{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bd2e788b",
   "metadata": {},
   "source": [
    "In this tutorial, we are going to see how to test for an association between two continuous variables in R. As we saw in the lectures, we can address this by running an association test using Pearson's correlations. In R, this can be accomplished with the `cor.test` function."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d4e7ed1",
   "metadata": {},
   "source": [
    "Let's first generate some fake data for this tutorial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "478a29fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>x</th><th scope=col>y</th><th scope=col>z</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></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>-1.2070657</td><td>-0.301309701</td><td> 0.41452353</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 0.2774292</td><td>-0.030464668</td><td>-0.47471847</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 1.0844412</td><td>-0.002444845</td><td> 0.06599349</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>-2.3456977</td><td>-0.336065971</td><td>-0.50247778</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 0.4291247</td><td> 0.026681517</td><td>-0.82599859</td></tr>\n",
       "\t<tr><th scope=row>6</th><td> 0.5060559</td><td> 0.106911171</td><td> 0.16698928</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & x & y & z\\\\\n",
       "  & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & -1.2070657 & -0.301309701 &  0.41452353\\\\\n",
       "\t2 &  0.2774292 & -0.030464668 & -0.47471847\\\\\n",
       "\t3 &  1.0844412 & -0.002444845 &  0.06599349\\\\\n",
       "\t4 & -2.3456977 & -0.336065971 & -0.50247778\\\\\n",
       "\t5 &  0.4291247 &  0.026681517 & -0.82599859\\\\\n",
       "\t6 &  0.5060559 &  0.106911171 &  0.16698928\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 3\n",
       "\n",
       "| <!--/--> | x &lt;dbl&gt; | y &lt;dbl&gt; | z &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 | -1.2070657 | -0.301309701 |  0.41452353 |\n",
       "| 2 |  0.2774292 | -0.030464668 | -0.47471847 |\n",
       "| 3 |  1.0844412 | -0.002444845 |  0.06599349 |\n",
       "| 4 | -2.3456977 | -0.336065971 | -0.50247778 |\n",
       "| 5 |  0.4291247 |  0.026681517 | -0.82599859 |\n",
       "| 6 |  0.5060559 |  0.106911171 |  0.16698928 |\n",
       "\n"
      ],
      "text/plain": [
