bert_mixmodel.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analiza danych behawioralnych - eksperyment Bert 1 (09-10.2015)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(\"lme4\")\n",
    "library(\"lmerTest\")\n",
    "library(\"phia\")\n",
    "library(\"psyphy\")\n",
    "library(\"ggplot2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "options(jupyter.plot_mimetypes = \"image/png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wczytywanie danych i porządkowanie nazw kolumn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dane = read.csv(\"anova.csv\", sep=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "names(dane)=tolower(names(dane))\n",
    "names(dane)[names(dane) == 'accuracy_rt'] = 'acc_rt'\n",
    "names(dane)[names(dane) == 'accuracy'] = 'acc'\n",
    "names(dane)[names(dane) == 'duration_type'] = 'dur'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>x</th><th scope=col>id</th><th scope=col>task</th><th scope=col>block</th><th scope=col>trial</th><th scope=col>fiksacja3</th><th scope=col>fiksacja3_dur</th><th scope=col>fiksacja</th><th scope=col>fiksacja_dur</th><th scope=col>stimulus_type</th><th scope=col>ellip.h</th><th scope=col>fiksacja2_dur</th><th scope=col>beh_response</th><th scope=col>response_dur</th><th scope=col>button</th><th scope=col>acc</th><th scope=col>acc_rt</th><th scope=col>pas_response</th><th scope=col>pas_response_dur</th><th scope=col>pas</th><th scope=col>pas_rt</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>0</td><td>dc1_01</td><td>low</td><td>1</td><td>2</td><td>12.0558</td><td>3.0095</td><td>15.0653</td><td>1.7399</td><td>sn3</td><td><e2><8b><af></td><td>2.0102</td><td>19.1211</td><td>1.5165</td><td>54</td><td>0</td><td>262.4</td><td>20.6494</td><td>1.4459</td><td>4</td><td>499.2</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>1</td><td>dc1_01</td><td>low</td><td>1</td><td>4</td><td>31.1591</td><td>2.0103</td><td>33.1694</td><td>1.7399</td><td>mn7</td><td><e2><8b><af></td><td>2.0103</td><td>37.1899</td><td>1.5165</td><td>54</td><td>0</td><td>510</td><td>38.7182</td><td>1.4812</td><td>4</td><td>397.6</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2</td><td>dc1_01</td><td>low</td><td>1</td><td>5</td><td>40.2112</td><td>2.0102</td><td>42.2214</td><td>1.7399</td><td>sc1</td><td><e2><8b><af></td><td>2.0103</td><td>46.2772</td><td>1.5165</td><td>44</td><td>1</td><td>457.1</td><td>47.8055</td><td>1.446</td><td>4</td><td>479.4</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>3</td><td>dc1_01</td><td>low</td><td>1</td><td>6</td><td>49.2632</td><td>1.011</td><td>50.2742</td><td>1.7399</td><td>mn7</td><td><e2><8b><af></td><td>6.0073</td><td>58.327</td><td>1.5165</td><td>54</td><td>0</td><td>1453.6</td><td>59.8553</td><td>1.446</td><td>4</td><td>1358.9</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>4</td><td>dc1_01</td><td>low</td><td>1</td><td>7</td><td>61.313</td><td>1.011</td><td>62.324</td><td>1.7399</td><td>mc1</td><td><e2><8b><af></td><td>2.0102</td><td>66.4151</td><td>1.5165</td><td>54</td><td>1</td><td>1153.3</td><td>67.9433</td><td>1.4108</td><td>4</td><td>195.3</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>5</td><td>dc1_01</td><td>low</td><td>1</td><td>8</td><td>69.3658</td><td>2.0103</td><td>71.3761</td><td>1.7399</td><td>sc9</td><td><e2><8b><af></td><td>4.0087</td><td>77.3951</td><td>1.5165</td><td>44</td><td>1</td><td>279.4</td><td>78.9234</td><td>1.4812</td><td>1</td><td>255.6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllllllllllllllllllllll}\n",
