": [
       "'Zbiór krytyczny: (-∞,- 2.63 ) ∪ ( 2.63 ,+∞)'"
      ],
      "text/markdown": [
       "'Zbiór krytyczny: (-∞,- 2.63 ) ∪ ( 2.63 ,+∞)'"
      ],
      "text/plain": [
       "[1] \"Zbiór krytyczny: (-∞,- 2.63 ) ∪ ( 2.63 ,+∞)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zk <- round(qt(1 - (alpha / 2), df_t),2)\n",
    "paste(\"Zbiór krytyczny: (-∞,-\",zk,\") ∪ (\",zk,\",+∞)\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość statystyki testowej przy założeniu prawdziwości hipotezy zerowej:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 722,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0210901051575368"
      ],
      "text/latex": [
       "0.0210901051575368"
      ],
      "text/markdown": [
       "0.0210901051575368"
      ],
      "text/plain": [
       "[1] 0.02109011"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p <- mean(sampleT$BPM)\n",
    "p0 <- 124\n",
    "stdev <- sd(sampleT$BPM)\n",
    "T <- (p - p0) / stdev * sqrt(n)\n",
    "T"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość statystyki tekstowej nie wchodzi w zakres zbioru krytycznego - nie ma podstaw do odrzucenia hipotezy zerowej."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test χ2 (niezależność)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test niezależności chi-kwadrat jest popularnym testem statystycznym wykorzystywanym w badaniach, gdzie stawiamy pytania badawcze dotyczące tego, czy jedna ze zmiennych jest zależna od innej. Warunkiem jego wykorzystania jest to, by zmienne były zmiennymi jakościowymi. Sformułowanie hipotezy:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "H0 : Analizowane zmienne są niezależne. <br>\n",
    "H1 : Analizowane zmienne są zależne."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Próg istotności:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 723,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Losowa próba 200 osób:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 724,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "library(\"dplyr\")\n",
    "sample <- data %>% sample_n(200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 725,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     \n",
       "      Improve No effect\n",
       "  No       34        13\n",
       "  Yes     120        33"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "whileWorking_musicEffects <- table(sample$While.working, sample$Music.effects)\n",
    "whileWorking_musicEffects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 726,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Wpływ muzyki w zależności od słuchania jej podczas pracy\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(whileWorking_musicEffects, main=\"Wpływ muzyki w zależności od słuchania jej podczas pracy\", col=\"#E8A9A9\", border=\"#46458C\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sumy obserwacji oraz liczebności brzegowe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 727,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "margin_rows <- margin.table(whileWorking_musicEffects, 1)\n",
    "margin_cols <- margin.table(whileWorking_musicEffects, 2)\n",
    "total <- sum(margin_rows)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Liczba stopni swobody:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 728,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df <- (length(margin_rows)-1)*(length(margin_cols)-1)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tablica wartości oczekiwanych dzięki funkcji <i>outer(margin_rows, margin_cols)</i>, wykonującej iloczyn zewnętrzny/Kroneckera (iloczyny wszystkich kombinacji współrzędnych wektorów)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 729,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Improve</th><th scope=col>No effect</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>No</th><td> 36.19</td><td>10.81</td></tr>\n",
       "\t<tr><th scope=row>Yes</th><td>117.81</td><td>35.19</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 2 of type dbl\n",
       "\\begin{tabular}{r|ll}\n",
       "  & Improve & No effect\\\\\n",
       "\\hline\n",
       "\tNo &  36.19 & 10.81\\\\\n",
       "\tYes & 117.81 & 35.19\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 2 of type dbl\n",
       "\n",
       "| <!--/--> | Improve | No effect |\n",
       "|---|---|---|\n",
       "| No |  36.19 | 10.81 |\n",
       "| Yes | 117.81 | 35.19 |\n",
       "\n"
      ],
      "text/plain": [
       "     \n",
       "      Improve No effect\n",
       "  No   36.19  10.81    \n",
       "  Yes 117.81  35.19    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "E = outer(margin_rows, margin_cols) / total\n",
    "E"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość statystyki testowej:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 730,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.753200111093129"
      ],
      "text/latex": [
       "0.753200111093129"
      ],
      "text/markdown": [
       "0.753200111093129"
      ],
      "text/plain": [
       "[1] 0.7532001"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chi2  <- sum((whileWorking_musicEffects - E)^2/E)\n",
    "chi2"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość krytyczna:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 731,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.84145882069412"
      ],
      "text/latex": [
       "3.84145882069412"
      ],
      "text/markdown": [
       "3.84145882069412"
      ],
      "text/plain": [
       "[1] 3.841459"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qchisq(1 - alpha, df)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość statystyki testowej jest większa od wartości krytycznej. Zatem odrzucamy hipotezę zerową."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 732,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's Chi-squared test\n",
       "\n",
       "data:  whileWorking_musicEffects\n",
       "X-squared = 0.7532, df = 1, p-value = 0.3855\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chisq.test(whileWorking_musicEffects, correct=FALSE)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Test χ2 (zgodność z rozkładem)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Test do analizowania danych jakościowych w celu sprawdzenia, czy dane (próba 120 os.) mają określony rozkład. Oczekujemy, że podane niżej serwisy streamingowe mają równy rozkład. Sprawdźmy, czy rozkłady są takie same. Sformułowanie hipotezy:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "H0 : rozkłady są takie same<br>\n",