       "  x          y            z          \n",
       "1 -1.2070657 -0.301309701  0.41452353\n",
       "2  0.2774292 -0.030464668 -0.47471847\n",
       "3  1.0844412 -0.002444845  0.06599349\n",
       "4 -2.3456977 -0.336065971 -0.50247778\n",
       "5  0.4291247  0.026681517 -0.82599859\n",
       "6  0.5060559  0.106911171  0.16698928"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1234)\n",
    "x<-rnorm(50)\n",
    "y<- 0.1*x + rnorm(50, sd = 1e-1)\n",
    "z<-rnorm(50)\n",
    "\n",
    "dat.tutorial<-data.frame(x,y,z)\n",
    "head(dat.tutorial)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d4fcc0f",
   "metadata": {},
   "source": [
    "Now, before performing any correlation test, it is always recommended to visualize the relationship between the two variables using a scatterplot. As usual, we can use **ggplot** for this task:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6f82a708",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "── \u001b[1mAttaching packages\u001b[22m ─────────────────────────────────────── tidyverse 1.3.2 ──\n",
      "\u001b[32m✔\u001b[39m \u001b[34mggplot2\u001b[39m 3.4.0      \u001b[32m✔\u001b[39m \u001b[34mpurrr  \u001b[39m 1.0.1 \n",
      "\u001b[32m✔\u001b[39m \u001b[34mtibble \u001b[39m 3.1.8      \u001b[32m✔\u001b[39m \u001b[34mdplyr  \u001b[39m 1.0.10\n",
      "\u001b[32m✔\u001b[39m \u001b[34mtidyr  \u001b[39m 1.2.1      \u001b[32m✔\u001b[39m \u001b[34mstringr\u001b[39m 1.5.0 \n",
      "\u001b[32m✔\u001b[39m \u001b[34mreadr  \u001b[39m 2.1.3      \u001b[32m✔\u001b[39m \u001b[34mforcats\u001b[39m 0.5.2 \n",
      "── \u001b[1mConflicts\u001b[22m ────────────────────────────────────────── tidyverse_conflicts() ──\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mfilter()\u001b[39m masks \u001b[34mstats\u001b[39m::filter()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mlag()\u001b[39m    masks \u001b[34mstats\u001b[39m::lag()\n",
      "\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n",
      "\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n"
     ]
    },
    {
     "data": {
      "image/png": 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+psTv8UsKFauxdj272Yd9x29Nq22f/V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STExMvHbt2lNPPaXebmmxWEwmUynvV2Bg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\nHQAAgCIodgAAAIr4fxENb5ZnHqNrAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[22m`geom_smooth()` using formula = 'y ~ x'\n"