       "  & x & id & task & block & trial & fiksacja3 & fiksacja3_dur & fiksacja & fiksacja_dur & stimulus_type & ellip.h & fiksacja2_dur & beh_response & response_dur & button & acc & acc_rt & pas_response & pas_response_dur & pas & pas_rt\\\\\n",
       "\\hline\n",
       "\t1 & 0 & dc1_01 & low & 1 & 2 & 12.0558 & 3.0095 & 15.0653 & 1.7399 & sn3 & <e2><8b><af> & 2.0102 & 19.1211 & 1.5165 & 54 & 0 & 262.4 & 20.6494 & 1.4459 & 4 & 499.2\\\\\n",
       "\t2 & 1 & dc1_01 & low & 1 & 4 & 31.1591 & 2.0103 & 33.1694 & 1.7399 & mn7 & <e2><8b><af> & 2.0103 & 37.1899 & 1.5165 & 54 & 0 & 510 & 38.7182 & 1.4812 & 4 & 397.6\\\\\n",
       "\t3 & 2 & dc1_01 & low & 1 & 5 & 40.2112 & 2.0102 & 42.2214 & 1.7399 & sc1 & <e2><8b><af> & 2.0103 & 46.2772 & 1.5165 & 44 & 1 & 457.1 & 47.8055 & 1.446 & 4 & 479.4\\\\\n",
       "\t4 & 3 & dc1_01 & low & 1 & 6 & 49.2632 & 1.011 & 50.2742 & 1.7399 & mn7 & <e2><8b><af> & 6.0073 & 58.327 & 1.5165 & 54 & 0 & 1453.6 & 59.8553 & 1.446 & 4 & 1358.9\\\\\n",
       "\t5 & 4 & dc1_01 & low & 1 & 7 & 61.313 & 1.011 & 62.324 & 1.7399 & mc1 & <e2><8b><af> & 2.0102 & 66.4151 & 1.5165 & 54 & 1 & 1153.3 & 67.9433 & 1.4108 & 4 & 195.3\\\\\n",
       "\t6 & 5 & dc1_01 & low & 1 & 8 & 69.3658 & 2.0103 & 71.3761 & 1.7399 & sc9 & <e2><8b><af> & 4.0087 & 77.3951 & 1.5165 & 44 & 1 & 279.4 & 78.9234 & 1.4812 & 1 & 255.6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "  x     id task block trial fiksacja3 fiksacja3_dur fiksacja fiksacja_dur\n",
       "1 0 dc1_01  low     1     2   12.0558        3.0095  15.0653       1.7399\n",
       "2 1 dc1_01  low     1     4   31.1591        2.0103  33.1694       1.7399\n",
       "3 2 dc1_01  low     1     5   40.2112        2.0102  42.2214       1.7399\n",
       "4 3 dc1_01  low     1     6   49.2632        1.0110  50.2742       1.7399\n",
       "5 4 dc1_01  low     1     7   61.3130        1.0110  62.3240       1.7399\n",
       "6 5 dc1_01  low     1     8   69.3658        2.0103  71.3761       1.7399\n",
       "  stimulus_type stimulus  dur duration   maska maska_dur fiksacja2\n",
       "1           sn3  16.8052 dur2   0.0470 16.8522    0.2469   17.0991\n",
       "2           mn7  34.9093 dur1   0.0117 34.9210    0.2469   35.1679\n",
       "3           sc1  43.9613 dur2   0.0470 44.0083    0.2469   44.2552\n",
       "4           mn7  52.0141 dur2   0.0470 52.0611    0.2469   52.3080\n",
       "5           mc1  64.0639 dur3   0.0823 64.1462    0.2469   64.3931\n",
       "6           sc9  73.1160 dur1   0.0117 73.1277    0.2469   73.3746\n",
       "  fiksacja2_dur beh_response response_dur button acc acc_rt pas_response\n",
       "1        2.0102      19.1211       1.5165     54   0  262.4      20.6494\n",
       "2        2.0103      37.1899       1.5165     54   0  510.0      38.7182\n",
       "3        2.0103      46.2772       1.5165     44   1  457.1      47.8055\n",
       "4        6.0073      58.3270       1.5165     54   0 1453.6      59.8553\n",
       "5        2.0102      66.4151       1.5165     54   1 1153.3      67.9433\n",
       "6        4.0087      77.3951       1.5165     44   1  279.4      78.9234\n",
       "  pas_response_dur pas pas_rt\n",
       "1           1.4459   4  499.2\n",
       "2           1.4812   4  397.6\n",
       "3           1.4460   4  479.4\n",
       "4           1.4460   4 1358.9\n",
       "5           1.4108   4  195.3\n",
