{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c47ebc4d-d172-4e70-9e16-cf6a0ba7153a",
   "metadata": {},
   "source": [
    "# Multiple Factor Parametric Tests - R"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ecefac5-3aac-4309-a413-d1e62eb0fc81",
   "metadata": {},
   "source": [
    "## Factorial ANOVA\n",
    "\n",
    "* **Samples:** `≥2`\n",
    "* **Levels:** `≥2`\n",
    "* **Between or Within Subjects:** Between\n",
    "* **Reporting:** \"Figure 8 shows an interaction plot with ±1 standard deviation error bars for X1 and X2. A factorial ANOVA indicated a statistically significant effect on Y of X1 (F(1, 56) = 9.35, p < .01) and X2 (F(1, 56) = 4.30, p < .05), but not of the X1×X2 interaction (F(1, 56) = 0.42, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c7fa707e-af25-4dab-a4f6-cddd99a5ca4e",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td> 9.939918</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td>12.271865</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>11.062279</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>12.763591</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td> 7.980861</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>10.468626</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>21.071315</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td>15.270048</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>22.125037</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td>10.955709</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>14.496724</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>12.731080</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td>14.110583</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td>13.587539</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>13.175990</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td>14.313530</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td>11.595727</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>13.723466</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>17.276898</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td>14.945042</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a &  9.939918\\\\\n",
       "\t2 &  2 & a & b & 12.271865\\\\\n",
       "\t3 &  3 & b & a & 11.062279\\\\\n",
       "\t4 &  4 & b & b & 12.763591\\\\\n",
       "\t5 &  5 & a & a &  7.980861\\\\\n",
       "\t6 &  6 & a & b & 10.468626\\\\\n",
       "\t7 &  7 & b & a & 21.071315\\\\\n",
       "\t8 &  8 & b & b & 15.270048\\\\\n",
       "\t9 &  9 & a & a & 22.125037\\\\\n",
       "\t10 & 10 & a & b & 10.955709\\\\\n",
       "\t11 & 11 & b & a & 14.496724\\\\\n",
       "\t12 & 12 & b & b & 12.731080\\\\\n",
       "\t13 & 13 & a & a & 14.110583\\\\\n",
       "\t14 & 14 & a & b & 13.587539\\\\\n",
       "\t15 & 15 & b & a & 13.175990\\\\\n",
       "\t16 & 16 & b & b & 14.313530\\\\\n",
       "\t17 & 17 & a & a & 11.595727\\\\\n",
       "\t18 & 18 & a & b & 13.723466\\\\\n",
       "\t19 & 19 & b & a & 17.276898\\\\\n",
       "\t20 & 20 & b & b & 14.945042\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a |  9.939918 |\n",
       "| 2 |  2 | a | b | 12.271865 |\n",
       "| 3 |  3 | b | a | 11.062279 |\n",
       "| 4 |  4 | b | b | 12.763591 |\n",
       "| 5 |  5 | a | a |  7.980861 |\n",
       "| 6 |  6 | a | b | 10.468626 |\n",
       "| 7 |  7 | b | a | 21.071315 |\n",
       "| 8 |  8 | b | b | 15.270048 |\n",
       "| 9 |  9 | a | a | 22.125037 |\n",
       "| 10 | 10 | a | b | 10.955709 |\n",
       "| 11 | 11 | b | a | 14.496724 |\n",
       "| 12 | 12 | b | b | 12.731080 |\n",
       "| 13 | 13 | a | a | 14.110583 |\n",
       "| 14 | 14 | a | b | 13.587539 |\n",
       "| 15 | 15 | b | a | 13.175990 |\n",
       "| 16 | 16 | b | b | 14.313530 |\n",
       "| 17 | 17 | a | a | 11.595727 |\n",
       "| 18 | 18 | a | b | 13.723466 |\n",
       "| 19 | 19 | b | a | 17.276898 |\n",
       "| 20 | 20 | b | b | 14.945042 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y        \n",
       "1   1 a  a   9.939918\n",
       "2   2 a  b  12.271865\n",
       "3   3 b  a  11.062279\n",
       "4   4 b  b  12.763591\n",
       "5   5 a  a   7.980861\n",
       "6   6 a  b  10.468626\n",
       "7   7 b  a  21.071315\n",
       "8   8 b  b  15.270048\n",
       "9   9 a  a  22.125037\n",
       "10 10 a  b  10.955709\n",
       "11 11 b  a  14.496724\n",
       "12 12 b  b  12.731080\n",
       "13 13 a  a  14.110583\n",
       "14 14 a  b  13.587539\n",
       "15 15 b  a  13.175990\n",
       "16 16 b  b  14.313530\n",
       "17 17 a  a  11.595727\n",
       "18 18 a  b  13.723466\n",
       "19 19 b  a  17.276898\n",
       "20 20 b  b  14.945042"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two between-Ss factors (X1,X2) each w/levels (a,b), and continuous response (Y)\n",
    "df <- read.csv(\"data/2F2LBs.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9c5f3020-cc55-4064-bb7d-867f7d1f37dc",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Coefficient covariances computed by hccm()\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 1 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>DFn</th><th scope=col>DFd</th><th scope=col>SSn</th><th scope=col>SSd</th><th scope=col>F</th><th scope=col>p</th><th scope=col>p&lt;.05</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><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;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>3</td><td>56</td><td>36.93165</td><td>149.7687</td><td>4.603036</td><td>0.005989026</td><td>*</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 1 × 7\n",
       "\\begin{tabular}{lllllll}\n",
       " DFn & DFd & SSn & SSd & F & p & p<.05\\\\\n",
       " <int> & <int> & <dbl> & <dbl> & <dbl> & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t 3 & 56 & 36.93165 & 149.7687 & 4.603036 & 0.005989026 & *\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 1 × 7\n",
       "\n",
       "| DFn &lt;int&gt; | DFd &lt;int&gt; | SSn &lt;dbl&gt; | SSd &lt;dbl&gt; | F &lt;dbl&gt; | p &lt;dbl&gt; | p&lt;.05 &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 3 | 56 | 36.93165 | 149.7687 | 4.603036 | 0.005989026 | * |\n",
       "\n"
      ],
      "text/plain": [
       "  DFn DFd SSn      SSd      F        p           p<.05\n",
       "1 3   56  36.93165 149.7687 4.603036 0.005989026 *    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ez) # for ezANOVA\n",
    "\n",
    "df$S = factor(df$S) # Subject id is nominal\n",
    "df$X1 = factor(df$X1) # X1 is a 2-level factor\n",
    "df$X2 = factor(df$X2) # X2 is a 2-level factor\n",
    "\n",
    "m = ezANOVA(dv=Y, between=c(X1,X2), wid=S, type=3, data=df) # use c() for >1 factors\n",
    "m$Levene # if p<.05, we have a violation of homoscedasticity, so use a White-adjusted ANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8ba5ecc7-a7e6-45ad-8879-8892536cb21c",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Coefficient covariances computed by hccm()\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 3 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Effect</th><th scope=col>DFn</th><th scope=col>DFd</th><th scope=col>F</th><th scope=col>p</th><th scope=col>p&lt;.05</th></tr>\n",
       "\t<tr><th></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></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>2</th><td>X1   </td><td>1</td><td>56</td><td>8.7309193</td><td>0.004569383</td><td>*</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>X2   </td><td>1</td><td>56</td><td>4.0094897</td><td>0.050096183</td><td> </td></tr>\n",
       "\t<tr><th scope=row>4</th><td>X1:X2</td><td>1</td><td>56</td><td>0.3876081</td><td>0.536086422</td><td> </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 3 × 6\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & Effect & DFn & DFd & F & p & p<.05\\\\\n",
       "  & <chr> & <dbl> & <dbl> & <dbl> & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t2 & X1    & 1 & 56 & 8.7309193 & 0.004569383 & *\\\\\n",
       "\t3 & X2    & 1 & 56 & 4.0094897 & 0.050096183 &  \\\\\n",
       "\t4 & X1:X2 & 1 & 56 & 0.3876081 & 0.536086422 &  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 3 × 6\n",
       "\n",
       "| <!--/--> | Effect &lt;chr&gt; | DFn &lt;dbl&gt; | DFd &lt;dbl&gt; | F &lt;dbl&gt; | p &lt;dbl&gt; | p&lt;.05 &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|\n",
       "| 2 | X1    | 1 | 56 | 8.7309193 | 0.004569383 | * |\n",
       "| 3 | X2    | 1 | 56 | 4.0094897 | 0.050096183 | <!----> |\n",
       "| 4 | X1:X2 | 1 | 56 | 0.3876081 | 0.536086422 | <!----> |\n",
       "\n"
      ],
      "text/plain": [
       "  Effect DFn DFd F         p           p<.05\n",
       "2 X1     1   56  8.7309193 0.004569383 *    \n",
       "3 X2     1   56  4.0094897 0.050096183      \n",
       "4 X1:X2  1   56  0.3876081 0.536086422      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m= ezANOVA(dv=Y, between=c(X1,X2), wid=S, type=3, data=df, white.adjust=TRUE) # heteroscedastic\n",
    "m$ANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "16bf5e4a-fa2e-481f-80c5-2b125fea8f32",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 4 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><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;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td> 1</td><td> 60.039468</td><td>60.039468</td><td>9.3545564</td><td>0.003408605</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td> 1</td><td> 27.571854</td><td>27.571854</td><td>4.2958818</td><td>0.042819437</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td> 1</td><td>  2.665445</td><td> 2.665445</td><td>0.4152944</td><td>0.521925508</td></tr>\n",