    "H1 : rozkłady są różne "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Próg istotności:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 733,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 734,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>opinion</th><th scope=col>number</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Apple Music                      </td><td> 7</td></tr>\n",
       "\t<tr><td>I do not use a streaming service.</td><td>10</td></tr>\n",
       "\t<tr><td>Other streaming service          </td><td> 4</td></tr>\n",
       "\t<tr><td>Pandora                          </td><td> 3</td></tr>\n",
       "\t<tr><td>Spotify                          </td><td>88</td></tr>\n",
       "\t<tr><td>YouTube Music                    </td><td> 8</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{ll}\n",
       " opinion & number\\\\\n",
       " <chr> & <int>\\\\\n",
       "\\hline\n",
       "\t Apple Music                       &  7\\\\\n",
       "\t I do not use a streaming service. & 10\\\\\n",
       "\t Other streaming service           &  4\\\\\n",
       "\t Pandora                           &  3\\\\\n",
       "\t Spotify                           & 88\\\\\n",
       "\t YouTube Music                     &  8\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| opinion &lt;chr&gt; | number &lt;int&gt; |\n",
       "|---|---|\n",
       "| Apple Music                       |  7 |\n",
       "| I do not use a streaming service. | 10 |\n",
       "| Other streaming service           |  4 |\n",
       "| Pandora                           |  3 |\n",
       "| Spotify                           | 88 |\n",
       "| YouTube Music                     |  8 |\n",
       "\n"
      ],
      "text/plain": [
       "  opinion                           number\n",
       "1 Apple Music                        7    \n",
       "2 I do not use a streaming service. 10    \n",
       "3 Other streaming service            4    \n",
       "4 Pandora                            3    \n",
       "5 Spotify                           88    \n",
       "6 YouTube Music                      8    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(\"dplyr\")\n",
    "sample2 <- data %>% sample_n(120)\n",
    "\n",
    "sampleServices <- data.frame(opinion = c('Apple Music', 'I do not use a streaming service.', 'Other streaming service', 'Pandora', 'Spotify', 'YouTube Music'), number = matrix(table(sample2$Primary.streaming.service)))\n",
    "sampleServices\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Liczba stopni swobody:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 735,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "dfServices <- length(sampleServices$number)-1"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tabela wartości oczekiwanych (rozkład nie jest równy ze względu na popularność jednego z serwisów - Spotify - przyjmując takie proporcje zwiększamy rzetelność testu):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 736,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "Expected <- c(10, 20, 20, 10, 40, 20)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość statystyki testowej:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 737,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "88.4"
      ],
      "text/latex": [
       "88.4"
      ],
      "text/markdown": [
       "88.4"
      ],
      "text/plain": [
       "[1] 88.4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chi2 <- sum((sampleServices$number-Expected)^2/Expected)\n",
    "chi2"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość krytyczna:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 738,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "11.0704976935164"
      ],
      "text/latex": [
       "11.0704976935164"
      ],
      "text/markdown": [
       "11.0704976935164"
      ],
      "text/plain": [
       "[1] 11.0705"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qchisq(1 - alpha, dfServices)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wartość krytyczna jest zdecydowanie mniejsza niż wartość statystyki testowej (znajdujemy się w obszarze krytycznym) - odrzucamy hipotezę zerową. Zatem rozkłady są różne."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wnioski i obserwacje"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Aby zaanalizować średnią liczbę beatów na minutę w słuchanych przez badanych utworach wykorzystany został test T. Przy poziomie istotności α = 0.01 nie było podstaw do odrzucenia hipotezy zerowej, która mówi, że średnia liczba uderzeń na minutę to 124.\n",
    "2. Przeprowadzenie testów ch-kwadrat pozwoliło zbadać zależności pomiędzy rozkładami. Pierwszym statystycznie potwierdzonym stwierdzeniem jest to, że słuchanie muzyki w trakcie pracy oraz wpływ muzyki na samopoczucie są ze sobą powiązane. Innym wnioskiem jest fakt, iż jest mocna nierówność wśród serwisów streamingowych. Zdecydowanym faworytem wśród słuchaczy jest aplikacja Spotify, co zostało udowodnione testem chi-kwadrat, w którym już z góry zostały załozone nierówne proporcje, a i tak hipoteza zerowa została odrzucona.\n",
    "\n",
    "Przeprowadzona analiza obejmowała różnorodne aspekty i cechy zawarte w wybranej bazie danych. W jej trakcie starałam się zbadać jak najwięcej atrybutów i powiązań między nimi w sposób graficzny, jak i poprzez różne testy. Moim głównym pytaniem, które towarzyszyło mi przez cały czas ich badania to, jaki wpływ ma na nas słuchanie muzyki. Mam nadzieję, że udało mi się odpowiedzieć na to ciekawe zagadnienie, korzystając z zależności między nimi oraz prognoz, które podlegały statystycznemu potwierdzeniu."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Propozycje dalszych kroków\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "W ramach kontynuacji projektu należy zrobić głębszy research w ramach tego tematu. Zagadnienie odnośnie terapii poprzez muzykę jest dopiero badane, ale powstało wiele dokładniejszych opracowań i zbiorów danych, które mogłyby posłużyć lepszej analizie. Postawione tezy mogłyby być bardziej szczegółowe, a wnioski jeszcze ciekawsze."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bibliografia\n",
    "1. https://statystyka.online/miary-tendencji-centralnej-teoria/\n",
    "2. https://predictivesolutions.pl/test-niezaleznosci-chi-kwadrat-pearsona\n",
    "3. https://www.tutorialspoint.com/r/r_bar_charts.htm\n",
    "4. https://www.rdocumentation.org/\n"
   ]
  }
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