       "6           1.4812   1  255.6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "head(dane)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Kontrola przypadków odstających"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sprawdzenie średnich poprawności"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sort((zbior=(aggregate(acc ~ id, dane, mean)))$acc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sprawdzenie odchylenia standardowego ocen na skali PAS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sort((zbior2=(aggregate(pas ~ id, dane, sd)))$pas))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "zbior=merge(zbior, zbior2,by='id')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sprawdzenie wartości d'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAM1BMVEX9/v0AAABMTUxnaGd7e3uLjIuZmpmmpqaxsrG7vLvFxsXOz87X2Nff4N/n6Ofu7+79/v1tTElJAAAAEXRSTlP/////////////////////ACWtmWIAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAABShSURBVHic7d3tQtrKAobRMwFERT7u/2oPIK3U3aQgLzMkrPVDaYt7AvLsJJME/rcDbva/1gsAUyAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIEFAhpAIjc/2rvEZI9x8CkoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCgksNXFEuJLjMsaK+lIQElylnX3v+8SpC4hmVb9///q9XEBLPSEgQICRIsI8EAWbtIMJxJLgvIUGAkCBASBAgJAgQEgQICQJqhrR9KWW+Oo07OLCQGJmKIW2742dtLj7HFRJTUjGkZXnb1/TWzY/jCokpqRhS9znWpptthMTEVAzpVzvb+VxITEzFkGZl++vWXEhMS8WQ3srL6damzIXEpNSc/l7+rmc1cD76gZAYmaoHZNeLX7c2L0JiSpzZAAFCggAhQUCrkEw2MCmPE1I5lxgC6rFpBwFCggAhQYCQIEBIECAkCKh6PdLFM9xCYmSqXkYhJKaq5qbd+vPtGi4gJEam7mUUZXnZHYXEyNSdbHgr64vuJyRGxqwdBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAm++cm77wgJ/nCs6OqUhAR/KGdfr/2pqwiJCSvfvl/5Y1cQEhMmJAgQEiTYR4IAs3YQ4TgSNCIkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASDypUpIvMyHxlI4VBVMSEk+pnH3N/feuIiRGr3z7HvsPXkFIjJ6QIEBIkGAfCQLM2kGE40jwcIQEAUJi2rJbcP3DXP8jQmI00nMK/QNd/yNCYjTSs9z/GOgqQmIs4sdd/znSFYTEWAgJAoQECfaR4Ap9k9xm7eBiQ7k4jgQXqrYB969FuIqQeCz1phT+vQxXEBKPRUh9hMQVhNRHSFzDPlIPIXGNapPcA4tw/Y8IiYdTaZJ7YAGu/xEhwXdCggAhQYCQIEBIEFA1pI/XRTlYLD+G7ygkRqZiSNtZ+TJPLxW0VDGkZene18dbm1VXlkN3FRIjUzGkrqx/316XbuiuQmJkKob0x7Hn4QPRQmJkrJEgoO4+0mpzvGUfiampOf09P5u1m23DSwUt1T2OtDweR+oWr44jMS3ObIAAIUGAkCCgVUiOIzEpjxNSOZcYAuqxaQcBQoIAIUGAkCBASBAgJAioej3SxTPcQmJkKob0JiQmq+am3bobfsuTL0JiZKruI62HL+f7IiRGpu5kw9vZ1eZDhMTImLWDACFBgJAgQEgQICQIEBLj8cCXfAqJsXiAzy7vJyTGopx9fThC4uH8fQuufPv+WITEg+nbghPS9R7zuSKqb+agbwtOSNd7zOeKoN6Zg/5e7CNd7UGfLHJ6qxgIyazdtR70ySLmX+udv78GHEe60sM+XYQM5PLQW3C9hEQLQyE98hZcLyHRxNB654G34HoJiSbGud7pJyQaGeN6p5+QIEBIECAkCBASBAiJ+5rWnEIvIXFPU5vl7iUk7mmc5/v8gJC4o8e+hihJSNyRkAYIif/omVIQ0gAh8U3/lIJ9pH5C4pv+XMza9RMSfxrcgHMcqY+Q+NPz7An1ExI3E5KQSHiaKYV+QuJ2TzOl0E9IJDzJlEI/IUGAkCBASBAgJAgQEgQICQKEBAFCggAhcbmnP+zaT0hcyolAA4TEpZyaOkBIXMjFEkOExIWENERIXEhIQ4TEpewjDRASlzJrN0BIXM5xpF5CggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAULiP3ye2PWExDc+4fInhMQ3PnP5J4T0tHo24Mq371ykZkibl9K97nZvs9Ith+/pl3h3vRtwQvqRiiFtu/3/A8vb6+FrmaeXiuv0bsAJ6UcqhrQs+/XQsisv2932eDu6VFxlIBf7SD9RMaTuOFYp2+O3buiufov3NhSSWbsfqBhSKV9f//GL8lu8t8ENOMeRrtdgjXT4urVGaswGXFaDfaTl9nQ7ulRcxwZcllm7p2UDLslxJAhwZgME3BzSanHYQlhsQsvzSUiMzK0hzctxU7t00ZKExMjcGNJbmW8PIb2VlyvHdRyJKbkxpK5sfzaR+t/7l3PXLxW0dGNIx826/BEJITEyN4Y0O62R1mUWW6SdkJKs36vI7COtuvIWW6SdkHKcwFDJrbN2i9NOzfCZCicfr593Xyw/4kvFXzmlrpLIcaSyeL/g57azs9kEpwhV4Sq9WqqetNq9r4+3NvtNQSet1iCkWm4MafGPk+bOdWX9+/baZRRVCKmWwPT3xUOVvj/8967XLRG97CNVEpj+vpQ1UgNm7Sq5MaTtYv6PCbgv+32k1ecZefaRKnIcqYqbN+2uOKtnfnbv2eCazK+ekakZ0u5jeTyO1C1eHUdiWlzYNw024BoT0hSYUmju5pDe55ee2XAFL4m/61vvmORuLnKF7KXn2l3MS+JvvO/9A7v57O9utf/m7O8avO/9A7v5gOznQVbXIyX9fQuuPxchtZc6RcgVslfr3eHp2YIbyMU+UnOxNdLgKT/XeoKXRP9EW18VQyGZtWvNPlIjP9jhGVrvOI7UmFm7Nn6yw2O988BuP4508RWyV5j+i+VnMwfWOw/LmQ1tmDmYGCE10p+LLbgxujWk7fIwXdctL7++7xJP8CoaysUW3PjcGNKmO70gvIn+1eQyJTeGNC8vh3XRdlkWqSU68ApjZJzZAAE3htSd3vxk++wh9W+n2YJ7CjeGtCzHNz/5mA+/mcm1xvbSGzjfxxTcc3BmQ8LAXHbvvzApmTMb5tEz7Ub3wnOBAw7IBggJIQUIiVtDepvtdptZmV38fqsXGdvrzj7S07sxpNVhQqo7zDZESxrbC8+s3dO7+cyG9+P7Nbxnp+3G98JzHOnJBc5sWB+OIT37AVmeXCCkRVkJiSd386bdenV435On37Tjyd0+2VDK62GFtIot0k5IjM7N09+fHxk2y75pg5AYGQdkIUBIECAkCBASBAgJAoR0Daf70ENIl3MCKr2EdDmXRNDrhpAOb54ffcuTLw/5YnWRHv2EdDEh0c+m3cWERD8hXc4+Er1u27Q713ipKjBrRy8hXcNxJHrcumm3OH4Y80f3ElqeT16ujMzN7/29Pn5fP/d7f/P0fKwLBNz8sS6/1khdZnk+CYmRuXnTrju8M+SqO7xxQ46QGJnUx7pEP/lSSIxN5mNdFtH3EBISo+PMBggQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAh/W14n7nMlYT038HLry9wKSH1DC4kriGkvrGVxBWE1De2kLiCkPrGFhJXEFLP4DriGkL67+Bm7bhazZC2y27/9XVWyvx9+J6OIzEyFUPadPvX53b/5WCeXipoqWJIL2Wx3X952eybeinL8FJBSxVDKmV7+rLfyivd4F1/OAQ0UjWk/ZeunP2h/64/HAIaqbppt97tXg9fDmukwZ0kITEyFUNal2653i26fUmrWVmFlwpaqjn9vTrN2B28Dt5TSIxM3QOy7y+zQ0WL183w/YTEyDizAQKEBAFCgoBWITmOxKQ8TkjlXGIIqMemHQQICQKEBAFVQ/p4XRz3gBbLj+E7ComRqRjSdnY2m+DCPialYkjL0r0fT/3ebVadC/uYlIohdZ9XUBytXdjHpNS+sO+vf/jvXX84BDRijQQBdfeRVp+XT9hHYmpqTn/Pz2btZtvwUkFLdY8jLY/HkbrFq+NITIszGyBASBDwxCG5WoOcpw3JZ06Q9Lwh1RqIp/CsIflcPqKEBAFCgoBnDck+ElHPG5JZO4KeNiTHkUh64pAgR0gQICQIEBIECAkChAQBQoIAIUGAkCBg+iE5gYEKph6SU+qoYvIhhf978FcTD8llR9QhJAgQEgRMPCT7SNQx+ZDM2lHD1ENyHIkqph8SVCAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCgoCphFSK+GhoGiEdK5IS7UwkpB/9FMRMIqTy7TvUJiQIEBIETCIk+0i0NpGQzNrR1jRCchyJxqYSEjQlJAgQEgQICQKEBAFNQvrnDJuQGBkhQUDFkMqfwksFLVUM6aMTElNVc9NuuyjzzXFQm3ZMTN19pPdS3ndCYnoqTzZs5mWxFRKTU33W7rV0KyExNfWnv9ezf5+pLSRGpsVxpBchMTVOEYIAIUFAq5AckGVSHieki097gMdj0w4ChAQBQoKAqiF9vC6Oe0CL5cfwHYXEyFQMaTs7m02Yp5cKWqoY0rJ07+vjrc2qK8uhuwqJkakYUlfWv2+vSzd0VyExMlUvNe/7w3/v+sMhoBFrJAiou4+0Ol5pbh+Jyak5/T0/m7WbbcNLBS3VPY60PB5H6havjiMxLc5sgAAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQLGFVIpEuMhjSmkY0VS4hGNKqSBf4OmRhRSGfpHaEpIECAkCBhRSPaReFyjCsmsHY9qTCE5jsTDGldI8KCEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBDxoSjMz1r/InWCMZ3/j3JyTjGz9ASMY3foCQjG/8ACEZ3/gBQjK+8QOEZHzjBwjJ+MYPEJLxjR8gJOMbP0BIxjd+gJCMb/yACiHB9AkJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAi4d0jLrnTL7Z0H6ffj90SPePs1cKNn4df4bZ6Ft9nvB93k8X+NX+Px3zmk+fERzO47SL9105DWvwZu9Cz8Gr/Ns7A8jtkdXslNHv/X+FUe/31D+ijderfuysddR+m3LotGIx8G706/u0bPwu/xmzwL6/KyPawTXxo9/rPxqzz++4a0LKv91/fyetdR+r01G/kw9vz0Qm7zLHyN3+RZWHyOfViEJo//bPwqj/++IS3KZtdyvfBW3hqNvP8VLnenF3KbZ+Fr/KbPQmn7KvgMqcLjv29IpZx/q29RVi/7Pc4mY6+/P/zKz8LX+A2fhW2ZN30VHMev8vinHtLRvNHwTUPanYXU7Fl4O2zVNXwVHMev8vinHVIp7/v/Ky1bbdo8SEjtnoVNt9i1fBX8Gr/C4592SJ+2rebfHySkTw2ehW03P1uM+o//NP7pD/d9/PcNqXuIkJqNfxq32bPw54j1x59/vnSbPf75H+ncd/was3ablkdzDhqH1OxZaBvSZjbfHG80evy/xz8Zc0ivxyMIq9Jm3uzw/8LDgfVmIZ9+dc2ehd9rxBbPwur33n2bx/81fpXHP+0zG5aHX97284BgA23PbPg9fpNnYfM1S9bk8Z+NX+Xx3/lcu1nT6ef93uZx/FYrxF8bE62ehdP4TZ6Fl/J1hluLx382fpXHf+eQtsfzfu87xr/GnzU7rv8rpFbPwvn4tZ+FchZSi8f/ffx7P37XI0GAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQxuDvH8jd6sPa+QshjYGQHp6QxkBID09IYyCkhyekMTgmU8pmUbrX418su7I8hfQ2K93hE7vn5WP/9aO8tFvMZyakMTiF1B0+7v5Q0vxwY3H828XhZpnvdpvS7f/Yddu2i/qshDQGp5Dm291bme1276Vb79bd4W9Xh7/czstqv2raN/Za3lsv65MS0hicQvo43Vwcb60+bx7WQNuy2B3WU2/H7zQgpDE4hfTr5mmW4fPmye6wcbffjWq4lE9NSGNwWUi7ZVm2W8YnJ6QxGArp617WSA0JaQy+hbQ4zC3sPr5uflrs95HmjZbw6QlpDL6FtPqatTtO4O2Okwzv+w271/LWeFGflZDG4FtInwePXo43j4eUSrfZbbvjcSQbd20IaQy+h7R7/ePMhvKyr+fldGaDjbsmhAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgT8H3y3JBV/b+aFAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(sort(unlist((zbior$dprim=lapply(zbior$acc, function(x) dprime.mAFC(x,2))))),ylab=\"d' score\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# po tabeli 'zbior' można odnaleźć osoby o odstających wynikach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>id</th><th scope=col>acc</th><th scope=col>pas</th><th