       "\t<tr><th scope=row>Residuals</th><td>56</td><td>359.419527</td><td> 6.418206</td><td>       NA</td><td>         NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 4 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
       "  & <int> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 &  1 &  60.039468 & 60.039468 & 9.3545564 & 0.003408605\\\\\n",
       "\tX2 &  1 &  27.571854 & 27.571854 & 4.2958818 & 0.042819437\\\\\n",
       "\tX1:X2 &  1 &   2.665445 &  2.665445 & 0.4152944 & 0.521925508\\\\\n",
       "\tResiduals & 56 & 359.419527 &  6.418206 &        NA &          NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 4 × 5\n",
       "\n",
       "| <!--/--> | Df &lt;int&gt; | Sum Sq &lt;dbl&gt; | Mean Sq &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| X1 |  1 |  60.039468 | 60.039468 | 9.3545564 | 0.003408605 |\n",
       "| X2 |  1 |  27.571854 | 27.571854 | 4.2958818 | 0.042819437 |\n",
       "| X1:X2 |  1 |   2.665445 |  2.665445 | 0.4152944 | 0.521925508 |\n",
       "| Residuals | 56 | 359.419527 |  6.418206 |        NA |          NA |\n",
       "\n"
      ],
      "text/plain": [
       "          Df Sum Sq     Mean Sq   F value   Pr(>F)     \n",
       "X1         1  60.039468 60.039468 9.3545564 0.003408605\n",
       "X2         1  27.571854 27.571854 4.2958818 0.042819437\n",
       "X1:X2      1   2.665445  2.665445 0.4152944 0.521925508\n",
       "Residuals 56 359.419527  6.418206        NA          NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the following also performs the same factorial ANOVA\n",
    "m = aov(Y ~ X1*X2, data=df)\n",
    "anova(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7096da78-01b5-4c53-8bbc-3c19cefe232f",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,20,by=5), labels=seq(0,20,by=5), limits=c(0,20), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48a1104e-721e-4dcc-ae03-4c685249f497",
   "metadata": {},
   "source": [
    "## Linear Model (LM)\n",
    "\n",
    "* **Samples:** `≥2`\n",
    "* **Levels:** `≥2`\n",
    "* **Between or Within Subjects:** Between\n",
    "* **Reporting:** \"Figure 8 shows an interaction plot with ±1 standard deviation error bars for X1 and X2. An analysis of variance indicated a statistically significant effect on Y of X1 (F(1, 56) = 9.35, p < .01) and X2 (F(1, 56) = 4.30, p < .05), but not of the X1×X2 interaction (F(1, 56) = 0.42, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f078a813-de50-482c-89f7-29e81d9cdfd2",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 1</td><td>a</td><td>a</td><td> 9.939918</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 2</td><td>a</td><td>b</td><td>12.271865</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 3</td><td>b</td><td>a</td><td>11.062279</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 4</td><td>b</td><td>b</td><td>12.763591</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 5</td><td>a</td><td>a</td><td> 7.980861</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 6</td><td>a</td><td>b</td><td>10.468626</td></tr>\n",
       "\t<tr><th scope=row>7</th><td> 7</td><td>b</td><td>a</td><td>21.071315</td></tr>\n",
       "\t<tr><th scope=row>8</th><td> 8</td><td>b</td><td>b</td><td>15.270048</td></tr>\n",
       "\t<tr><th scope=row>9</th><td> 9</td><td>a</td><td>a</td><td>22.125037</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>10</td><td>a</td><td>b</td><td>10.955709</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>11</td><td>b</td><td>a</td><td>14.496724</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>12</td><td>b</td><td>b</td><td>12.731080</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>13</td><td>a</td><td>a</td><td>14.110583</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>14</td><td>a</td><td>b</td><td>13.587539</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>15</td><td>b</td><td>a</td><td>13.175990</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>16</td><td>b</td><td>b</td><td>14.313530</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>17</td><td>a</td><td>a</td><td>11.595727</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>18</td><td>a</td><td>b</td><td>13.723466</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>19</td><td>b</td><td>a</td><td>17.276898</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>20</td><td>b</td><td>b</td><td>14.945042</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 &  1 & a & a &  9.939918\\\\\n",
       "\t2 &  2 & a & b & 12.271865\\\\\n",
       "\t3 &  3 & b & a & 11.062279\\\\\n",
       "\t4 &  4 & b & b & 12.763591\\\\\n",
       "\t5 &  5 & a & a &  7.980861\\\\\n",
       "\t6 &  6 & a & b & 10.468626\\\\\n",
       "\t7 &  7 & b & a & 21.071315\\\\\n",
       "\t8 &  8 & b & b & 15.270048\\\\\n",
       "\t9 &  9 & a & a & 22.125037\\\\\n",
       "\t10 & 10 & a & b & 10.955709\\\\\n",
       "\t11 & 11 & b & a & 14.496724\\\\\n",
       "\t12 & 12 & b & b & 12.731080\\\\\n",
       "\t13 & 13 & a & a & 14.110583\\\\\n",
       "\t14 & 14 & a & b & 13.587539\\\\\n",
       "\t15 & 15 & b & a & 13.175990\\\\\n",
       "\t16 & 16 & b & b & 14.313530\\\\\n",
       "\t17 & 17 & a & a & 11.595727\\\\\n",
       "\t18 & 18 & a & b & 13.723466\\\\\n",
       "\t19 & 19 & b & a & 17.276898\\\\\n",
       "\t20 & 20 & b & b & 14.945042\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 |  1 | a | a |  9.939918 |\n",
       "| 2 |  2 | a | b | 12.271865 |\n",
       "| 3 |  3 | b | a | 11.062279 |\n",
       "| 4 |  4 | b | b | 12.763591 |\n",
       "| 5 |  5 | a | a |  7.980861 |\n",
       "| 6 |  6 | a | b | 10.468626 |\n",
       "| 7 |  7 | b | a | 21.071315 |\n",
       "| 8 |  8 | b | b | 15.270048 |\n",
       "| 9 |  9 | a | a | 22.125037 |\n",
       "| 10 | 10 | a | b | 10.955709 |\n",
       "| 11 | 11 | b | a | 14.496724 |\n",
       "| 12 | 12 | b | b | 12.731080 |\n",
       "| 13 | 13 | a | a | 14.110583 |\n",
       "| 14 | 14 | a | b | 13.587539 |\n",
       "| 15 | 15 | b | a | 13.175990 |\n",
       "| 16 | 16 | b | b | 14.313530 |\n",
       "| 17 | 17 | a | a | 11.595727 |\n",
       "| 18 | 18 | a | b | 13.723466 |\n",
       "| 19 | 19 | b | a | 17.276898 |\n",
       "| 20 | 20 | b | b | 14.945042 |\n",
       "\n"
      ],
      "text/plain": [
       "   S  X1 X2 Y        \n",
       "1   1 a  a   9.939918\n",
       "2   2 a  b  12.271865\n",
       "3   3 b  a  11.062279\n",
       "4   4 b  b  12.763591\n",
       "5   5 a  a   7.980861\n",
       "6   6 a  b  10.468626\n",
       "7   7 b  a  21.071315\n",
       "8   8 b  b  15.270048\n",
       "9   9 a  a  22.125037\n",
       "10 10 a  b  10.955709\n",
       "11 11 b  a  14.496724\n",
       "12 12 b  b  12.731080\n",
       "13 13 a  a  14.110583\n",
       "14 14 a  b  13.587539\n",
       "15 15 b  a  13.175990\n",
       "16 16 b  b  14.313530\n",
       "17 17 a  a  11.595727\n",
       "18 18 a  b  13.723466\n",
       "19 19 b  a  17.276898\n",
       "20 20 b  b  14.945042"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two between-Ss factors (X1,X2) each w/levels (a,b), and continuous response (Y)\n",
    "df <- read.csv(\"data/2F2LBs.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "19bdbacd-d73b-407a-8ab2-66a471213b20",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 4 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Df</th><th scope=col>Sum Sq</th><th scope=col>Mean Sq</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><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;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>X1</th><td> 1</td><td> 60.039468</td><td>60.039468</td><td>9.3545564</td><td>0.003408605</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td> 1</td><td> 27.571854</td><td>27.571854</td><td>4.2958818</td><td>0.042819437</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td> 1</td><td>  2.665445</td><td> 2.665445</td><td>0.4152944</td><td>0.521925508</td></tr>\n",
       "\t<tr><th scope=row>Residuals</th><td>56</td><td>359.419527</td><td> 6.418206</td><td>       NA</td><td>         NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 4 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & Sum Sq & Mean Sq & F value & Pr(>F)\\\\\n",
       "  & <int> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tX1 &  1 &  60.039468 & 60.039468 & 9.3545564 & 0.003408605\\\\\n",
       "\tX2 &  1 &  27.571854 & 27.571854 & 4.2958818 & 0.042819437\\\\\n",
       "\tX1:X2 &  1 &   2.665445 &  2.665445 & 0.4152944 & 0.521925508\\\\\n",
       "\tResiduals & 56 & 359.419527 &  6.418206 &        NA &          NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 4 × 5\n",
       "\n",
       "| <!--/--> | Df &lt;int&gt; | Sum Sq &lt;dbl&gt; | Mean Sq &lt;dbl&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| X1 |  1 |  60.039468 | 60.039468 | 9.3545564 | 0.003408605 |\n",
       "| X2 |  1 |  27.571854 | 27.571854 | 4.2958818 | 0.042819437 |\n",
       "| X1:X2 |  1 |   2.665445 |  2.665445 | 0.4152944 | 0.521925508 |\n",
       "| Residuals | 56 | 359.419527 |  6.418206 |        NA |          NA |\n",
       "\n"
      ],
      "text/plain": [
       "          Df Sum Sq     Mean Sq   F value   Pr(>F)     \n",