     ]
    },
    {
     "data": {
      "image/png": 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XfT5XKVl5eXlZU184T6YwwGQ4ALDQ+a\npgkhmv8ORDSXy6Xq3rndbiFETU2N0+mUXUtQ6G/Ompoa2YUEhb53FRUVqh5b9COn7CqC5XiO\nnBdffPGSJUt83sBjx461Wq3BLS4Q2sKR0+FwyK4lKPw/cjocDv1JjibUwa55R44c2bFjh3cz\nNzfX5XId8/eiy+UKcl2SqZoMdGrvndvtVnsHmz++RDq1jy1qvzPFsXbwxBNPnD9//l//+lfv\nr9ihQ4fOmTMnUr4tkVJn62iapvaxxZ+9O+Z/fXgFu+HDh3/33XfezWnTpqWmpqanpzfzT6xW\na2JioslkCn51EpSWlrrdbovFIruQoNA0rby8PCUlRXYhQeF0OsvKyuLi4hITE2XXEhQ2m00I\nER8fL7uQoKisrLTZbMnJydHR0bJrCQqr1ZqUlGQ0qtnxqqSkRAhxzCPnnXfeecUVV3z44Yel\npaUDBw48//zzI2KCVu0jp8PhsFqt8fHxZrNZdi1B4f+R0+FwNP+TG17BDgCAkOnateu0adNk\nVwEEkpof1wAAANoggh0AAIAiCHYAAACKkHWOXadxT70zTtJrAwAAKIkZOwAAAEUQ7AAAABRB\nsAMAAFAEfewAhJGioqIXXnhh9+7dnTp1uvrqq3v06CG7IgCIJAQ7AOFi06ZNI0eO1G8bIIRY\nuHDhSy+9dOWVV8qtCgAiCEuxAMKCpmkTJkzwpjohRHV19dSpU/Py8iRWBQCRhWAHICxs3759\n165dPoNHjhz56KOPpNQDAJGIYAcgLFRWVjY5XlFREeJKACByEewAhIXevXvHxsY2Hh8wYEDo\niwGACEWwAxAWkpOT58+f7zM4YcKEM844Q0o9ABCJCHYAwsVf/vKX559/vlevXiaTqXPnznPm\nzFm+fLnsogAgktDuBEC4MBgMU6dOnTp1qqZpRiMfOwGgxTh0Agg7pDoAaB2OngAAAIog2AEA\nACiCYAcALZOXl1f/DhkAED4IdgBwvNasWdO9e/esrKy0tLQBAwZ8+eWXsisCgAYIdgBwXDZs\n2HD55Zf/9ttv+uYPP/xw0UUXeTcBIBwQ7ADguDz44IM+I1ar9bHHHpNRCwA0jWAHQGU///zz\n2LFjO3bs2LVr10mTJh08eLDVT7Vr167Ggzt37vSjOgAIMBoUA1DW/v37zzjjjNLSUn3zpZde\nWr9+/ebNm1NTU1vxbBaL5cCBAz6D6enp/lYJAIHDjB0AZd1zzz3eVKfbv3//ww8/3Lpnu/ba\na49zEABkIdgBUNY333xznIPH44477hg3blz9kfvuu++SSy5p3bMBQDCwFAtAWXFxccc5eDyM\nRuNrr702ffr0DRs2xMbGnnfeeX379vWvQAAIMIIdAGX98Y9/3Lp1q8/gxRdf7M9znnnmmWee\neaY/zwAAwcNSLABlzZkzZ8CAAfVHRo4cecstt8iqBwCCjRk7AMqKj4//6quvVq5c+cUXX0RH\nR48YMWLChAlGIx9oASiLYAdAZdHR0TfeeOONN94ouxAACAU+uQIAACiCYAcAAKAIgh0AAIAi\nCHYAAACKINgBAAAogqtiAUBZBw4cWLp06fbt27OyssaNG3feeefJrghAcBHsAEBNmzZtGjZs\nWGVlpb65YsWK+fPn33fffXKrAhBULMUCgJquvfZab6rT/fWvf/3pp59k1QMgBAh2AKCg/fv3\nb9++vfH4f//739AXAyBkCHYAoCC73d6icQBqINgBgIK6devWoUOHxuODBw8OfTEAQoZgBwAK\nMplMy5Yt8xmcMGHCsGHDpNQDIDQIdgCgpj/96U/r16+/4IILsrKyBg4c+MQTT7z44ouyiwIQ\nXLQ7AQBlDR8+fPjw4bKrABA6zNgBAAAogmAHAACgCIIdAACAIgh2AAAAiiDYAeGuoqKCprIA\ngONBsAPC14cffnjyyScnJSWZzeaRI0c2eYcoKQoKCtavX79p06bq6mrZtQAA6hDsgDD1v//9\n7/LLL9+6dasQwul0fvTRRyNGjCgoKJBbldvtvueee3Jyci6++OKzzz67Z8+e3HsUAMIHwQ4I\nU/fcc4/PfFheXt7jjz8uqx7dU089tWDBAu/S8O+//z5mzJg9e/bIrQoAoCPYAWFq27ZtjQf1\nCTyJnnjiCZ+R8vLy559/XkoxAAAfBDsgTCUnJzceTElJCX0lXm63+/fff288vm/fvtAXAwBo\njGAHhKlx48Y1HrzqqqtCX4mXwWDIzs5uPJ6TkxP6YgAAjRHsgHD08ccfHzlyxCdF3XXXXZdc\ncomsknQzZszwGTGbzVOmTJFSDADAR5