scope=col>dprim</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>dc1_01</td><td>0.6554622</td><td>1.182613</td><td>0.5658411</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>dc1_03</td><td>0.6996047</td><td>1.108715</td><td>0.7400242</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>dc1_04</td><td>0.7068273</td><td>1.073069</td><td>0.7695138</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>dc1_05</td><td>0.7509881</td><td>1.099638</td><td>0.9582748</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>dc1_06</td><td>0.7519685</td><td>1.001143</td><td>0.9626515</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>dc1_07</td><td>0.75</td><td>1.104674</td><td>0.9538726</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>dc1_09</td><td>0.6914062</td><td>1.273312</td><td>0.7068858</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>dc1_10</td><td>0.7755906</td><td>1.151471</td><td>1.071095</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>dc1_11</td><td>0.7929515</td><td>1.210489</td><td>1.154995</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>dc1_12</td><td>0.7114625</td><td>1.337315</td><td>0.7886534</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>dc1_14</td><td>0.736</td><td>1.276925</td><td>0.8924532</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>dc1_16</td><td>0.6719368</td><td>1.065547</td><td>0.6297034</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>dc1_17</td><td>0.647541</td><td>0.908556</td><td>0.5355486</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>dc1_18</td><td>0.6996047</td><td>1.064855</td><td>0.7400242</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>dc1_19</td><td>0.7041667</td><td>1.112093</td><td>0.7585868</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>dc1_20</td><td>0.7689243</td><td>1.118707</td><td>1.039855</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>dc1_21</td><td>0.6220472</td><td>1.103897</td><td>0.4396216</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>dc1_22</td><td>0.8102767</td><td>1.274635</td><td>1.242971</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>dc1_23</td><td>0.704918</td><td>1.024715</td><td>0.7616676</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>dc1_24</td><td>0.5691057</td><td>1.119061</td><td>0.2462091</td></tr>\n",
       "\t<tr><th scope=row>21</th><td>dc1_25</td><td>0.718254</td><td>1.057417</td><td>0.816938</td></tr>\n",
       "\t<tr><th scope=row>22</th><td>dc1_26</td><td>0.7714286</td><td>1.31358</td><td>1.051578</td></tr>\n",
       "\t<tr><th scope=row>23</th><td>dc1_27</td><td>0.745098</td><td>1.173836</td><td>0.9321691</td></tr>\n",
       "\t<tr><th scope=row>24</th><td>dc1_28</td><td>0.7193676</td><td>0.9061106</td><td>0.8216069</td></tr>\n",
       "\t<tr><th scope=row>25</th><td>dc1_29</td><td>0.743083</td><td>1.191246</td><td>0.923311</td></tr>\n",
       "\t<tr><th scope=row>26</th><td>dc1_30</td><td>0.7061224</td><td>1.096697</td><td>0.7666142</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       "  & id & acc & pas & dprim\\\\\n",
       "\\hline\n",
       "\t1 & dc1_01 & 0.6554622 & 1.182613 & 0.5658411\\\\\n",
       "\t2 & dc1_03 & 0.6996047 & 1.108715 & 0.7400242\\\\\n",
       "\t3 & dc1_04 & 0.7068273 & 1.073069 & 0.7695138\\\\\n",
       "\t4 & dc1_05 & 0.7509881 & 1.099638 & 0.9582748\\\\\n",
       "\t5 & dc1_06 & 0.7519685 & 1.001143 & 0.9626515\\\\\n",
       "\t6 & dc1_07 & 0.75 & 1.104674 & 0.9538726\\\\\n",
       "\t7 & dc1_09 & 0.6914062 & 1.273312 & 0.7068858\\\\\n",
       "\t8 & dc1_10 & 0.7755906 & 1.151471 & 1.071095\\\\\n",
       "\t9 & dc1_11 & 0.7929515 & 1.210489 & 1.154995\\\\\n",
       "\t10 & dc1_12 & 0.7114625 & 1.337315 & 0.7886534\\\\\n",