       "X1         1  60.039468 60.039468 9.3545564 0.003408605\n",
       "X2         1  27.571854 27.571854 4.2958818 0.042819437\n",
       "X1:X2      1   2.665445  2.665445 0.4152944 0.521925508\n",
       "Residuals 56 359.419527  6.418206        NA          NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df$S = factor(df$S) # Subject id is nominal (unused)\n",
    "df$X1 = factor(df$X1) # X1 is a 2-level factor\n",
    "df$X2 = factor(df$X2) # X2 is a 2-level factor\n",
    "m = lm(Y ~ X1*X2, data=df)\n",
    "anova(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0a25d332-bd7b-4ee2-92c0-fa053258bd1c",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(ggthemes)\n",
    "library(scales)\n",
    "library(plyr)\n",
    "\n",
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,20,by=5), labels=seq(0,20,by=5), limits=c(0,20), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cef44a6d-3ed8-437d-8ac1-f3dcb9ea680b",
   "metadata": {},
   "source": [
    "## Factorial Repeated Measures ANOVA\n",
    "\n",
    "* **Samples:** `≥2`\n",
    "* **Levels:** `≥2`\n",
    "* **Between or Within Subjects:** Within\n",
    "* **Reporting:** \"Figure 9 shows an interaction plot with ±1 standard deviation error bars for X1 and X2. A factorial repeated measures ANOVA indicated a statistically significant effect on Y of X1 (F(1, 14) = 5.45, p < .05), but not of X2 (F(1, 14) = 0.18, n.s.), or of the X1×X2 interaction (F(1, 14) = 0.12, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "40c6aa5f-3555-40c9-9322-d659f62138d3",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td>a</td><td>a</td><td>11.4749213</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>1</td><td>a</td><td>b</td><td>14.8431021</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>1</td><td>b</td><td>a</td><td> 0.1430649</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>1</td><td>b</td><td>b</td><td>15.0210806</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>2</td><td>a</td><td>a</td><td>16.9487115</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>2</td><td>a</td><td>b</td><td>12.9088880</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>2</td><td>b</td><td>a</td><td> 7.3433619</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>2</td><td>b</td><td>b</td><td>11.1885220</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>3</td><td>a</td><td>a</td><td>12.3397073</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>3</td><td>a</td><td>b</td><td>14.8390688</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>3</td><td>b</td><td>a</td><td>21.5131754</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>3</td><td>b</td><td>b</td><td> 0.2390247</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>4</td><td>a</td><td>a</td><td>11.7081257</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>4</td><td>a</td><td>b</td><td>13.8740498</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>4</td><td>b</td><td>a</td><td> 4.3615137</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>4</td><td>b</td><td>b</td><td> 2.3686943</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>5</td><td>a</td><td>a</td><td>15.3668561</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>5</td><td>a</td><td>b</td><td>13.6340391</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>5</td><td>b</td><td>a</td><td> 4.9401806</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>5</td><td>b</td><td>b</td><td>13.5781464</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1 & a & a & 11.4749213\\\\\n",
       "\t2 & 1 & a & b & 14.8431021\\\\\n",
       "\t3 & 1 & b & a &  0.1430649\\\\\n",
       "\t4 & 1 & b & b & 15.0210806\\\\\n",
       "\t5 & 2 & a & a & 16.9487115\\\\\n",
       "\t6 & 2 & a & b & 12.9088880\\\\\n",
       "\t7 & 2 & b & a &  7.3433619\\\\\n",
       "\t8 & 2 & b & b & 11.1885220\\\\\n",
       "\t9 & 3 & a & a & 12.3397073\\\\\n",
       "\t10 & 3 & a & b & 14.8390688\\\\\n",
       "\t11 & 3 & b & a & 21.5131754\\\\\n",
       "\t12 & 3 & b & b &  0.2390247\\\\\n",
       "\t13 & 4 & a & a & 11.7081257\\\\\n",
       "\t14 & 4 & a & b & 13.8740498\\\\\n",
       "\t15 & 4 & b & a &  4.3615137\\\\\n",
       "\t16 & 4 & b & b &  2.3686943\\\\\n",
       "\t17 & 5 & a & a & 15.3668561\\\\\n",
       "\t18 & 5 & a & b & 13.6340391\\\\\n",
       "\t19 & 5 & b & a &  4.9401806\\\\\n",
       "\t20 & 5 & b & b & 13.5781464\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 | 1 | a | a | 11.4749213 |\n",
       "| 2 | 1 | a | b | 14.8431021 |\n",
       "| 3 | 1 | b | a |  0.1430649 |\n",
       "| 4 | 1 | b | b | 15.0210806 |\n",
       "| 5 | 2 | a | a | 16.9487115 |\n",
       "| 6 | 2 | a | b | 12.9088880 |\n",
       "| 7 | 2 | b | a |  7.3433619 |\n",
       "| 8 | 2 | b | b | 11.1885220 |\n",
       "| 9 | 3 | a | a | 12.3397073 |\n",
       "| 10 | 3 | a | b | 14.8390688 |\n",
       "| 11 | 3 | b | a | 21.5131754 |\n",
       "| 12 | 3 | b | b |  0.2390247 |\n",
       "| 13 | 4 | a | a | 11.7081257 |\n",
       "| 14 | 4 | a | b | 13.8740498 |\n",
       "| 15 | 4 | b | a |  4.3615137 |\n",
       "| 16 | 4 | b | b |  2.3686943 |\n",
       "| 17 | 5 | a | a | 15.3668561 |\n",
       "| 18 | 5 | a | b | 13.6340391 |\n",
       "| 19 | 5 | b | a |  4.9401806 |\n",
       "| 20 | 5 | b | b | 13.5781464 |\n",
       "\n"
      ],
      "text/plain": [
       "   S X1 X2 Y         \n",
       "1  1 a  a  11.4749213\n",
       "2  1 a  b  14.8431021\n",
       "3  1 b  a   0.1430649\n",
       "4  1 b  b  15.0210806\n",
       "5  2 a  a  16.9487115\n",
       "6  2 a  b  12.9088880\n",
       "7  2 b  a   7.3433619\n",
       "8  2 b  b  11.1885220\n",
       "9  3 a  a  12.3397073\n",
       "10 3 a  b  14.8390688\n",
       "11 3 b  a  21.5131754\n",
       "12 3 b  b   0.2390247\n",
       "13 4 a  a  11.7081257\n",
       "14 4 a  b  13.8740498\n",
       "15 4 b  a   4.3615137\n",
       "16 4 b  b   2.3686943\n",
       "17 5 a  a  15.3668561\n",
       "18 5 a  b  13.6340391\n",
       "19 5 b  a   4.9401806\n",
       "20 5 b  b  13.5781464"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two within-Ss factors (X1,X2) each w/levels (a,b), and continuous response (Y)\n",
    "df <- read.csv(\"data/2F2LWs.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "96b0bba2-1307-44cc-9912-e962598717ee",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NULL"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ez) # for ezANOVA\n",
    "\n",
    "df$S = factor(df$S) # Subject id is nominal\n",
    "df$X1 = factor(df$X1) # X1 is a 2-level factor\n",
    "df$X2 = factor(df$X2) # X2 is a 2-level factor\n",
    "\n",
    "m = ezANOVA(dv=Y, within=c(X1,X2), wid=S, type=3, data=df) # use c() for >1 factors\n",
    "m$Mauchly # p<.05 indicates a sphericity violation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "645b631f-7056-4bb8-b0fe-2a37d3919c28",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 3 × 7</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Effect</th><th scope=col>DFn</th><th scope=col>DFd</th><th scope=col>F</th><th scope=col>p</th><th scope=col>p&lt;.05</th><th scope=col>ges</th></tr>\n",
       "\t<tr><th></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;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>2</th><td>X1   </td><td>1</td><td>14</td><td>5.4537088</td><td>0.03492658</td><td>*</td><td>0.070392015</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>X2   </td><td>1</td><td>14</td><td>0.1797949</td><td>0.67799256</td><td> </td><td>0.003762924</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>X1:X2</td><td>1</td><td>14</td><td>0.1223175</td><td>0.73173975</td><td> </td><td>0.002019078</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 3 × 7\n",
       "\\begin{tabular}{r|lllllll}\n",
       "  & Effect & DFn & DFd & F & p & p<.05 & ges\\\\\n",
       "  & <chr> & <dbl> & <dbl> & <dbl> & <dbl> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t2 & X1    & 1 & 14 & 5.4537088 & 0.03492658 & * & 0.070392015\\\\\n",
       "\t3 & X2    & 1 & 14 & 0.1797949 & 0.67799256 &   & 0.003762924\\\\\n",
       "\t4 & X1:X2 & 1 & 14 & 0.1223175 & 0.73173975 &   & 0.002019078\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 3 × 7\n",
       "\n",
       "| <!--/--> | Effect &lt;chr&gt; | DFn &lt;dbl&gt; | DFd &lt;dbl&gt; | F &lt;dbl&gt; | p &lt;dbl&gt; | p&lt;.05 &lt;chr&gt; | ges &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|\n",
       "| 2 | X1    | 1 | 14 | 5.4537088 | 0.03492658 | * | 0.070392015 |\n",
       "| 3 | X2    | 1 | 14 | 0.1797949 | 0.67799256 | <!----> | 0.003762924 |\n",
       "| 4 | X1:X2 | 1 | 14 | 0.1223175 | 0.73173975 | <!----> | 0.002019078 |\n",
       "\n"
      ],
      "text/plain": [
       "  Effect DFn DFd F         p          p<.05 ges        \n",
       "2 X1     1   14  5.4537088 0.03492658 *     0.070392015\n",
       "3 X2     1   14  0.1797949 0.67799256       0.003762924\n",
       "4 X1:X2  1   14  0.1223175 0.73173975       0.002019078"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m$ANOVA # use if no violation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8a1f1fc4-6b57-409c-ba1d-0b7ecb179aac",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$GGe.DFn</dt>\n",
       "\t\t<dd></dd>\n",
       "\t<dt>$GGe.DFd</dt>\n",
       "\t\t<dd></dd>\n",
       "\t<dt>$HFe.DFn</dt>\n",
       "\t\t<dd></dd>\n",
       "\t<dt>$HFe.DFd</dt>\n",
       "\t\t<dd></dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$GGe.DFn] \n",
       "\\item[\\$GGe.DFd] \n",