       "\t11 & dc1_14 & 0.736 & 1.276925 & 0.8924532\\\\\n",
       "\t12 & dc1_16 & 0.6719368 & 1.065547 & 0.6297034\\\\\n",
       "\t13 & dc1_17 & 0.647541 & 0.908556 & 0.5355486\\\\\n",
       "\t14 & dc1_18 & 0.6996047 & 1.064855 & 0.7400242\\\\\n",
       "\t15 & dc1_19 & 0.7041667 & 1.112093 & 0.7585868\\\\\n",
       "\t16 & dc1_20 & 0.7689243 & 1.118707 & 1.039855\\\\\n",
       "\t17 & dc1_21 & 0.6220472 & 1.103897 & 0.4396216\\\\\n",
       "\t18 & dc1_22 & 0.8102767 & 1.274635 & 1.242971\\\\\n",
       "\t19 & dc1_23 & 0.704918 & 1.024715 & 0.7616676\\\\\n",
       "\t20 & dc1_24 & 0.5691057 & 1.119061 & 0.2462091\\\\\n",
       "\t21 & dc1_25 & 0.718254 & 1.057417 & 0.816938\\\\\n",
       "\t22 & dc1_26 & 0.7714286 & 1.31358 & 1.051578\\\\\n",
       "\t23 & dc1_27 & 0.745098 & 1.173836 & 0.9321691\\\\\n",
       "\t24 & dc1_28 & 0.7193676 & 0.9061106 & 0.8216069\\\\\n",
       "\t25 & dc1_29 & 0.743083 & 1.191246 & 0.923311\\\\\n",
       "\t26 & dc1_30 & 0.7061224 & 1.096697 & 0.7666142\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "       id       acc       pas     dprim\n",
       "1  dc1_01 0.6554622 1.1826135 0.5658411\n",
       "2  dc1_03 0.6996047 1.1087150 0.7400242\n",
       "3  dc1_04 0.7068273 1.0730689 0.7695138\n",
       "4  dc1_05 0.7509881 1.0996380 0.9582748\n",
       "5  dc1_06 0.7519685 1.0011431 0.9626515\n",
       "6  dc1_07 0.7500000 1.1046739 0.9538726\n",
       "7  dc1_09 0.6914062 1.2733120 0.7068858\n",
       "8  dc1_10 0.7755906 1.1514707  1.071095\n",
       "9  dc1_11 0.7929515 1.2104892  1.154995\n",
       "10 dc1_12 0.7114625 1.3373152 0.7886534\n",
       "11 dc1_14 0.7360000 1.2769253 0.8924532\n",
       "12 dc1_16 0.6719368 1.0655474 0.6297034\n",
       "13 dc1_17 0.6475410 0.9085560 0.5355486\n",
       "14 dc1_18 0.6996047 1.0648553 0.7400242\n",
       "15 dc1_19 0.7041667 1.1120928 0.7585868\n",
       "16 dc1_20 0.7689243 1.1187073  1.039855\n",
       "17 dc1_21 0.6220472 1.1038974 0.4396216\n",
       "18 dc1_22 0.8102767 1.2746349  1.242971\n",
       "19 dc1_23 0.7049180 1.0247148 0.7616676\n",
       "20 dc1_24 0.5691057 1.1190612 0.2462091\n",
       "21 dc1_25 0.7182540 1.0574170  0.816938\n",
       "22 dc1_26 0.7714286 1.3135804  1.051578\n",
       "23 dc1_27 0.7450980 1.1738360 0.9321691\n",
       "24 dc1_28 0.7193676 0.9061106 0.8216069\n",
       "25 dc1_29 0.7430830 1.1912458  0.923311\n",
       "26 dc1_30 0.7061224 1.0966966 0.7666142"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zbior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model mieszany dla analizy poprawności względem czasu prezentacji"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>AIC</th><th scope=col>BIC</th><th scope=col>logLik</th><th scope=col>deviance</th><th scope=col>Chisq</th><th scope=col>Chi Df</th><th scope=col>Pr(>Chisq)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>m12</th><td>9</td><td>6203.177</td><td>6264.081</td><td>-3092.588</td><td>6185.177</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>m11</th><td>17</td><td>6210.824</td><td>6325.866</td><td>-3088.412</td><td>6176.824</td><td>8.352371</td><td>8</td><td>0.399828</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllll}\n",
       "  & Df & AIC & BIC & logLik & deviance & Chisq & Chi Df & Pr(>Chisq)\\\\\n",
       "\\hline\n",
       "\tm12 & 9 & 6203.177 & 6264.081 & -3092.588 & 6185.177 & NA & NA & NA\\\\\n",
       "\tm11 & 17 & 6210.824 & 6325.866 & -3088.412 & 6176.824 & 8.352371 & 8 & 0.399828\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Data: dane\n",
       "Models:\n",
       "m12: acc ~ -1 + dur/(pas) + (1 | id)\n",
       "m11: acc ~ -1 + dur/(pas * task) + (1 | id)\n",
       "    Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)\n",
       "m12  9 6203.2 6264.1 -3092.6   6185.2                         \n",
       "m11 17 6210.8 6325.9 -3088.4   6176.8 8.3524      8     0.3998"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m11 <- glmer(acc ~ -1 + dur / (pas * task) + (1|id), dane, family = binomial,\n",
    "                           control = glmerControl(optimizer=\"bobyqa\", optCtrl = list(maxfun = 1000000)))\n",
    "m12 <- glmer(acc ~ -1 + dur / (pas) + (1|id), dane, family = binomial,\n",
    "                           control = glmerControl(optimizer=\"bobyqa\", optCtrl = list(maxfun = 1000000)))\n",
    "anova(m11,m12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
      "  Approximation) [glmerMod]\n",
      " Family: binomial  ( logit )\n",
      "Formula: acc ~ -1 + dur/(pas * task) + (1 | id)\n",
      "   Data: dane\n",
      "Control: glmerControl(optimizer = \"bobyqa\", optCtrl = list(maxfun = 1e+06))\n",
      "\n",
      "     AIC      BIC   logLik deviance df.resid \n",
      "  6210.8   6325.9  -3088.4   6176.8     6403 \n",
      "\n",
      "Scaled residuals: \n",
      "    Min      1Q  Median      3Q     Max \n",
      "-9.2795 -0.9343  0.2059  0.7325  1.4878 \n",
      "\n",
      "Random effects:\n",
      " Groups Name        Variance Std.Dev.\n",
      " id     (Intercept) 0.05804  0.2409  \n",
      "Number of obs: 6420, groups:  id, 26\n",
      "\n",
      "Fixed effects:\n",
      "                    Estimate Std. Error z value Pr(>|z|)    \n",
      "durdur1             -0.12357    0.19562  -0.632 0.527601    \n",
      "durdur2             -0.30714    0.18468  -1.663 0.096289 .  \n",
      "durdur3             -1.48181    0.23225  -6.380 1.77e-10 ***\n",
      "durdur4             -1.34523    0.36078  -3.729 0.000193 ***\n",
      "durdur1:pas          0.21285    0.13561   1.570 0.116519    \n",
      "durdur2:pas          0.48562    0.10290   4.719 2.37e-06 ***\n",
      "durdur3:pas          1.21474    0.10774  11.275  < 2e-16 ***\n",
      "durdur4:pas          1.38657    0.14578   9.511  < 2e-16 ***\n",
      "durdur1:tasklow      0.04159    0.25762   0.161 0.871735    \n",
      "durdur2:tasklow     -0.23869    0.25307  -0.943 0.345580    \n",
      "durdur3:tasklow      0.40631    0.34561   1.176 0.239736    \n",
      "durdur4:tasklow     -0.44744    0.51726  -0.865 0.387031    \n",
      "durdur1:pas:tasklow -0.13793    0.17806  -0.775 0.438553    \n",
      "durdur2:pas:tasklow  0.06858    0.13845   0.495 0.620367    \n",
      "durdur3:pas:tasklow -0.07853    0.15789  -0.497 0.618922    \n",
      "durdur4:pas:tasklow  0.16892    0.21068   0.802 0.422687    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n"
     ]
    }
   ],
   "source": [
    "dane$pas<-as.numeric(dane$pas)\n",
    "print(summary((m1 <- glmer(acc ~ -1 + dur / (pas * task) + (1|id), dane, family = binomial,\n",
    "                           control = glmerControl(optimizer=\"bobyqa\", optCtrl = list(maxfun = 1000000))))), corr = F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(interactionMeans(m1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model mieszany dla analizy poprawności względem oceny na skali PAS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generalized linear mixed model fit by maximum likelihood (Laplace\n",
      "  Approximation) [glmerMod]\n",
      " Family: binomial  ( logit )\n",
      "Formula: acc ~ -1 + pas/task + (1 | id)\n",
      "   Data: dane\n",