       "\\item[\\$HFe.DFn] \n",
       "\\item[\\$HFe.DFd] \n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$GGe.DFn\n",
       ":   \n",
       "$GGe.DFd\n",
       ":   \n",
       "$HFe.DFn\n",
       ":   \n",
       "$HFe.DFd\n",
       ":   \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$GGe.DFn\n",
       "numeric(0)\n",
       "\n",
       "$GGe.DFd\n",
       "numeric(0)\n",
       "\n",
       "$HFe.DFn\n",
       "numeric(0)\n",
       "\n",
       "$HFe.DFd\n",
       "numeric(0)\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if there is a sphericity violation, report the Greenhouse-Geisser or Huynh-Feldt correction\n",
    "p = match(m$Sphericity$Effect, m$ANOVA$Effect) # positions of within-Ss effects in m$ANOVA\n",
    "m$Sphericity$GGe.DFn = m$Sphericity$GGe * m$ANOVA$DFn[p] # Greenhouse-Geisser DFs\n",
    "m$Sphericity$GGe.DFd = m$Sphericity$GGe * m$ANOVA$DFd[p]\n",
    "m$Sphericity$HFe.DFn = m$Sphericity$HFe * m$ANOVA$DFn[p] # Huynh-Feldt DFs\n",
    "m$Sphericity$HFe.DFd = m$Sphericity$HFe * m$ANOVA$DFd[p]\n",
    "m$Sphericity # show results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "df267f65-f620-44ca-9046-3165759d2347",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Error: S\n",
       "          Df Sum Sq Mean Sq F value Pr(>F)\n",
       "Residuals 14  592.5   42.32               \n",
       "\n",
       "Error: S:X1\n",
       "          Df Sum Sq Mean Sq F value Pr(>F)  \n",
       "X1         1  160.3  160.28   5.454 0.0349 *\n",
       "Residuals 14  411.4   29.39                 \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Error: S:X2\n",
       "          Df Sum Sq Mean Sq F value Pr(>F)\n",
       "X2         1    8.0    8.00    0.18  0.678\n",
       "Residuals 14  622.5   44.47               \n",
       "\n",
       "Error: S:X1:X2\n",
       "          Df Sum Sq Mean Sq F value Pr(>F)\n",
       "X1:X2      1    4.3    4.28   0.122  0.732\n",
       "Residuals 14  490.1   35.01               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the following also performs the equivalent repeated measures ANOVA, but does not address sphericity\n",
    "m = aov(Y ~ X1*X2 + Error(S/(X1*X2)), data=df)\n",
    "summary(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "040dbc37-94be-4934-8559-f21a5ece3c03",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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t4EpRvKXfTpqQkJCUlGTrWgBkSUlJOXPmjK2rQJHm5ORUsmRJW1dRPNg22CXt/TK4S//Pjjb6X2RkSMMSVxpqGIZksVguuzYtLa0gSoTJ8E8FKGr4qcRV2aCDR7Flu2BnnPp17EM9x68t2eXd1V8Nb5p5hq5MmTLSyUtOzZ07d04qfbmJU3Z2duXK0QoFV8KsWKCoYVYskO9sdI+dcfyHAa3uG7+p9vORfy3IluokeXl7O+jCgQMnc2yQun//IalOnTqFWycAAEDxYZNgF/vL8wG9P41pM2nlqnc6Vc5VgmOr1ndatGHVqvhsC1PX/bLygrzatKlRqIUCAAAUIzYIdqe+e+7RKTu9X/hxwYhmed0JWbX3E/7OFyJDwzYkWJek7gsfP/uoXeMn+99ZmIUCAAAUK4X/5InNIXXuCNvndf/Q3k1ccq2q1mXU4DbuUvKOyR1ajlxj1At87KHm5eP//Wnu1xviG4/6dW1oC26Owo3iHjugqOEeOyDfFX6w+6anJejbvFc1n3Rg/YiakqT4nV+MH/3u1yv/OXaxRIXb/R4cNH7c083KFl6VMB+CHVDUEOyAfFf4wQ6wDYIdUNQQ7IB8VxSePAEAAIB8QLADAAAwCYIdAACASdj+WbEAANP65x8dO3bZtYbheO6cg4OD0u98rVBBjRsXWmmAKRHsAAAFZtIkzZ59uZUWKcekiR499N13BV8TYGYEOwBAgencWZUq5V4YHq6kJA0ZIunixYt2dnZOTk6S5ONT6PUBZkO7E9wqaHcCFBV16ujcOZ08SbsTIN8xeQIAAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCYIdAACASRDsAAAATIJgBwAAYBIEOwAAAJMg2AEAAJgEwQ4AAMAkCHYAAAAmQbADAAAwCQdbF5A/DMOIi4uzdRUo0tLS0iQlJSWlfwPAVlzT0iyGEXf+vGEYklJTU8+fP2/rolCkOTo6Ojs727qK4sEkwc5isbi4uNi6ChRpKSkpycnJDg4O/FMBbMtisaR/aBuGkZSUZGdnx08lrszOjguM18okwU6Sg4N53gsKQvq5ATs7O/6pADZmsUhycHBI/6m0WCz8VAL5hQgMAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQIdgAAACZBsAMAADAJgh0AAIBJEOwAAABMgmAHAABgEgQ7AAAAkyDYAQAAmATBDgAAwCQcbF0AULC2b1fbtunfOhpGOUkWy5XGb9okL69CqAsAgPxHsIPJ2dvL3V2SDMNIS0uzs7OzWHTunE6dUoUKKlUqj/EAABRTBDuYXP362rdPkpKTU86ePevi4uLq6jp9ugYP1uTJ6tvX1vUBAJB/uMcOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAnbBbvkQwtfalfR3mLxDf0v55q4z7pa8tL09X9tUikAAECx4GCTo17Y+cULjz0Xvkdl8lobGxsruTR7ZGhAjRzLq7QuVyjVAQAAFEu2CHbnvnykeZ/ffJ6L2Nj+h4ZB8y5ZHxsbK1UIeCE01NcG1QEAABRTtrgUm+LQ8LkfNv8+vWcd5zzXx8bGSmXLli3ksgAAAIo3W5yx8wh6Y/KV1sfGxkp1ypaVlBp/8lisxb1ieVfbXDMGAAAoPopgXko9ezZeiv/zvZ7TZyzYfjpZsnOr3a7/uKmhj/m4XGYbwzASExMLtUwUN6mpqZJSUlISEhKSk+0lx+Tk5ISEVFvXBdxynAxDhpGYkGAYhqS0tLSEhARbF4Uizd7e3tHR0dZVFA9FMNjFxsZKWv/1F+6PDwkbXsvt7O4Vs6d9ObVv653xG5YEe1vy2sYwjLi4uEIuFEVNmaAguwMHLrfWUcq89m9/vp80PiEhIS6O3weAwuaYlmbJ9qGdmprKBziuzNnZmWB3jYpgsCsZ8GpExGD3Rvd1vL1U+pIBQ/o09Ws+atlL435+Yk5npzy2sVgspUqVKtQyUfTY29tb7HLeNpqWZjl4UCVLGhUrSkpLS8vsniPJ2dm5VCk+KYDCZmdnJ4ulVKlShmHEx8fb29u7uFzuegwgSfb29rYuodgogsHOpW6HnnVzLnJsMHx459GPfrdq1VZ1vjOPbSwWi7Nz3lMxcAtZvjz3kpgYeXqqfXvLwoXJyclnz551cXFxdXW1TJcGy9HR0dmZYAcUOotFFouzs3N6sLOzs+MDHMgvxeXJEyUqVCgrcbYeAADgsopesIv754cZk1+ftzE5x9LoHTtOSV5eXjaqCgAAoMgrepdiS55d8ebI90+3dm76ywif9Pvp0qJ/Cpn8m+yaPvRAbRtXBwAAUGTZINjFrJo26ecjkqR9m1OkqMVhIbFlJKlKp5FD7ynXKmRqvwVBc0a2aPjLww/cWdUueseKb79bH13qzgkzX6h7xT0DAADcymwQ7M6s+ywsbEPW6+OrPgxbJUlqUnbA0HvKqUqPT35f2WrSpE9+WvzJypMXSnh6N3t0zLBXX3ygLtOmAAAALssGwa5OyHoj5MpDHKr4Bb/rF/xu4RQEAABgCkVv8gQAAABuCMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHQAAgEkQ7AAAAEyCYAcAAGASBDsAAACTINgBAACYBMEOAADAJAh2AAAAJkGwAwAAMAmCHW4dZzd9PKCxZynnx37ItfzvaQ/f5mK5ZHlORvSqyY/71fF0cXJxr9Wi76TVp7KtTNz37ajAJlXcnF3Led3Vc+ySqLTL7yjtwCddy5UP/PywcZV6E/dHjn+0Vd0qpV1Kla/Z6N5np/0RfbmhcVs+HRLgU6mUk3OZ6s0efHXBoZTMVaf//mjIfY29PFxdPb0aBTz74d+nJV38c3TTUvWHrjp3lRIAAMULwQ63BOPU75N7NO82da+Ta+7lbwU2uSd0l1Opq+xg9zvd7w1ZXuaxqZHLFkzrU3rpqPu6Td5pjWYxkU/d8/AXqQ++F7ly2dyQev+GdQt8c+dlYlvSxgkPDNre84u5j1W3XPGIpyOD23WftKPBkGk/Lv1p1uiA8/OH+Pd4b29eQ49+3qf9gAi7h96JXPXr/HGtD0990P/F1YmSlLL9rcB2wd+p+/gvFy2a/UrHc18/G9D7o8NyuXvCtxMrfxbUd+7RK79vAEDxYgAmduqUIRldukTPuK+y/5jIf9e+XF9Ofb6fNs2QjDlzjOgZ91UJGP/byR1jfOTU5/vL7ifl58dLq/LTSxKsry8uHlBJ7k8sTjIMw9jwcl3VHrYuY13yjh+nfbJkz4U8d3RoalunUl0/i861+OLcLvKZsDPbkvNf9/JwaTV5f+aCw++2llpOibp0n5tD6sjj0e/iMl4ffM/P3jHgk2jDSF0xsLwq9P/pYubh32kl+U07bhiGkbJp9O2WSgMWx126R6BgeXsb5csbhpGWlhYdHR0bG2vrggDz4IwdbgluXT/6e+HoFuVynyRz6/rRpsWvtil/5ZNn0sGtW8/Z+fm3d7K+dr7v4e5lzyxdul7Stm+/2V239+MtMtY51O826Ml767jksZu01ZPf/K3CwJcf87xqxaV6fR1zYe3/amUucHZ2lhwc7C8ZeWDp0r2O/g90zjwXWeOBB+5IXrl4RaIsd09Yt/33sADnjFXVatZ00IkTJyTJvun/RnU689mEj45ctRgAQDFBsMMtwala9Qp5/WO/3PLcEhMTZV+iRLZUVblyJR3ds+eCLmzZskc+XmmfDg7wqeJexrPW3Q+PX34073vs/vrxx+PlOwe2uDSdXVZqYvzZ6IObIt98bPzqmk+NeKTiJSN2796t6nXqOGUtqVGnTonkXbv2y1KygrePd3nHjBXxS35amVKhXbv66S/du3Zrk7puwaJTuXcJACimHGxdQL5JSUm5+iDcalJSHCTDMFJTUlJTUyUZkozUtLQ0yS41NTUlJf1WuNQ0QzJSL/uvqLr3bQ7Jf/2xIbnrHekn985t2XZIqnj2TMqxY8cNu+MTnox97Pkp371u/9+St0aM79zNfvO6UXVznwc8tHLVQfvWre9KtR5m31t31xu9MXP1T/Utr0qSyj29+PgHHa0LB1Z8YE68HKq0fz5i5Rud3S4pMTXmTJzcSrlmX1HKzU1nYk7lHJt29NunB3yS0PXTl9parGvc27RtkDZh5cqkJx/gdzwUHnvDsEgpKSmGYUgyDIMPcFyZnZ2dnR0fU9fEJMHOMIz4+HhbV4Eix3LhQmkpNTU1Pj4+/b+QVENKSUxMTJRcEhMT4+NjNs4cNuC17w+WkEPDxGz/is6lL4/qNu/EzC5Sxyceq9Jj+rOjms18vl3VuL+nDxy93FFaP7Sa41BJ0pGtUaH9fw2VpHbP9Crz4YTWJV6JvaSe6mXl0dQ9OT4+WZLk0Wvm6rYXJSlpybCO7/zj1vTFz0LvrWBxKFc7s5Kmw77/qUf04a3LPpra6549UxbM6u1lzYvH5/S8a+jyGq+GektpSRey/wRcTE6TkXLmz/BBr0z74a/9Z+096zZv7Lp7+Y4aL3/z4YMe8fHxiQcWvPlS2Nerd0Ur5dCEEQsajutYOWn9BP9uka0jfglr7VYAfxlABjfDULYP7fSfUNuWhCKuRIkSLi553eCCS9n0Dj+ggGVMnjAMIykpKTr69+yTJzvIr0QAACAASURBVGZPXxvW1culahMfT9mXyZo8kRadtTxrRsWZtW90quksSRbXWp1f/+KVFnK8f8Ivv34/vLF024C5v/7669J3Hyhnd/voNZ/eLzUZNP/XbJa++0A5u2qNS6ruyxsvLTNx3YOl5ej7yZkrvJX4ZcFVVKrvj4npL6NmB5Z1dHRQk4mznnZTrZc2ZBua9v3DjvLp2cHdUvHeV+etWLf07e5V7CXXDrOsBzi1oE9V+2qdxn79a2gHizwqOJW4Y8KONMNI3Tu1vVv5bnPymKEB5CMmTwAFhhObuHXF/T1+SuJTSzZ92TPnjWsx3+S1vGyrlxftO3V87+4DJ6L3/jTK8+QeNerQp0O7B7rcWVYJbrXbta284YufSz79/suNjFSpnE+7LNZVL7b10NmzZy8p5HD4yAUXVCGgVdnMRcaxvyI+Gexnafj6v9YlJe+8s4Hiduw4JEknvnzu+dX+wb3KSfKuX1+Hd+26mLW//bt2JZcw1qywPDLju/HdXZe89tqSso8OuDNh9RffnZKkje+MmOc0OOL7Mb2albc31Dj4o3cG3+WYINl5P/fOUI/IF8cs4fQJABRLBDvculya5j0lNq+psjEbv5k5e/VJ14ret9Us72IXt2BWxJnmQQ/WkuTXuZPb4e++XvjJ86/vvi/s9YCUX375WxUbNSqfufGxz9JXda9eWaeOHUvOebi01ZPfXOPR+r7H7i6TtdBybtn4AR/sUNbYxA0bdsihWrVK0qmvBg1d1eKdKQ97SlLlTp18UpZ/tyCz2fDeb77d4lzn4nFH/wc6J/0Q3HX8id7f/DrnlYetU2WzT+M9duyYHKvc0SdzGi9TZQGgWDPJPXbAFRlHt6zcEZ0SH7/r4AWlndi+Z09ZSUctd6VsW7nyzKH/4qUUpZ3YvnJlWUllb2vV1E4HPx05c7/SrBNIXY4ufPWJn77Y/f64HnWMXd+Nfz7CY9CSQd6S5Nx99Kt33jmq91BLxb5zKy577cHnv0pq//4Iv4yDJ6wY8+rS20dt6+1ZY51fjdR5q9cZj7S1SFLSyd07jl7Y9lHEcfe2Eyb29jqxefMJSXLwrNPw9idffmDSoz8c/HZWRIuuFZMP/DL11Y+O1+g/+IFSp759etAihzJ11q45m95Vud7gCX0+fGhIj9Gpr3Srlbh51qgJW5r07Lz384Q6NdaPeWReQocJQa47Vu5PKO2QvGHxVyvL7F6dMY33rc9X7pJD3OzXl9/9in+V9F/z3Lt2a5P63IJFp4YPvHpTFgBAEWPra8FAQbLeY3fvjI55/OOv13dXnsvvef+YYRg7J9ST5PBgxj12cRs/HND+9gpuTk5u1Zo9OHbRoeRsx9n0vLedQ6lSzo5O7rX8+r299lTWqoNT2zqWffj7c4ZhGCm/DqoorxF/pKSv2jOx+bX/qDrePnDFkSTj9I+PVHRt2a2+1Pr9H4dVVJOJewzDuLBj3vP3NahYsoRTGa87H3nzl6gve0pNQxeNuT2vXZWWXdVqTTq8/GFIGye72zu1r2rv6Pvmv2kZFf/7ekM5PvpdasH+1eBWxj12QIEh2MHUck+eiI6LizMMI/PJE4ZhGMbOyzx24nLLL5G28cU6qjZkVcrVVx18z8/JLXB2tuD3x/BqqvDciszXiSd2bUr35xtt5D3oe+urbYfPG0ZsZL8qrvdM3Z8ewlZnBrvcUr7qKTUN3Zt92YqBHqrxwu/GnolNJLeHvjyz5bX6lopP/RwXv+jJ8irz9JKMZHf2kwCp/fQTV3/jwI0h2AEFhkuxwE374/N5e2s8+ljbPPoO515V45n3Qj5t/drLy7qFB6RPlYiNjVXZslnTJkpUqNu0giQpYXtpOVeq17RpPeuqc0uefub7upM2D651tSdl2Lu7u+Wap2GcPXteHh4eKl26tHRbswqfPx98KnDa+PtdS8a3ba5Pd+yI0r3VJKm0u7ud9sTGShVu4A8DAGBDTJ4Abta2xYujPO/v5HtNq5yav/bD9IbfPNp37uH03shly5bNc6psHlZ/9VVU3G9D6jo6pGs39YS2jK7n4NDxg5hcQ+vnOVXWqX79WqpQt25ZRS14JiSqX8TcvlUkpaamSk5OGc+uOHfmTFqOrAkAKC4IdsBNOrZ8+Q5L8zt98/hhynOVXa2nFsZER/atnn7arXLlvKbKSpJ97fZ9Ahtlmyrb9vW/tm3dsjnTrD7ldPvQyM2bP+6dO4VVz2uqrMt9gR1LpE/jPXG807Jt799TWpLO5ZrGe+zYMTlWrszUCQAofrgUC1Pz9JSkn36SxaKkpJzrUs4cWrNypaRD/8VnnxJ7V4VTf+0+c+nyVk2rljj4aZ+HPnB5ccnHvcpl7mf//v2qFFQ3r4c1XGFVphp+eU2VlSSV7DjiYWWfKlutfsOq2TaNLecg54q3NWxYS5Jy1pbXVNkXPwwqo4xpvCG9Hiz/3ogOHkcXv5FzGm/Mb7/tsLQe7MdvfShAky88lxomw9CFCy729vbOzlca3L276tW70gAAWWx9kx9QMKQ8v7JNnjjzhE8ePxH3vH/lqbJNpNbvH8t2oNSIh+xV75XNedRwhVXZXONU2XLBy3JvmXPyxCW15Z4qezzbPNfote8+3trbPY9pvLGzA13sW71z6MpFAzfD29vJkniZn9E8vr76ytYFA8WHxTCMfA2KgK1ZrjazwDCmT9fgwZozR337FkpJV3FoSpu6r7rPPLCgX7mrDy5YaVvHNGwa3mrRvo/vd7V1LTCvOnW+jW6b9vGnhmHExcXZ29uXLFly3z699JI6dVL//rmHt2ih6tVtUSdQDHEpFrcei0XTitTvM5dOlbWRtP0fPP9e+lRZW5aBW8BDTgsVJMNQTEyio6NjmTL6+29JqlNHQUG2Lg4ozriNBuZy1dN16QYPLuA6rs8lU2VtIuGv1x7KmioLACiGOGMHFAV2tZ5aGPOUbWtwvuv1TXGv27YGAMBNIdjBRK52us6Q5Rd1/FHdf1YnSRMnauNG9eihtm0LpTwAAAoYl2Jxq9ikO1roj4f07Wl53K5dkho2VFSUOnfWPfdo505b1wcAwE0j2OGWsFBd22j1XfrrgGrNU5+WWiepY0fNn6/9+1W7tlq21K+/2rpKAABuDpdiYX7nVLq3vpqsEc/owxwrVq9W19oVqladNUu3364HH9Sff6puXRtVCQDATeOMHUzkMk0Zt6nR45qdO9VJmjdP1arJx0chISF+azrdbwwbVuA1AgBQcAh2ML84lRqv1/JY0auX/P21Z4/CwtSmzVvL7lixNGXTW8t07lwegwEAKPIIdjCXvE7aVdDJcorJsWjCBEnq0EHLlun4cc2fr4EDqzkcb5/2y4+jfle5cvLzU1iY/v23UIoGACB/cI8dzK+kLuxX7azX+/adniZJ+/dr/35JHmoepOZBGvFBnVditmytIddIrV2rtWsVEqLatdW1qwID1batSpSw0TsAAOCa8KxYmFS2nnY/qUtXLbzG7SpU0IkT0n//aelSRUZq+XIlJEiSq6vat1dgoLp1U6VKBVEycKuoU0fnzunkScMwYmJiHB0dy5Qp8/ffuusuDRmiqVNtXR5QnHEpFiZlGJmXZetq9+nTOnEiec+emCNHLpw+rZdflqSKFa1jvb31xhvav1/PP6927SRJNWtq4EBFRur0aS1bpqFD5e6uhQsVHKyqVeXrq7FjtWHD5aZrAABgEwQ7mNqpU5LOVqzr7i53d5Uta5Qta7i7y8VFksaN0/r16ttXhw5p9GjVr6/PP1epUjn34OIif39NmaLDh7V9u0JD1bKlNm3SuHHy9VXlyurXTxERiouzwbsDACAngh3MLzpaUVF5r2reXHPm6PBhhYbK01PR0fr0U/n6auZMxcdfMtrHR6NGac0anTih+fPVt68SEjR3rnr1UoUKCgiw5j8AAGyEYAfz8/DQiBFXGlCxokaOVOPG8vPT/fdr0yYFB6taNe3Zc5kNPD0VFKQ5cxQTo9WrNWqUatXS8uUaPlw1aqQ3xtPy5UpJKYB3AwDAZRHsYH4NG2rpUo0fb3+5AWlpGjFCmzfrq6/088/avVsjR6pBA9Wpc7Vd29vLz0+hofrnH+3bp/Bwde2qvXsVFqaAAFWqpF69NGeOYmPz9x0BAJAngh3Mz9VVCxZoxgy7/v1LHzxoybV21y516aKvv9ZPP6lqVUny9tZbb2nt2uwzayXpgw+ueKG1du2s+RYLFmjgQJUooYgIPf64PD2tjfE2bMjvNwcAQBaCHW4JrVtr3bqUlBQ1aVKyY0ctWyZJ33+vNm3UsKHKlNHff+uOO660h82bNWiQatZUQIAiIpSaevmhrq4KDFR4uI4c0fr1Cg1Vixb6/XeFhMjXV97eCg5WZKQSE/P3PQIAQLDDraJmTWPu3HPr1l3s0ME6h/XcOXXtqn/+0VdfqUqVq2zu7a3p09WggZYvV69eqldPkycrJuaK29jZqXlz63yL48c1e7aCghQdrZkz1a2bPDwUGKiZMy87swMAgOtEsMOtpX79tNGj9eSTkvTssxo1SnXrXtOGbm567jlt26b16zVwoKKiNHKkqlZVr15avvwatq9QQf36af58nTxpbYzn6WltjFetmnW+xZo1NMYDANwMgh1wfZo3V3i4oqL03nuqUkUREQoIUIMGmjLl2prZOTtbG+MdPKh9+/Tee/L31549CgtTmzaqWNHaGO/cuQJ/JwAA0yHYATfC3V3DhmnvXi1cqC5dtGuXhg+/SlOVPNSurWHDtGyZjh+3NsZLSbE2xqtYUQEBCgvTv/8WyBsAAJiRg60LAIoxOzt16aIuXfTffwoPV69eN7ojDw8FBSkoSKmp2rxZkZFauFDLl2v5coWEqHZtde2qwEDdc48cHfPzDQAAzIUzdkA+qFlTEyfmnlc7a5ZGj9bBg9ezI3t7NW+usWO1fr3277c2xouK0tSpWY3xZs7U8eP5Wj4AwCQIdkBBmTFDb74pb28FBmrRIqWlXef2tWplNcZLn2/h4qKICOt8C19fjR2rDRuYbwEAyESwAwrKb79p9mw1amS9D69GDY0dq5Mnr39HJUta51scOaLt262N8TZt0rhx8vVVrVoKDlZExLXN3QAAmBnBDigozs7q10+bNlk7pJw5o3HjVL26tUPKDZ5o8/HJ3RgvNlYzZ6pXL1WooIAATZlyxedjAADMjGAHFLj0DikHD+qtt1S9urVDSpMmmjFDCQk3utPy5a2N8U6d0urVGjVKNWtq+XINH64aNayN8ZYvV0pKfr4TAEDRRrADComnp0aO1O7dWrZMQUHauVOjR1//jXeXcnCQn59CQ7VjR1ZjvL17FRamgABVrqxevTRnjmJj8+E9AMAt5eRXPcpZLBaLxWLf6NWNuX9Rjl8+oFr6WkvN51ZczFoR90/EuMcDmtTwcC3h6OxWvlaz+54Y9/W2wmlPSrADCpWdnfz9NX++9u3TvHkqWTLH2is9gvZaZDbGO31aCxZo4EA5OioiQo8/Lk9P+fkpLEw7dtzcMQDgllGh97RJnd0kKW37pMHT9mW/hyb57wlDP01/JGT53lPe6OBiXX4yMvjO5r3Gzlm+9fCZC8kpiXGn/tu0dPbY3r7N+39fCB0NCHaAbdSooU6dciw5dkyVK2vYMO3ff9N7d3VVYKDCw3XkiNav15gxatpUv/+ukBD5+MjbW8HBioxUUtJNHwkAzKzqkx+82c5VkhLXjR02+0TGcmPP1MHv7jQkya3LW293d7cuPx0x5PGZ/yZKksWjXvvuPbq2qukqSUra+9lT//u+wE/bEeyAomLzZiUlaepU3XabOndWZORNn8CTZGeX1Rjv2DHrfIvoaM2cqW7d5OGhwEDNnKmjR/PhDQCACXk9Fz7+bidJOvvTqFELz0qSjn86bPxfSZLk3Hrc1MerZAw+8cX0b89Iksr1mL39nxU/fBe5dtef45qnPw/izA8Rywv6xmeCHVBUdOpkfbRYixb6+Wd166YaNRQSoiNH8ukA6Q+inT9fJ05YG+OVK6eFCxUcrOrV5eurkBCtWUNjPADIzq7usI9GN3OQpJNzhr/2e6Jifxz50s/nJMm+YcgHQ2pbMoYa/+w7Uc3Ly8vLq+GAYX0qp4esEj49utRNX3/h4MHogq62gPcP4Do4OysoSGvXWjukxMYqLEze3jfXIeVSLi7WxngHD1rnW3TooC1bFBamNm1UqZL69VNEhM6fz6fjAUCxZt8o5KMRPvaSjH0fDB4fPvqFeen5zHvwB6MaZ3s6q6XDuzv/+++///77b1voPZkRK+3kyVPWb8uUKV3AtRLsgKIovUPK4cOaPFleXtYOKQ0bKjIyv4+UOd8i/Wxh375KStLcuVmN8cLCtGtXfh8VAIoVx2ZjZg6rY5GUsunNZz7Yb0hSpX5Tx7dxvtqmRtSssM/Te9Nb7u7Q3rVgCyXYAUWYh4f+9z/t3q3VqxUUpD178qM9yuWUK6egIM2Zk9UYz8dHy5crJET16snbW8OGaflyJScXWAUAUHQ5txr/YbBXtgVle7w9qfNVz7/FrgnpNnRZ+oOByvd++elaBVVfBoerDwFga35+8vNTVJQqVsyx/NAhVagg56v+wnhd7O2tx5N04ICWLVNkpJYt09SpmjpVHh7q2FH+/urePXc1AGBmTh7ly9hJGb9fu5Qr53LF8Uo79vOwTkHTtlyQJAfvZ+ZM61amgGvkjB1QjFStKoecv4v176/KlRUcXGDN6WrV0sCBiozMaozn4qKICAUHq2pV+fpq7Fht2MB8CwCml7br3eCwrdmumhz7dOj4vy/fMypx9+yHW3abtiVekkrUffqbVdPv9yjwKgl2QPGVlqYmTSRp5kw1aqT779cPP+RHh5Q8lSyZ1Rhv+3aFhqpFC23cqHHj5Our2rWtjfFu/BFpAFCUHZz+zLj0GFexyyPt03sW754y6J2ded4gk7D1/S5+/b85mCJJ7i1H/7w6vHvVwolcBDuguLKz0zvvWOc8dOigJUvUo4eqV1dIiA4dKsgD+/ho1CitWaMTJ6yN8U6fzmqMFxCgKVPyr0cLANje0c8GvbIyXpJKd3rr43nhY1qWkKTkv18f/Mnh3INT9s3udd+wX6INSY61e8/989fXO1Sw5B5VUAh2QPHm5KSgIC1bZu2Qcu6cwsJUu7YCA/O1Q0qeype3NsaLibHOt/Dy0vLlGj5c1avLx8faGK8AZ3wAQMGL+XbYyJ/OSVKJVmOm9K1kuW3Y9Bca2ElS/IqX/jf/dPbBCX+/0uPpyOOGJJeGz/249ovHbnMqzGIJdoBJpHdIOXJE776rOnW0cKECAtSkSaFMY3VwkJ+fQkO1c6e1MZ6/v/butTbGq1hRvXppzhydPVvwpQBA/jq/aMSwb05Jkn2DEdOH3maR5HDHK+8HV5ckxUT8b/Ty+IzBKX+89thb25IlqWynGT9P61Sp0E7VWTErFjCVsmU1fLiGD9eGDZoyRWlpcnQs3ArSG+MNG6b4eK1YoYULtWCBIiIUESF7e7VoocBABQaqQYPCLQsAbsSF30YP+ixKklQ9eNrophm5ybXDG5ODIh6OOCUdmTlkwoCtoc0dpZNzXnt/d/qVEovT0S8GdPoy9/58//fD6wH528ogJ4IdYE7Nm2vOnNyXYi9c0Pz5evhhuVxlkn5+cHW1ZrgZM7RpkyIjtXChfv9da9cqJES1a8vfX1276r77VKJEwVcDANcvacO4Z6b/J0nyfPid19uXzLbOvdc7b85cNPCXeKX9+86g9/qvG3m75ej+/RlTyIwTW5Yu2XLpLnsX8MNiuRQLmJkl50WAL77I6pCyfXthFWFnp+bNNXas1q/XgQMKD1dQkE6ezJpvERiomTN17FhhFQQA1yJ121sDrdNeXTtOnNzTPdf6ak+9/8qdjpKU/Of4IZ9GFXqBeSHYAbeQDh00YoQcHDRzpho3lr+/vv1WKQX862MOXl4aOFDz5+vkSS1bpqFD5eGhhQsVHKxq1eTra51vQWM8ALZn3+iVDcmGYRiGEbd8QLVLB9jVD/krKX3A+aVPVZWavr7XuLLFT5Qq2KIJdsAtpHZtTZqkqCjNn6+OHfXLL+rZ09oh5eDBwi3FxUX+/poyRYcOWRvjdeigLVus8y0qVVK/foqI0PnzhVsWABRvBDvglpPZIWXHDg0dqrg4a4eUgABFRtriZFl6Y7xly6xN+fr2VVKS5s5Vr16qUMHaGK9gW/MBgEkQ7IBbV/361l7C77+vevW0fLm6ddOnn9quoHLlFBSkOXN06pS1MZ6Pj7UxnpeXvL01bJiWLy+UDi4AUCwR7IBbXZkyGjxY//yjlSv12GPq2dPWBUmyt7c2xlu/Xvv2KTxcXbsqKkpTpyogQJUqWRvjnTlj60IBoGgh2AGwuucezZ2rMmVyLHz9dX38seLjL7NNIahdWwMHKjJSp09rwQINHChnZ0VE6PHHVb68fH01dqw2bLBdfQBQhBDsAFxWXJwmTtTTT6tqVQ0bpp07bVpNyZIKDFR4uKKirPMtWrTQxo0aN06+vqpdW8HBioxUYqJNqwQAWyLYAbisUqW0e7fGjFGJEpo6VQ0ayNdXc+YUgZvc0udbrFmj48c1e7aCghQTk9UYL32+RVTRaCoFAIWIYAfgSqpW1dixOnJE8+fL318bN+rxx60dUv77z9bFSapQQf36af58nTihZcs0apSqV7fOt6hWTT4+1sZ4aWm2LhQACgPBDsDVlShh7ZCyebOeeUYXLigsTHXq6IEHtGSJrYtL5+wsf3+Fhurff7Vvn957T/7+2rMnd2O8s2dtXSgAFCCCHYDr0LixZsxQVJTCw9WwoX78UePH27qmS9WurWHDshrjDRwoe3trYzxPT/n5KSzM1jcMAkCBINgBuG5ubho4UJs3a/VqhYbaupor8PBQUJDCw3XkiNav15gxatJEv/+ukBA1aJDVGC8pydaFAkD+INgBuHF+fmrTJseSxYutfY/j4mxUU57s7dW8ucaO1fr1OnBA4eEKCtLJk9bGeB4eCgzUzJk6dszWhQLATSHYAchPGzdq924NH66qVa19j4scLy8NHKj583XypJYt09Ch8vDQwoUKDla1almN8WzwbDUAuFkEOwD56eWXdfiwQkNVurSmT1fDhvL11cyZunjR1pVdysVF/v7WB9GmN8Zr2VKbNlkb41WubJ1vcf68rQsFgGt17cEu+uhRm7euAlAMVKmiUaO0b19Wh5TgYNWsqZAQHThg6+IuJ7Mx3okTmj9fffsqIcE636JiRWtjvEOHbF0lAFzFtQe7VcPqNes7Zc3J1AKsBoBpZHZI2bZNgwYpIcHaISUwUDt22Lq4K/D0VFCQ5sxRTIxWr9aoUapVy9oYz8sra75FSoqtCwWAPFzHpVjj/PbPh7etd+eT4X/F5EOvz+RDC19qV9HeYvEN/e/StWe3zHrhAd+a5VydnMtU8fEf8PbK4yRKoFjy8dG0aTpxQrNnq3FjLVokFxdb13Qt7O3l56fQUP3zj/btU3i4unbVkSPW+RaVKqlXL82Zo9hYWxcKAFmu9x4748ymWc+0vL3Vc59ujr3xO4sv7PzimRaNA6dvzvuZjgkbXuvQ8sl3VyX79hn52ivP3F9u5+wR/q2e/jnmhg8IwMacndWvnzZt0rZtqlUrx6rDh21U07WrXVsDByoyUqdPa8ECDRwoJydFROjxx7Ma423YYOsqAeA6gl35KpUdrN+mxfw54ynfem2fn7f9Rm4qPvflI837fG3XJ2Ljx10d81h/YMbQiRuNVmFr138zdezoV8I+XbVhbk/3A7MGvbmOs3ZAcdegQY6XSUm6807Vq6ewMJ05Y6Oarp2rqwIDFR6uw4e1fr1CQ9WihbUxnq+vatdWcLAiI5WY9y+tAIoTiyWPryLv2oPdPVN3bf1ipH+1EtbXqSfWvPfYHfU7vvjtrvjrO2aKQ8Pnftj8+/SedZzzWv3f1/N+T3HrMWpog4zUZ6nU++UnvXVg3ty19B8AzCUmRi1aaO9ehYTIy0vPPqutW21d07Wws1Pz5tb5FsePa/ZsBQXp1CnNnKlu3bIa40VF2bpQANfvChmuyGe767kU61b/kbeW/bvt25c71XSyLkqJWjGpZ+MGXV5bcCDhmvfjEfTG5O5eeZ2rk6TEP/7YJPn6+eVIfU3b+LnpxB9/FNkpdQBuSOXK+uEHHTqk0FCVLasPP1STJkW4Q0qeKlRQv35ZjfFGjVL16lmN8Xx8FBKiNWtojAcUD1eNbkU72113HzvXug++sWjnPwvGBXpn3P+cdGjRhO4NatZtmIcXll3vAQ7u35+mUl5eHjmWWry8qkv79++/3t0BKAbSO6QcOKAFC7I6pFSpomHDVJx+6p2d5e+v0FD9+6/27dN778nfX3v2KCxMbdqoYkVrY7xz52xdKICbU4SzncPVh+TB2TvwtQX3PrH47f8Nf/Ob9CuxCSf2/HPi0pH1zl7vvs+fPy+VKlUq12I3Nzfp/OU+Dw3DiGVuGi5hiY0tKyUnJ8edOWMYhqSEhISkpKQLF5ykkvHx8WfO8JDQosXPT35+2r3bftYspy+/LDF1qmXaND32WOJ7712wdWnXyd1d/fqpXz/LmTOOv/3muHix45IllrlzNXeuHBxSmjdPvv/+5M6dU2+7zdaF2kCZtDSLYcRm3FOZkpJy5syZ8+cdJLfExMQzZ4rb3zUKnpOTU8mSJQvjSNee2CyWonka/iaePOFUpWnbe3xruuZfMVdiGIZkKcIRGUC+qVs3deLEC7t2nZ01K97XN6VmzXzosGQrhrt7Uvfu8TNmxO7Zc27FioRRo1IbNnT480+XceNK3313mWbNSr70kuOqVUridwwA+cG4IQkHl4Y+7ON29d0/FHGl3UT2cZKaTzyQfdmeiU2kkv0W5Bq6+ZV6kvuzv9xYvbhVnTplSEaXLoZhJCUlRUdHx8XFGYYxbZohGXPm2Lo8XJuU2fp9IAAAIABJREFUlBwv9+0zVq60USn55cABIzzc6NrVcHIyJEMyXF2Nrl2N8HDj2DFbF1fwvL2N8uWNtJO/vtXvrpoeziWcy9a8u9OQ3yRjyJA8N4j5a+bgexvVcC9ZslyNhv7PzPgrJmNNwr4F4x5peVtlN2dXT6+GAc+8v+7kFQ6cuv/jLh6eXeceSruGKmP/er9XHWc59fk+5/Lzmz8Z7N+gomsJp9LV7ujxyo8Hky+zgyvUlnZy5aR+rb3Lpb/3x976LdowDOPCHy83ca03ZOXZa6gO+WXLFqNatayv9J/Ha/zK3Kp+fVu/jSzXH+zi93w/ppt3jv6iLnW6T1h6KPH6j55XsEua/6CD1GbKiRwjU757tKR059sHr/8guJUR7MzouecMyahb1wgNNWJirj6+SIuPN5YtM4YOzfofxc7OaN7cGDPGWL/eSLuW/FEMeXsb5cvvmtyyhH0V/5Ef/rDo+89HB7hbXKQdeQW75G1hrUpaqtz7ymeLV65cOHPYXe4qEzDzkGEYRsyCx6tbSjV5auq3K35bGTnz+RYecm397p7LHDZxw9jGTl4Dl565aoFp0WvDunq5VG3i45k72EXN7eZuqXjvq/NWrPt98SeDfUvb3/b8bwl57OMKtaWlv/fOY+YtW7X089EBFSwuLSftSDMMI3Xv1PZu5bvNibpqicgvy5dfX5jL88ve3tZvI8t1Bbuz2754sWP1EtkznZPX/a8u2HfxBo+eV7Azjrzd0qKSD86Py7YsZfWgKpLXC3/d4IFwqyLYmdGvvxoPPmg4OFjPcz39tLFxo61ryhfbtxuhoUbr1oadnfV/Cy8vY+BAY/584/x5WxeXr7y9jfJlHi+tyk8vjoqOjo2NNYyLU7tXkp7oPuiSwakrBpZXhf4/Zf5Hc+idVpLftOOGcf7rXh4urSbvzxx7+N3WUsspeceiQ1PbOpXq+ll0rsUX53aRz4SdOZZFz7ivSsD4307uGOOTK9htDqkjj0e/y/wP6uB7fvaOAZ/k3ukVa0v5+fHSqvz0kow4eHHxgEpyf2JxkmEYRsqm0bdbKg1YHHfJHlEw4uONlSuzvq4rz2VutXatrd9GlmsPdpsmtaponz3TOVTpOPLrXfE3c/Q8g50RFR7gLMdmr67P+DFO2Ts9oJTsGo/bdjMHw62IYGdeR48aoaFGjRrWD9jmzY3wcCP+pj6Riozo/7d333FV1Y8fx9/3skEEFQduxRFppjl+pmiamDmbmGU2TLEyR0PRyiytb9rUlmlladM0K5wpWc7MUdmw3Kk5EQVFmZfz+wMcICqi3gMfX88Hf3DPPfec9/UB3LfnfM7nxFtffmn16mUFBeW8PT8/KzLSGjfO2rHD7nAXQ1iYVTqgkZxRX6TF5xQ7a9Vb/aSKjaJOWznr6L7Nf27en35ywcy7PFV7xLp8Nhw/oZ3U6u29+TzlWjKwgqo8tiIz7xP5FbvUnTv2uSzL+jtvsdv60jXy6v7lKUfo/n2libyipuV3zO5M2baMbSRn1LST78ha2C9YFR9bkf3g4OROPp4tX995zi3iUjivYneBMvf+NPnpO6+7qmbFUn5e3gEh1Rt36jdu0a7TfkbPT8Gvit28csW+4zd+8Cjf8uFX332+Z/2SBX75SQmL33p53n+SpC2/ZUq75o8dlhgkSRU7Dhl4XRlVvH/c6I+vHTK6baPf7r6tcdmj/8z5eNrazKtjJj5evxC7A2Ck0FDFxGjIEC1apPHjNWeO+vXT0KG64w4NGpT3/hbFTEiIoqIUFSWXSz/9pNmzFRuruDjFxWnwYF15pbp2VWSk2rSRZ+FmNigS0uTh7X3K4YKQUGl3YuIxKffFjw7/cmH1yp18fPS7OT9mluvcJvzkIlfa0eTDB7au/HT4qKXVH5h+Z/l8drfq22/3lu3UtblHPs+dxqdylXL5PrFx40ZVubGWz8klVWvV8s5Yv2GrFJ7vK/LJ9nda3vceGlpBuzdtOqZr/aVSXbq1cj0cO/fA4OiQgoSFTS70ktg9M++P6P7xVpd/tWvbtmtRynlo88+L5k4cPC/25y9/+ez2ChcSrICm3yZJcpZp+uB7aw9dwMCPTS82PkOWq188MTIief2nQ29pUq2Un7dvUOWrOw+ctPbcgyKA03DE7rLxzz/Wo49apUrljFL7/Xe7A110W7bkXG/h7Z1ztKBMGSsqypoyxTpU3P4+hoVZISVv9lSd4Wv2Hz9i98MLt0uqdF1+R9tOcu2aflclle46JdeRy1n3BkiSZ8XrY2b/l//H0/axTeVxy6cnBoOf6ZOoTL+Fp7wq7xG7zC9ulxqO2Xzqln/oV0ZVHj3jmbh8sqV8cbOn6gxfeyJp0he3+0tt3jr+3v95vr687prpOus/BS4Ztxyuy1o1tLqkoA7vbz9xhC5905uRAZJqDFl7IfELvOb02xTU8N43f47nRw3FB8XuMnPsmDV5snX33XbnuKSSk63YWCs62goNPTlwu2VLa8wYa80au8MVTFiYVTZkQXRlBTYb9NnPO/bt3fnDC40rBUuq0vYsl8Ok/j05qppnUMtRKw7nfuLgxhU/Lvh6ytjoZiE+NaKmbM2n260cXFnlHl504nHavg2/Zvv5hVYK6/91zqM/dp46nLEgxW5RdGlVPX4a9XT5ZUvJfu/DZm9MTD2284cX2tQMDpbaTzz+3pM+aC+1fXvfmbaJS+5Sn4S1rLSdq+d+/cWUeetzXXma+lk3p6SWb17AxfEFD7dx+ZI9F3jeF3A3ih0sy7Ksxx6zvv/euGtMXS5rzRpr5EircWPL4cj5vKlZ04qOtmJjrdRzj/qyTfZ0J4eWP59zg0pHQI1OD41+WvKu2/lMnzOHlj7bupRHpZveXnfszBs+urBfRZXo9e3pszTMv6+E6jyZ31U2+Y2xO+60MXbf9Q1UjeGnHk7J+voOLzV8/p8zh8ov26HlL3Ss7nv8vT//2dPN5d3z6xPvfWZ3pxq9sOGc28QldClbXS6ZxxL27Ni6edOmTZs2bfqkR7Ck+gX4gTqjgk9QXLtFqwoFGpsAAEXJypV67TW1a6crr9T48TLnJjVOpxo31rPPas0a7d2rKVMUFaX4eE2apG7dVLq0unbVpEnavdvuoGcQ3OLJOZs3rl+99vdN8Zvn3BO8X6ofEpLv58zRVc91vHHMgR4zV858uMGJ6basPaumT/1i5f6T6/k3bXqlktev33H6zoKDlZR03vdCyis8PFw7N2w45TbGWzdsyPAJD6+RZ8VzZAtu8eTcLQf2bt64bV/85jkxIfs3qf7VVx9/74cPHcpScHDwhabFhbCsfEbR5buwsDs4sPLd/h0blA8sUSa0as1atWvXrl279t1fJErZ92QorAu48wQAFAfNm2vNGvXqpS1bNHiwKlRQ9+5avtzuWBdXuXK65x59+aX279fChRo4UCEhmj1b/fqpUiXVq6dhw7RsWVG6A1LWLzMmTVm6379s9bCqIX7O5CWzp0tRYfldknfom35dRu3rMeOHd7pVPvVDy3F44ah7ez7x2fYTS9LWrl0vz8qVTx94HhoaqgN79mScvnWPmm17dr0qqGCpq3TsWC8zbmbsidtbbp7x1Tq/Dl3beedZ8azZErLfe0D5sNrVy/o5k2M/nH6ocdStJ8rhnj175BUayqUTRUB2kzvxdfEcXRbT6rqH3pm/qURE32fHvTfls2nTp0+fPv3Z9gW498M5XLRjiUARxKlYnGLPHmvMGKtatVwzpCQbPF/Yli3WuHFWZKTl5ZXznsuVs3r1sr780kqy9eYGYWFW2ZBZ95ZTyHWDJ337ww+zPxnetpRHmHQ4e4Lifz+4q3HjB6YdsCzLslKXDaihwMjR83/IZd3uDMva/dltFRRQ755Xvly4ZPHcKc/cWNXTWbXvwvxm/Vv+aFWVe2jx8dPxJ8fY5fbHziOWlbHrt+ydTLm3urwiR2c/+PW/NMuy4mf2LO8oe/2Tny5auWLeu30bBHg3HLk2+94TuWKfLdvR7Pf+5Oc/rl79wyfD25b1DBvw/clxgwcm3eB0tHn3bLfQQHG3983rPCTVfuSH3ANGF/QuKZ1xbECBUOxgNIodTuNyWQsXWlFRloeHJVlBQVZ0tPWH2bNkHjiQMzFe9mXDkuXra0VGWmPGWP9cwFieQsseY5f8y4Q+bWuFlPDxKVH5mlv7jtuh47cU+3v01SfHj/8xsm5+RyU6vHfIsizr6IavnrmjeZ2KQb7+pavWa3Pfy4v+S893n5k/9C+vak+szBnHdtarYg9NaJfPU9flBDq2/tNHO1xZ3t/bJ6ha0zv/9/3e45cU5op99mzJv7zbp23dcoE+PoGVr7n12bk7TrktWeKUrn4eLV4zYsZCnMnsu30l1R2Z5y/Pf+Oai2IHnAXFDme2ebMVE2OFhFiS1f/0Gx4YKTPz5PUWJ0aC16xpDRxoLVxopedfiS6+7GJnWVlZWScnKF5l6Yz3ir0oto+L8AnsOuXApdvDxeBa90y4o/wD8ww+kgzLsubeE6Bcs7xZlmWl/Tw0ezbEK0etL/ymGWMH4DIVFqYxY7Rzp6ZM0YABdqdxDw+Pk9dbbN2qiRPVpYt27dIbb6h9+5zhh5Mmae9eu4NeClUfHDesxoJnnlxYhC+fydr6zqPjDnR9edSNAXZHwSUVfmW4pL9nx27OylmSuuHj+++cUaFNTUl7d+8u/Hg+ih2Ay5qvr+65R3Vzn+0bO1bt22vWrKJ0scFFV6OGoqM1a5YOHsy53sLPT9Onq18/Va6sJk307LNau9akfwKfxs9883b9GXf1+nhn0XxTqaueuW3Yrnumf9yrot1RcIlV7zO0eymlLx/SvMktffs/dG/XxtWv6rfutg9mPBYRJB2c0r/Lg4M/+r1Qm6bYAUBeS5YoLk7duqluXb36qg4etDvQJeXvr8hIjR+v//7Tn39qzBg1b65ff9Vzz6lJE9WooX79NH26kpPtDnrhnDUemJ0QP6tXFYfdSfLl2+z5X5P/efO6wtytE8VMmaj3FrwbfX0djw1zpk79aum+qndNXLb8pTalOz/9Vs9GFZz/Lo5d+m/KuTeTD4dl0P/GgLwSEhQSos6dNXt2RkZGUlKSn59fQEDA22/rkUc0dap69bI7IYqqtWs1aZI+/lgpKfLxUbduio5WZKTdsdwmPl7z5mn2bC1YoOzp3/z81LKlunTRrbeqSpUL2nitWjp8WPv3W5aVkJDg5eUVFBS0erWaNdOAAXrjjYvyBoDLFEfsACAfjRtr4kRt26YxY1SxoqZPV/v2OVMcm3Do6pzKls2ZGO/AAS1dqpgYVa+uuDgNHqyqVXMmxouLU2bm+W3W4ZDDoS1bFB8vh8Ph5DMIuMj4pQKAMypfXjEx2rRJsbHq2FEbNmjwYFWurIEDDbqDxdl5eioiQmPGaP16bdmiceMUGanNm3PGIYaGqnt3TZ2qc97UIbvSnSakbNkgbrEAXDwUOwA4Bw8Pde2quXO1Y4dGjpSPj6ZPl7+/3bHcr2ZNDRqkhQt18KBiYxUdLU9PTZ+ue+9VmTKKiNDYsVq/Pp8X5lfpzm8FAAVDsQOAgqpUSc8+qx079N138s59E6kDB2zKZIuAAHXtqokTtWuX1qzRyJFq2FArVmjYMNWrp7Aw9eunWbOUni4VuLQ1a3ZJIwOXCYodAJwfHx81aJBryfbtqlhR7dtr+nS5XDbFsoXTeXJivD17NGWKoqK0f78mTVK3bipdWl272h0RKLyUFK1fr6++0rZtxeZXm2IHABdqzx5dcYXi4tS9u+rW1csvX2YH8LKVL59zvcX+/TkT45Upo9mz7Y4FFMbixeraVaVLq1493X67atZUhQrq21dbt9qd7FwodgBwoZo31++/a80aRUdr924NHapKldS9u+Li7E5mCz+/nInxtm+3Owpw3tLSdN99uvFG1aypxYu1dKl8fXX4sD76SPHxCg/Xm2/aHfGsKHYAcHFkz5Cye7fGjVPlyjkzpISHa+xYHTpkdzgABZCZqW7dtHq1fv9d48erWbOc0bSBgercWd98o6+/1ogReu45u4OeGcUOAC6m4GANGqRNmzRnjrp21aZNGjZM1atr0iS7kwE4lxEjtHmzFi9W7dr5r9Cpk+bN05gxmj/fvckKjGIHABef06lOnRQbqx07NGaMSpZUtWp2Z7IFNzdC8bFjh15/XR9+qJCQs6127bUaPlxPPKGsrMLva+9bbRwOR4n7Lv4gVIodAFxCFSsqJkZbtqh9+1zLf/1V//5rTyQA+frkEzVrptatz73mY49p2zatXHnpM50/ih0AXHLe3spz96z+/RUWljNDyvnelwvApRAXp27dCrRmiRJq21YLF17iQIXiaXcAALjsWJbuu08pKYqLU1ycqldXv37q3Vvlytmd7FKwrALNUbxqlZiiGG63YoXatMn5PiNDP/6omJi862RlKTBQnqc0powMHTumuXP1wguS5OOjI0fckbYgOGIHAO7mcCg6Wr/+mjNDyv79Gj5cVarkzJBi4LC0c74lA98ziofMzJNfkixLWVl5vySlpurYsZNfaWmyLFlWzgszMux9E7lQ7ADANtkzpOzapYkTVatWrhlSDh60O9zFlf0xeJoD8fFJiYnujwNka936ZIFr1UrjxuX8qJ74+vln+foqI0NpaSe/MjJ08816+umcF6amFnLvDofDOrBsXN8b6lcu7efjX7p645se/+iPCzv4R7EDAJsFBys6Wn/8ofnzdfPN2rxZw4apbt3Cf1oUXdkflWFhKltWlmVdyFWFwMXWtq3mzi3QmqmpWrRI119/oXv0cq2NaX19TOze8k3bdb6+vv++X2Jfuz+i02v/XMBvBmPsYJDmzbVxY64l2YN7Fi5U6dJeUpnsAwYOh9L6SC/ZkhE4E6dTHTqoQwf9958mTVJKinx97c4EXE569tSLL2rtWjVufI41J0xQSIhatbrQPR6dMeaT68f9tubhcH9JSvn7jS7XDlq07Jmnv+w9o0dw4bbJETsYpGRJlSqV66t0adWoocqVVaqUFRycFRSUs9zf3+6swBlVrqxRo/Tyy7kWHj6s4cOLwX0qgeKrTh316aP771dy8tlW++svjRypF1/MdTlF4aSnNRo+MafVSfILH/BCnxrS0TnT56UUdpsUOxhkwQJt2XKmr8wNGw6tWXPsjz+0ZYuefdburMD5+eQTjRmj2rXVsaNiY+Vy2R0IMNGrr8rXVx06aN++/FdYtUo33KB771X37hdjf1d17Fjp1MeOZq0jfKXUdes2FHaTFDsAKAZ699aXX+raazV/vm66SVWratgw7dxpdyzALH5+WrhQQUEKD9eLL2r79pzllqW1a/Xgg4qI0H33afz4i7M7R1hYjdxLnJUrh0rau3dvYbdJsQOAYsDXV1FRWrYsZ4aUpCSNHasaNdS1q6EzpAA2CQrSnDl6913NnKkaNXTDDUpLU2CgWrTQrl1asUIvvJB3vvFC8w0I8Mi7yNdXUmrhL52i2AFAcXLqDClXXKHZs9W+va64wsQZUgCbOBzq3l2rV2vnTn31lUaP1nffKT5es2apSZOLuaP0tLS8i7IrnX/hR4JT7ACg+AkKUnS0/vxTS5cqKkrbtmnYMH39td2xALNUqqR27fTUU2rZUiVLXvztu3bs2JV7ibV7915JlSpVyvcFBUCxA4BiLCJCX36pbds0apR69LA7DYDz8sv33x/KvWD58hQpoFGj2oXdJMUOAIq9SpU0YoQCAnItfPBBPf64Nm2yKROAc/Gwvh/9xKx9x6cjztwx9bn3Nkulbu3Rwbuw26TYAYCBUlL0zTd67TXVrasbbtDXX+fcCrOoO/R8fUc+bnw/v9uOWfGLX7k3olaIn49fqRrNe7289ED28n/OZyOSlLXtgy5lynb9ZGfBL0LZ/X7HYIej4ZjNZ1rh4Or3BnRoUK10QEBItavaP/Tu6pMjIJPXTR7Qvl6FEj6+QVWuuXVE7I5MSSk/P9WwRPjAxYcLHAHFmcvlklSu14hOS2+/ot4NPfv1f+ieTg2uvm9WgkI6vjSqW8A5t3Am3HkCAAzk56ft2xUbq0mTtHChFi5UaKjuuUcPP6yqVe0OdxaBvT78IeLoKQsyfht/5+N/N7km8LRVrY2v3XTDsO2RT78x6/qy+xa8/FhMh26OtcufCHdULfhGJCn9l9E39//z9lm/3V3FUcCYu6c+OOT7Y2f+BM3886WubYb9G/HU/z6PrJ658etRMQ+13+Lxx4K+VaTdn/Rs2+fnpk+/NqtTjfT1nz396K2RR3/447VW/zf6qxd/ahTVq+lv3/aqWMAcKLayr5EoUb7TuGWtqgwbNXnWp9sS0v0rNrntoSdeHNG9+oVs2gIuD+np6fHx8cnJyZZlvfWWJVlTp9qdCXCLtWut6GgrIMCSLKfTioy0YmOtrCz7AoWFWWXLWpaVlZUVHx+fmJhoWdaqVZZkDRiQe03XPy829anSb8HR0zeSOe/ekgrt+11qzuOU+X0qqNR989NPW/MsG7Esy9rxRmufEl0+is+zOOXjzqo3+u/8XrH3s5tKB9/+SM/yuvrFTfmt4FoUXVbl7p+TcmIfr7WQIt7aa1nWb8NqqfRdM5OPP7V9XISHV/sP4i3LsjJ/faquo0Kf+cn5bBMoGE7FAoDhrrlGEyfqv/80frzq1FFcnLp1U3i4xo2zO9m57Pno0ec3dhj7fPt8pn7Y/vvvh50RkW19ch77drjjpuBDCxasOZ+NSFlLX/nfknLRT94dUtBQB77oP3Bx89fG33HmVzj+b/RPf64Y2/7EzX4rV6/uqX379knbFizY7BV5c6cTZ9qq3nxzo4wf5y9Kk+TR8PGYjoc+Gv3efwUNA+RFsQOAy0JwsAYO1N9/a80a9eqlrVs1e7bdmc4uddHIEQvqxozpkW+DSktLk4e39ynTu4aGVtDuTZuOncdGpFXffru3bKeuzfNOE3smB74aMHBho1ffvf9sZ0sd/uXC6oWV9Tr++Oh3c37MLNemTbi0ceNGValVy+fkylVr1fLO2LAh+zbApbp0a+X6KXbugQLGAfKi2AHA5aVxY02dqu3b9cYbuZa7XDp27AyvscOO95776NjtIx4Jz3/gW406dTwzVq/67cT1Dof//HOHdOTIkfPYiHYsWbLdI6J1i+NPbx7TJOdSC79ec/TXiPCcRyEPxknSodiB/WddPXZS7yoFfx9Zu2dE9/kgtevLI673kisxMVklc82I5ggKCtShQzmTXpRt06Ze1rLFS7Py3RZwTlw8AQCXo9BQhYbmWhIbq/vuU48eGjBA9evbFOsE69e331hSvtfirvlf8CD53vRw78o3vPXQky0/GRZZ+chPr/d6Ms5b8vLyOo+NaM+ePSrTNPTE1BJVe3/2643HJCl97sD/m9zg6xl9qkuSZ0gtKWn24Idir3jxj37VC/w20v75sNeN0Quqj5r36T1nKoOWZcnhOF4tQ0NDlbFnzwGpXIH3ApzEETsAgCQlJsrbW5MmqUEDtWunGTOUkWFfmpWffLq56p13tz7zKVLf9mOnvRCxf1yXOsG+AVf0Xh75/CNXyLtcuaDz2UhiYqKCg4NPPPYuV6dhtgZVS8q3whU5j+pXLnH4uyce/LrOy5MfqVHQa2cTlz13Q4u+KxqOX7JwxLXZ3dKjVKlAJSUlnbKWlZR0RKVLl855WLJUKacSE880MwtwDhQ7AIAk3X+//vtPX36pdu20aJGiolS1qoYN0/btNoT5Y/78XSE3djz7fTmDWzw5d8uBvZs3btsXv3lOTMj+Tap/9dUnW1wBNhIcHJynZ53R0i++2JW8ZEAdL89sbd7Yp3VPXeHp2e6dhHxWP7rquY43jjnQY+bKmQ838DuxODw8XDs3bEg5ueLWDRsyfMLDa+Q8PHzoUFaurgmcF4odACCHj4+iorRwodav18CBSk7W2LGqWVPt22v6dLlcbguyJy5uvaNx0yZn+4xK+GXGpClL9weUD6tdvayfMzn2w+mHGkfdWuO8NhIaGqoDe/bkc2jSo2bbnl2vOuXwX+vnV/3x+7rfTviwZxnVHTjrt9/e73F6Czv0Tb8uo/b1mPHDO90q59p/lY4d62XGzYw9MQ/x5hlfrfPr0LXd8bPBe/bskVdoaIEv0gVyY4wdACCv8HCNH6/Ro/Xxx5owQXFxiotT7dr66CO1aOGG/W/dulUVourkGRq3fXLP297xG/rd+93LSPLbPXvEfXM+2/jmc7fUsjbMHPXo9NL9v+sfdq6N5FY1IqKq69OlP1l3tnZIUvr+jet3Z19C4t/uiTu077ff9kmSZ0it+pXD6596Y/bEMp7yLV+7fv0ap2VLWz7ysU9Trx8dFbD+xx/Xn3hF6boRDUKveGR0z3dvG3DLU66nu9VI++3DmNHrrh76btTxBpmwZMl6R8tHIjjsgkKi2AEA8leypPr3V//+WrtWkybp889VrZpbdpy1Z0+8goKC8ixO2f3X2rUl9uccXvPv8vb8d70ef31Q11eTVLZe+/6xU566PvCcG8nj/7p1Lf/67FmrXK3/z0PSjsl3NRq+9vTVyvRbeODdyLNsJ1e2TQsXbNORbSNujMu1Tof3Ds3vExxyy3s/fPLUoy881uWVRK/QBp2emvd6zDXHP4yT5sxa6rj2hU5lz54aOCOHZRX81nhAMZaRkZGUlOTn5xcQEPD223rkEU2dql697I4FFB9Hjigw9+GvlSt11VUKON/bWtaqpcOHtX+/ZVkJCQleXl5BQUGrV6tZMw0YkHcSlktvx/hWdUaUmrQt9p4ybt7zabJ+H1m/4cQWc7e8f2PhbxWKyxwHewEABZKn1aWkqHNnVayofv30++82ZboIqj44bliNBc88udDuC1Gztr7z6LgDXV8eRavDBaDYAQAKIy1NffvKx0eTJunqq9WmjaZNU3q63bHOn0/jZ755u/6Mu3p9vNPGU1ipq565bdiue6Z/3Ots97Q847XTAAAYKUlEQVQAzoViBwAojOBgjRmTM0NKZKSWLFGPHjkzpPz7r93hzo+zxgOzE+Jn9apS0BnqLgHfZs//mvzPm9eVPPeqwFlQ7AAAheftfXKGlJgYpadr7FiFhRV0hhTL0rx5Xr16qXt3SfrgA7Vvr3HjxAS9QOFQ7AAAF8EVV2jMGG3frgkTVL++4uLUvbs6dz7bS/7+WzfcEPzww34lSig6WpIaNFDbtpo8WWFhmjzZPcEBo1DsAAAXTWCgHnxQ69Zp2TL17Klu3c645ooVatHCUb9+5q+/HpkwQZGRklS+vJ58UuvWafx4DR6sYcPcFhwwBPPYAQAuvpYt1bJl3oV//KHlyxWdJWXp5ps1aJA1YECyl5dXntUcDt19t+rV03XXqXZtPfCAmzIDBuCIHQDATV5/XQ89pO3blZiounU1cuTZVm7USBMmaOhQHTrkrnxA8UexAwC4yfPPa8wYORxyubRsmZo1c0yd6puaesZrUe+6S1Wq6KOP3BgRKOYodgAAN6lYUTExKl1aTqciI/XLL3r88RJ16wYOGqRdu/JZ3+HQHXdo1iy3BwWKLcbYAQDcKj1dnh6KidEdd1gzZ2YsXuz1xht6801Jio9XXO77q1qW1q+3JSZQLFHsAABulZYmZWZPXOewLC8vLwUEKCVFlqXVq3MmtDshM1PHjtmTEyiOOBULAHArf395e+vgQSUkWJs2JWzffjg5WStXSlKnTjp4MNfX5MmqWdPuxEDxQbEDALiVj4/S05WZWaCVf/hBzZpd4kCAQSh2AAC38vOTw6EZM869ZmKipk3T7bdf+kyAKSh2AAC3cjjk769hw5SQcI41hw1T9eq66Sa3xAKMQLEDALibn5/CwnTTTY6DB884id0LL+jzzzVlihxnXAVAXhQ7AIANZsyQr68iI0vNnOnlcuV66q+/1KWLxo3TrFmqV8+mfEDxRLEDANigVCnNn2898EDK44/7VaigoUMl6Zdf1KCBGjRQUJDWrlXr1nanBIobh2VZdmcALqE//zz52ZD90+5wONLSlJKSM+dCHr/+qmrV3BsRuNzUqqXDh7V/v2VZCQkJLpfXmjVB336r997TVVdp4EB16qSKFe0OCRRPTFAMw/n45EyCZVmWy+VyOp1O59kG7Hh5uSkYgGy+vurcWeXK6b331KaN+vSxOxBQnFHsYLjatbVmjSRlZGQmJSX5+fkFBATYHQoAgEuCMXYAAACGoNgBAAAYgmIHAABgCIodAACAIQy5eMKyrOTkZLtToEjLysqSlJ6env0NALsEZGU5LCv5yJHsGYhcLteRI0eOHfOQ/NPT048cSbM7IIocLy8vX19fu1MUD4YUO4fD4efnZ3cKFGmZmZkZGRmenp78qAD2cjgc2X+0LctKT093Op1+fn4+Pg5Jnp6efn6cSkJeTic/FQVlSLGT5OlpznvBpZB9bMDpdPKjAtjMkdPhTswZ7unp6eEh5fyG8hEOFB6/PwAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIawodglf9TFkZ+Gz//j/jAAAADG8HT/LhMTEyW/a+4c2L5qruUVW5ZxfxgAAABj2FXsyrV/bMyYJu7fOQAAgLFsOBWbmJgoBQcHu3/PAAAAJrO32LmO7v9vV/zRTPeHAAAAMI77i50rKemodPTncbdfVcavRPkqlcuVLB3WbtAnf6W4PQoAAIBJ3D/GLjExUdKaaZ+VunfA2ME1ApM2Lpry1udv9Gr599G13/ULcxRqo5ZlpaWlXdygMIzL5ZKUmZmZmppqdxbgsuZjWbKstNRUy7IkZWVlpaampqc7JW+Xy5WammF3QBQ5Hh4eXl5edqcoHtxf7Pzbj5g+/ZFSV3VoV7dE9pI+A3o2jGgcs3D4c/Pum9rJpzAbtSwrOTn5YsaEoTIyMjIy+NgA7OSVleU45Y+2y+VKTk4+dsxT8k5PT09OPmpvPBRBvr6+FLsCcn+x86tz/e11ci/yunLw4E5P3TVz8eLf1alpYTbqcDhKlChxMeLBWC6XKyUlxcvLy8enUP97AHCROJ1OORwlSpSwLOvo0aMeHh5+fn7+/k5J3t7eJUoU7swNTObh4WF3hGLDhulO8uNdrlywVPiDbg6Hw9fX96JGgmkyMjJSUlI8PT35UQFs5nDI4fD19c0udk6n09fX19tbkjw8PHx9+QgHCs/tF08k//XNhFee//SX3CfD4tevPyBVq1bN3XEAAACM4fYjdv5Ji/435M2DLX0bfv9EvewzYlnxc4a9skTOhrfdXNPdcQAAAIzh9mLnbDHsjXtio6YOaV7/+ztublrJGb9+0Vcz18SXaDp60mN1zv16AAAA5M+GMXYVb/lgxY8tXn75gznzP/hx/zHvkLBr7ho5aMTQm+v4uT8MAACAMWy5eMKzYkS/1yP6vW7HvgEAAExlwy3FAAAAcClQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEJ52BwAAXHZ6Hp6Q0V2SIy0t0Ol0ennp4EFJmjdP3bvnXXnwYLVo4faIQPFEsQMAuNtX6V3Tpmd/63Pq8s2btXlz3pVvu809oQATUOwAAO72d6kW1uo1lmUlJiZ6enoGBgaeZeVy5dyWCyj2KHYAAHer4bFDNWVZSkhweXk5g4LsDgSYgosnAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMISn3QEumszMTLsjoEhzuVySsrKy+FEB7OVhWQ4pMzPTsixJlmXxW4mzczqdTieHogrEkGJnWVZKSordKVCkZWVlScrMzORHBbBXgGXJslJSUrKLXVZWFr+VODsvLy9fX1+7UxQPhhQ7h8MRGBhodwoUaRkZGUlJSd7e3gEBAXZnAS5vTqccjsDAQMuyEhISPDw8+AMOXCwc2AQAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOAADAEBQ7AAAAQ1DsAAAADEGxAwAAMATFDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQNhW7pHUfPnZzk+plAnx8gyrWi+zz6o97XfYkAQAAMIWnDftMXfvM9a1G/+LT4LZeQxqVS9my4JMpT0Qu+mvW6skdy9gQBwAAwAw2FLttEwa++IvVYuzyH4de6SVJTz16Q/er7vyw///6bnr1Wg/3BwIAADCC+0/F/jvt0xWZgbfEDMxudZIcFXo82TtM2z79eLnl9jgAAACmcHuxS1u58lepSUSE76lLG7aKCNS+lSu3uTsOAACAMdxe7LZv3ZqlEtWqlc611FGtWhVp69at7o4DAABgDLePsTty5IhUokSJPIsDAwOlI4cPF3KrWVlZhw4dutBsuAykpKSkpqbanQK4rAW7XI6srEMJCdkPMzIyEo5/D+TL19c3ICDA7hTFgx1XxebHsizJ4XAU8uUOh8PpZE4+nI1lWZZl8aMC2M7hcJz4TXS5XPxW4pwK3w8uP24vdkFBQdL+0w7NHT58WCoZFFTIrTocjlKlSl1oNhgtIyMjKSmJ//YB9nM65XCUKlXKsqyEhARPT8+gQv/1B5Cb2/+TVC0szFPHtm3bn2upa+vWHVKtWrXcHQcAAMAYbi92Xi1aNnVo7eLFR09Z6Prp+x+PqVqrVlXdHQcAAMAY7h/WUKnHfZG+x2aNGbv2+Ah215aJo6bsdjbofX9Tt6cBAAAwhg0XT1S8f9zoj68dMrpto9/uvq1x2aP/zPl42trMq2MmPl7f/WEAAACMYcdVsV5XPjF/ZcVRT70+7YvXvkvxLlc3YsCkUc/1vYYR7QAAABfAYVncxguXheyrYv38/LgqFrBZrVo6fFj792dfFevl5cVVscDFwtRBAAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQAAGIJiBwAAYAiKHQAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhnBYlmV3BsBNsn/aHQ6H3UGAy1tSkixLwcHitxK42Ch2AAAAhuBULAAAgCEodgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYAQDcZ+9bbRwOR4n7ZtsdBDATxQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwBMUOpnPtW/nhiLvaNAirVNrf26dE2RpNOj84/ofdLrtzAZczh8NhHVg2ru8N9SuX9vPxL1298U2Pf/THEbtjAcUfxQ5m2zPz/hYRvZ//fPXh8o3a3XbHzW1qWevnThzcrkmvGXvtzgZcvrxca2NaXx8Tu7d803adr6/vv++X2Nfuj+j02j9ZdicDijmHZVl2ZwAuFWt1TM1mL/0b1OH93+c8UNVDkpSx+a1ODQfEHa0xZO3Wl66xOSBw2dn7VpvQAYu9/fzKXP/K918+HO4vSSl/v9Hl2kGLkgJu+/y/GT2C7c4IFGMcsYPJMkKj3vn6iylfvN4rp9VJ8qrVt3c7p7RtxQqO2QE2SU9rNHxiTquT5Bc+4IU+NaSjc6bPS7E1GFDcedodALiEvCs36Vi5iSS5Ug7GH0g6muayJGX5l5QSk5KSpAo2JwQuU1d17Fjp1MeOZq0jfF/dlrpu3Qbd2dCuVEDxR7GD2awDKyeOfO6dGYv/2p+SZ/AOwxAA2zjCwmrkXuKsXDlU2rZ3L0fSgQtBsYPJji6LadXu5X/SfWu27/tw5yY1ypX093JKf03q/exCrr8D7OMbEOCRd5Gvr6TU1FQ78gDGoNjBYPs+fPq1f9JV+5F5a99sE3hyedC8B+wLBUBKT0vLuyi70vn7++ezOoCC4uIJGGzNzz+7pLp39Tu11Um71q8/bFckAJLk2rFjV+4l1u7deyVVqlQp3xcAKBiKHQzmdHro+AmeE9JXvTFxpcQYO8BOv3z//aHcC5YvT5ECGjWqbVMiwAwUOxgs/MpwSX/Pjt18/LqJ1A0f33/njAptakrau3s3zQ6wh4f1/egnZu07/puZuWPqc+9tlkrd2qODt63BgOKOMXYwWPU+Q7uP7f7l8iHNmyy95doK6TtWfffd3yGD5y5p9WHNH7cenNK/i3Vj1MPj7mtgd1Dg8uFyuSSV6zWi09Lbr6h3XafWtUumbFs8a/7fiQrp+NKobgF2BwSKN47YwWRlot5b8G709XU8NsyZOvWrpfuq3jVx2fKX2pTu/PRbPRtVcP67OHbpv8yGCrhT9jUSJcp3GrdswVPXun6d9elH037cF9zktuHTVnzVp7rd8YDijluKAQAAGIIjdgAAAIag2AEAABiCYgcAAGAIih0AAIAhKHYAAACGoNgBAAAYgmIHAABgCIodAACAISh2AAAAhqDYASgCji0fVMfDkc2n8Yt/uU5fJX5aVEjOGo4yN3+yP8/T1sFVE3o3CDq+RuXBK90SHACKFIodgCLAv+WYKY/X9ZAkpf8yqs+rG7Nyr3AoduCgGQnZ3wd3Gjfh7nKnPJm8/vNBEeHXPvzhH4fdExcAiiiKHYAiwe/a0VOG1M+udqkrn41+a8sp97E+PPexh7/Yl/19yY6vTuwVevyZjB1zn+10ZaO73lixP08VBIDLEMUOQBHh83/PTR3WwEuSlLL4qej3duQ8kfx9zEMf7cr+PjDypYm9K5980YbJjz03b2e65FO9yzMT+jd0b2QAKGIodgCKDO9GI6eOaOgtSUpeNPShyXskpSwb3m9iTscLaPPSe9FV8r7Mq8oNw2b++des57pU93FnXAAocih2AIoQr6uHTx3ZNLvaJc19ov9n2396pu87OWdl/a578f1+1R25XlCyycAv1v393Yu31PJ3e1gAKHIodgCKFM+rYqaOau4rSTr09SNNb3r9n+zBc34tn3+/f5gjz+pVuzx8R3iAmzMCQFFFsQNQxHhcMWTKiy38JEmH4uOzZz7xaTb6g8G1+IsFAGfFn0kARY6zzsD/PVDx1CWlez47qC5/rwDgHPhDCaDo2fnh/6buPnXBwWkvf7DdrjQAUGxQ7AAUNTsn9nlsQfZUw56entnLjv4wtN/7u2wMBQDFAcUOQNGyfWKfITm1zrvpqO+nRpXNXn74uyce/niPjcEAoOij2AEoQqztE3sPWXBEkuR19fD3h7S+883x3UpnP5kU+2j/aXnvEQsAOIliB6DIsLa/03vIouxa53Hl0A+ebOAplb/znVc6l8xeIeHrgQNnHLQxIQAUbRQ7AEWEtfWd3jE5tc5Z99H3RzTOnqhYle6fMDYyMPv7/dMeeXTWIZsSAkBR57As69xrAcAlZm19u22DRxYflSRHzUeW/PFmhP+pz7513VUDlh6TJFW6f/76yR2yD+KtebvnK0tdOWulbIiL/S1BkuRXJ7JbozI5y6/oPfHZG4Lc8jYAwFYUOwBFgLV1fNsGg7Nrnao+FPfXO+1K5Fljw6sRVz+xIk2SVO3BhX9NiAyQ9M3dnrd86tLZtXxzz7JHKlz81ABQ1HAqFoDtrM1v9n4yp9Wp0v0TxuRtdZIcdQe//0yTnJOz2ydGP7nkmBsTAkDxwBE7AAAAQ3DEDgAAwBAUOwAAAENQ7AAAAAxBsQMAADAExQ4AAMAQFDsAAABDUOwAAAAMQbEDAAAwxP8DP1/h+mR5N1AAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,20,by=5), labels=seq(0,20,by=5), limits=c(0,20), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfea9298-a5b4-40ea-907a-4c9e5785c837",
   "metadata": {},
   "source": [
    "## Linear Mixed Model (LMM)\n",
    "\n",
    "* **Samples:** `≥2`\n",
    "* **Levels:** `≥2`\n",
    "* **Between or Within Subjects:** Within\n",
    "* **Reporting:** \"Figure 9 shows an interaction plot with ±1 standard deviation error bars for X1 and X2. A linear mixed model analysis of variance indicated a statistically significant effect on Y of X1 (F(1, 42) = 4.42, p < .05), but not of X2 (F(1, 42) = 0.22, n.s.), or of the X1×X2 interaction (F(1, 42) = 0.12, n.s.).\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2c04a1f2-efe9-4489-8be5-d828ebe8b06c",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 20 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>S</th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>Y</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>1</td><td>a</td><td>a</td><td>11.4749213</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>1</td><td>a</td><td>b</td><td>14.8431021</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>1</td><td>b</td><td>a</td><td> 0.1430649</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>1</td><td>b</td><td>b</td><td>15.0210806</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>2</td><td>a</td><td>a</td><td>16.9487115</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>2</td><td>a</td><td>b</td><td>12.9088880</td></tr>\n",
       "\t<tr><th scope=row>7</th><td>2</td><td>b</td><td>a</td><td> 7.3433619</td></tr>\n",
       "\t<tr><th scope=row>8</th><td>2</td><td>b</td><td>b</td><td>11.1885220</td></tr>\n",
       "\t<tr><th scope=row>9</th><td>3</td><td>a</td><td>a</td><td>12.3397073</td></tr>\n",
       "\t<tr><th scope=row>10</th><td>3</td><td>a</td><td>b</td><td>14.8390688</td></tr>\n",
       "\t<tr><th scope=row>11</th><td>3</td><td>b</td><td>a</td><td>21.5131754</td></tr>\n",
       "\t<tr><th scope=row>12</th><td>3</td><td>b</td><td>b</td><td> 0.2390247</td></tr>\n",
       "\t<tr><th scope=row>13</th><td>4</td><td>a</td><td>a</td><td>11.7081257</td></tr>\n",
       "\t<tr><th scope=row>14</th><td>4</td><td>a</td><td>b</td><td>13.8740498</td></tr>\n",