      "Control: glmerControl(optimizer = \"bobyqa\", optCtrl = list(maxfun = 1e+06))\n",
      "\n",
      "     AIC      BIC   logLik deviance df.resid \n",
      "  6327.4   6388.3  -3154.7   6309.4     6411 \n",
      "\n",
      "Scaled residuals: \n",
      "    Min      1Q  Median      3Q     Max \n",
      "-9.7052 -0.9551  0.2344  0.7630  1.3231 \n",
      "\n",
      "Random effects:\n",
      " Groups Name        Variance Std.Dev.\n",
      " id     (Intercept) 0.08189  0.2862  \n",
      "Number of obs: 6420, groups:  id, 26\n",
      "\n",
      "Fixed effects:\n",
      "             Estimate Std. Error z value Pr(>|z|)    \n",
      "pas1          0.14035    0.08176   1.717  0.08607 .  \n",
      "pas2          0.47896    0.09520   5.031 4.88e-07 ***\n",
      "pas3          2.12373    0.15613  13.603  < 2e-16 ***\n",
      "pas4          4.20555    0.30921  13.601  < 2e-16 ***\n",
      "pas1:tasklow -0.18480    0.08627  -2.142  0.03218 *  \n",
      "pas2:tasklow  0.16452    0.10493   1.568  0.11691    \n",
      "pas3:tasklow -0.02187    0.19547  -0.112  0.91092    \n",
      "pas4:tasklow -0.96131    0.35479  -2.710  0.00674 ** \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n"
     ]
    }
   ],
   "source": [
    "dane$pas<-as.factor(dane$pas)\n",
    "print(summary((m2 <- glmer(acc ~ -1 + pas / task + (1|id), dane, family = binomial,\n",
    "                           control = glmerControl(optimizer=\"bobyqa\", optCtrl = list(maxfun = 1000000))))), corr = F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(interactionMeans(m2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model mieszany dla analizy oceny na skali PAS względem czasu prezentacji"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dane1=dane[dane$acc==1,]\n",
    "dane1$pas<-as.numeric(dane1$pas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear mixed model fit by REML t-tests use Satterthwaite approximations to\n",
      "  degrees of freedom [lmerMod]\n",
      "Formula: pas ~ -1 + dur/task + (1 | id)\n",
      "   Data: dane1\n",
      "\n",
      "REML criterion at convergence: 11109.9\n",
      "\n",
      "Scaled residuals: \n",
      "    Min      1Q  Median      3Q     Max \n",
      "-3.7559 -0.6135  0.0933  0.7363  3.3641 \n",
      "\n",
      "Random effects:\n",
      " Groups   Name        Variance Std.Dev.\n",
      " id       (Intercept) 0.07655  0.2767  \n",
      " Residual             0.64098  0.8006  \n",
      "Number of obs: 4597, groups:  id, 26\n",
      "\n",
      "Fixed effects:\n",
      "                 Estimate Std. Error        df t value Pr(>|t|)    \n",
      "durdur1         1.321e+00  6.698e-02 5.300e+01  19.721  < 2e-16 ***\n",
      "durdur2         1.771e+00  6.530e-02 4.800e+01  27.125  < 2e-16 ***\n",
      "durdur3         2.828e+00  6.319e-02 4.200e+01  44.755  < 2e-16 ***\n",
      "durdur4         3.458e+00  6.179e-02 3.800e+01  55.968  < 2e-16 ***\n",
      "durdur1:tasklow 4.060e-02  5.584e-02 4.566e+03   0.727    0.467    \n",
      "durdur2:tasklow 2.217e-01  5.107e-02 4.565e+03   4.342 1.44e-05 ***\n",
      "durdur3:tasklow 6.017e-02  4.465e-02 4.566e+03   1.347    0.178    \n",
      "durdur4:tasklow 4.779e-02  4.150e-02 4.565e+03   1.152    0.250    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n"
     ]
    }
   ],
   "source": [
    "print(summary((pm1<-lmer(pas ~ -1 + dur / task + (1|id), dane1))), corr=F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(interactionMeans(pm1))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.2.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}