       "\t<tr><th scope=row>15</th><td>4</td><td>b</td><td>a</td><td> 4.3615137</td></tr>\n",
       "\t<tr><th scope=row>16</th><td>4</td><td>b</td><td>b</td><td> 2.3686943</td></tr>\n",
       "\t<tr><th scope=row>17</th><td>5</td><td>a</td><td>a</td><td>15.3668561</td></tr>\n",
       "\t<tr><th scope=row>18</th><td>5</td><td>a</td><td>b</td><td>13.6340391</td></tr>\n",
       "\t<tr><th scope=row>19</th><td>5</td><td>b</td><td>a</td><td> 4.9401806</td></tr>\n",
       "\t<tr><th scope=row>20</th><td>5</td><td>b</td><td>b</td><td>13.5781464</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 20 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & S & X1 & X2 & Y\\\\\n",
       "  & <int> & <chr> & <chr> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 1 & a & a & 11.4749213\\\\\n",
       "\t2 & 1 & a & b & 14.8431021\\\\\n",
       "\t3 & 1 & b & a &  0.1430649\\\\\n",
       "\t4 & 1 & b & b & 15.0210806\\\\\n",
       "\t5 & 2 & a & a & 16.9487115\\\\\n",
       "\t6 & 2 & a & b & 12.9088880\\\\\n",
       "\t7 & 2 & b & a &  7.3433619\\\\\n",
       "\t8 & 2 & b & b & 11.1885220\\\\\n",
       "\t9 & 3 & a & a & 12.3397073\\\\\n",
       "\t10 & 3 & a & b & 14.8390688\\\\\n",
       "\t11 & 3 & b & a & 21.5131754\\\\\n",
       "\t12 & 3 & b & b &  0.2390247\\\\\n",
       "\t13 & 4 & a & a & 11.7081257\\\\\n",
       "\t14 & 4 & a & b & 13.8740498\\\\\n",
       "\t15 & 4 & b & a &  4.3615137\\\\\n",
       "\t16 & 4 & b & b &  2.3686943\\\\\n",
       "\t17 & 5 & a & a & 15.3668561\\\\\n",
       "\t18 & 5 & a & b & 13.6340391\\\\\n",
       "\t19 & 5 & b & a &  4.9401806\\\\\n",
       "\t20 & 5 & b & b & 13.5781464\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 20 × 4\n",
       "\n",
       "| <!--/--> | S &lt;int&gt; | X1 &lt;chr&gt; | X2 &lt;chr&gt; | Y &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 | 1 | a | a | 11.4749213 |\n",
       "| 2 | 1 | a | b | 14.8431021 |\n",
       "| 3 | 1 | b | a |  0.1430649 |\n",
       "| 4 | 1 | b | b | 15.0210806 |\n",
       "| 5 | 2 | a | a | 16.9487115 |\n",
       "| 6 | 2 | a | b | 12.9088880 |\n",
       "| 7 | 2 | b | a |  7.3433619 |\n",
       "| 8 | 2 | b | b | 11.1885220 |\n",
       "| 9 | 3 | a | a | 12.3397073 |\n",
       "| 10 | 3 | a | b | 14.8390688 |\n",
       "| 11 | 3 | b | a | 21.5131754 |\n",
       "| 12 | 3 | b | b |  0.2390247 |\n",
       "| 13 | 4 | a | a | 11.7081257 |\n",
       "| 14 | 4 | a | b | 13.8740498 |\n",
       "| 15 | 4 | b | a |  4.3615137 |\n",
       "| 16 | 4 | b | b |  2.3686943 |\n",
       "| 17 | 5 | a | a | 15.3668561 |\n",
       "| 18 | 5 | a | b | 13.6340391 |\n",
       "| 19 | 5 | b | a |  4.9401806 |\n",
       "| 20 | 5 | b | b | 13.5781464 |\n",
       "\n"
      ],
      "text/plain": [
       "   S X1 X2 Y         \n",
       "1  1 a  a  11.4749213\n",
       "2  1 a  b  14.8431021\n",
       "3  1 b  a   0.1430649\n",
       "4  1 b  b  15.0210806\n",
       "5  2 a  a  16.9487115\n",
       "6  2 a  b  12.9088880\n",
       "7  2 b  a   7.3433619\n",
       "8  2 b  b  11.1885220\n",
       "9  3 a  a  12.3397073\n",
       "10 3 a  b  14.8390688\n",
       "11 3 b  a  21.5131754\n",
       "12 3 b  b   0.2390247\n",
       "13 4 a  a  11.7081257\n",
       "14 4 a  b  13.8740498\n",
       "15 4 b  a   4.3615137\n",
       "16 4 b  b   2.3686943\n",
       "17 5 a  a  15.3668561\n",
       "18 5 a  b  13.6340391\n",
       "19 5 b  a   4.9401806\n",
       "20 5 b  b  13.5781464"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example data\n",
    "# df has subjects (S), two within-Ss factors (X1,X2) each w/levels (a,b), and continuous response (Y)\n",
    "df <- read.csv(\"data/2F2LWs.csv\")\n",
    "head(df, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b05ba358-5774-42be-966b-920e6546dbf4",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: Matrix\n",
      "\n",
      "Loading required package: carData\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 4 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>F</th><th scope=col>Df</th><th scope=col>Df.res</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></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><th scope=row>(Intercept)</th><td>148.4297541</td><td>1</td><td>14</td><td>7.698544e-09</td></tr>\n",
       "\t<tr><th scope=row>X1</th><td>  4.4167657</td><td>1</td><td>42</td><td>4.162596e-02</td></tr>\n",
       "\t<tr><th scope=row>X2</th><td>  0.2203147</td><td>1</td><td>42</td><td>6.412279e-01</td></tr>\n",
       "\t<tr><th scope=row>X1:X2</th><td>  0.1180081</td><td>1</td><td>42</td><td>7.329188e-01</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 4 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & F & Df & Df.res & Pr(>F)\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t(Intercept) & 148.4297541 & 1 & 14 & 7.698544e-09\\\\\n",
       "\tX1 &   4.4167657 & 1 & 42 & 4.162596e-02\\\\\n",
       "\tX2 &   0.2203147 & 1 & 42 & 6.412279e-01\\\\\n",
       "\tX1:X2 &   0.1180081 & 1 & 42 & 7.329188e-01\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 4 × 4\n",
       "\n",
       "| <!--/--> | F &lt;dbl&gt; | Df &lt;dbl&gt; | Df.res &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| (Intercept) | 148.4297541 | 1 | 14 | 7.698544e-09 |\n",
       "| X1 |   4.4167657 | 1 | 42 | 4.162596e-02 |\n",
       "| X2 |   0.2203147 | 1 | 42 | 6.412279e-01 |\n",
       "| X1:X2 |   0.1180081 | 1 | 42 | 7.329188e-01 |\n",
       "\n"
      ],
      "text/plain": [
       "            F           Df Df.res Pr(>F)      \n",
       "(Intercept) 148.4297541 1  14     7.698544e-09\n",
       "X1            4.4167657 1  42     4.162596e-02\n",
       "X2            0.2203147 1  42     6.412279e-01\n",
       "X1:X2         0.1180081 1  42     7.329188e-01"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(lme4) # for lmer\n",
    "library(car) # for Anova\n",
    "df$S = factor(df$S) # Subject id is nominal\n",
    "df$X1 = factor(df$X1) # X1 is a 2-level factor\n",
    "df$X2 = factor(df$X2) # X2 is a 2-level factor\n",
    "contrasts(df$X1) <- \"contr.sum\"\n",
    "contrasts(df$X2) <- \"contr.sum\"\n",
    "m = lmer(Y ~ X1*X2 + (1|S), data=df)\n",
    "Anova(m, type=3, test.statistic=\"F\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b2fbf392-41f7-4595-a443-2292d33715ba",
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Interaction plot\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-plot-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-error-bars-quick-start-guide-r-software-and-data-visualization\n",
    "# http://www.sthda.com/english/wiki/ggplot2-point-shapes\n",
    "# http://www.sthda.com/english/wiki/ggplot2-line-types-how-to-change-line-types-of-a-graph-in-r-software\n",
    "df2 <- ddply(df, ~ X1*X2, function(d) # make a summary data table\n",
    "  c(NROW(d$Y),\n",
    "    sum(is.na(d$Y)),\n",
    "    sum(!is.na(d$Y)),\n",
    "    mean(d$Y, na.rm=TRUE),\n",
    "    sd(d$Y, na.rm=TRUE),\n",
    "    median(d$Y, na.rm=TRUE),\n",
    "    IQR(d$Y, na.rm=TRUE)))\n",
    "colnames(df2) <- c(\"X1\",\"X2\",\"Rows\",\"NAs\",\"NotNAs\",\"Mean\",\"SD\",\"Median\",\"IQR\")\n",
    "ggplot(data=df2, aes(x=X1, y=Mean, color=X2, group=X2)) + theme_minimal() + \n",
    "  # set the font styles for the plot title and axis titles\n",
    "  theme(plot.title   = element_text(face=\"bold\",  color=\"black\", size=18, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.x = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.title.y = element_text(face=\"bold\",  color=\"black\", size=16, hjust=0.5, vjust=0.0, angle=90)) + \n",
    "  # set the font styles for the value labels that show on each axis\n",
    "  theme(axis.text.x  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) + \n",
    "  theme(axis.text.y  = element_text(face=\"plain\", color=\"black\", size=12, hjust=0.0, vjust=0.5, angle=0)) + \n",
    "  # set the font styles for the legend\n",
    "  theme(legend.title = element_text(face=\"bold\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  theme(legend.text  = element_text(face=\"plain\", color=\"black\", size=14, hjust=0.5, vjust=0.0, angle=0)) +\n",
    "  # create the plot lines, points, and error bars\n",
    "  geom_line(aes(linetype=X2), position=position_dodge(0.05)) + \n",
    "  geom_point(aes(shape=X2, size=X2), position=position_dodge(0.05)) + \n",
    "  geom_errorbar(aes(ymin=Mean-SD, ymax=Mean+SD), position=position_dodge(0.05), width=0.1) + \n",
    "  # place text labels on each bar\n",
    "  geom_text(aes(label=sprintf(\"%.2f (±%.2f)\", Mean, SD)), position=position_dodge(0.05), hjust=0.0, vjust=-1.0, color=\"black\", size=3.5) +\n",
    "  # set the labels for the title and each axis\n",
    "  labs(title=\"Y by X1, X2\", x=\"X1\", y=\"Y\") + \n",
    "  # set the ranges and value labels for each axis\n",
    "  scale_x_discrete(labels=c(\"a\",\"b\")) + \n",
    "  scale_y_continuous(breaks=seq(0,20,by=5), labels=seq(0,20,by=5), limits=c(0,20), oob=rescale_none) + \n",
    "  # set the name, labels, and colors for the traces\n",
    "  scale_color_manual(name=\"X2\", labels=c(\"a\",\"b\"), values=c(\"red\", \"blue\")) +\n",
    "  # set the size and shape of the points\n",
    "  scale_size_manual(values=c(4,4)) +\n",
    "  scale_shape_manual(values=c(16,10)) +\n",
    "  # set the linetype of the lines\n",
    "  scale_linetype_manual(values=c(\"solid\", \"longdash\"))"
   ]
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