TsAgD4mjlz5uLFi72bFovlpptuuuyyywYNGiSxKt0d\nd9yxf//+pUuX6puZmZnPP/98z5495VYFANAR7IDw8t///rd+qhNClJSU/Pbbb+GQ6oQQRqNx\nyZIld95559dff202m8855xyz2Sy7KACAB8EOCC9r1qxpPLh69Wq3220wGEJfT5NycnLS09OF\nEPHx8bJrAQDU4Rw7ILxUVVU1HqypqdE0LfTFAAAiC8EOCC8DBgxoPNivXz+TyRT6YgAAkYVg\nB4SXqVOnnnLKKT6DS5YskVIMACCyEOyA8BIXF/fRRx9NnTq1Q4cOCQkJZ5999meffTZ06FDZ\ndQEAIgAXTwBhJyMjg5t0AQBagRk7AAAARRDsAAAAFEGwAwAAUATBDgAAQBEEOwAAAEUQ7AAA\nABRBsAMAAFAEwQ4AAEARBDsAAABFEOwAAAAUQbADAABQBMEOAABAEQQ7AAAARRDsgMDTNO2F\nF14455xzMjMzTzrppKeeesrlcskuCgCgvijZBQAKmj9//pw5c/Svt23bdtttt+3bt2/RokVy\nq/LTnj17XnrppX379nXv3n3y5MlpaWmyKwIA+CLYAQGWl5c3b948n8G//e1v06ZN69Gjh5SS\n/PfOO+9cddVVNptN31y0aNFbb7117rnnSi0KAOCLpVggwDZv3ux0OhuPb9q0KfTFBITVar3+\n+uu9qU4IUVlZef3111dXV0usCgDQGMEOCLD4+PgmxxMSEkJcSaB88cUXxcXFPoN5eXnffvut\nlHoAAEcT1kuxbrfb5XI1f9a5/piQlSSFqjuoaZqS/30DBw7MzMzMz8+vP5iamjp48OAI3dmK\nioomxysrKyN0j47J7XYLITRNU3gHXS6XvpuqUvX/TtUjp07TNKH0b3Z9B/3Zu2P+27AOdpqm\nVVVVHe2Xis7lclVVVRkMhpBVFUr6O6D570DkcrvdmqYpuXfPPPPM+PHjvSuVcXFxf//736Oi\noiJ0Z3v27Nl40GQynXjiiRG6R8ekHzptNpvCx5aqqirZVQSL2kdOIYSqR05R+39nt9vVDnZN\nnq5znBwOh/4kRxPWwc5kMiUlJSUnJzfzGKvVmpiYaDKZQlZVKJWWlrrd7ua/A5FL07Ty8nIl\n9+5Pf/rTTz/9tGzZsgMHDuTm5l5//fUnnHCC7KJab8CAATNmzFiyZEn9wdmzZ3fp0uVo686R\nrrKy0mazmc3m6Oho2bUEhdVqTUpKMhrVPBunpKRECKHksUUofeQUQjgcDqvVGhsbazabZdcS\nFPrJyv4cOR0OR/M/uWEd7IDI1bVr13vvvTcuLi4xMVF2LQGwaNGizp07P/vss3q7k+nTp19z\nzTWyiwIA+CLYATi26OjomTNnzpw50ztS/yJZAECYUHMeHgAAoA0i2AEAACiCYAcAAKAIgh0A\nAIAiCHYAAACKINgBAAAogmAHAACgCPrYoe369ttvv/nmm9jY2OHDh+fm5souBwAAfxHs0BZp\nmjZx4sR//OMf+mZsbOzcuXNnz54ttyoAAPzEUizaoscff9yb6oQQNTU1d99997p16ySWBACA\n/wh2aIteeuml4xwMiPfee++qq64aNmzYtGnTdu3aFaRXAQCApVi0RYWFhcc56L+5c+c++OCD\n+teff/75qlWrPvjgg3PPPTcYrwUAaOOYsUNb1LNnz8aDvXr1CvgL7dixw5vqdDU1NRMnTnS5\nXAF/LQAACHZoi+bMmeMzkpycPHPmzIC/0Oeff954cP/+/bt37w74awEAQLBDW3TBBRe8+uqr\nWVlZ+ubJJ5/87rvvdu3aNeAvdLSZOWbsAADBwDl2aKPGjx8/bty43377LS4uLjs7O0ivctZZ\nZzUezMjI6N27d5BeEQDQljFjh7bLYDB07949eKlOCHHqqafedtttPoPPP/98VBSfqQAAgcdv\nFyC4nnzyyQEDBrzyyisHDx488cQTZ82a1eQ0HgAA/mPGDgguo9F43XXXffzxxzt37nz77bcj\nItU5nc4nn3yyb9++7dq1O+2001599VW32y27KADAsTFjB8DX7bff/vTTT+tfb9q06eqrr87P\nz69/1fCePXuef/7533//vUePHpMnT+7cubOkSgEADRDsADSwdetWb6rzuvfeeydNmpSamiqE\nWLt27dixY6urq/W/+tvf/vb222+PHDky1IUCABphKRZAA5s2bWo8WFNTs2XLFiGE1WqdNGmS\nN9UJIaqqqq699tqqqqrQlQgAOAqCHYAG4uLimhyPj48XQmzcuLG4uNjnr/Lz87/66qugVwYA\nOBaCHYAGzj333MTERJ/BnJycU089VQhxtJk5ZuwAIBwQ7AA0kJmZ+eyzz8bExHhHzGbzK6+8\nEh0dLYTQ450Pk8nU5DgAIMS4eAKArwkTJvTv33/VqlX79u074YQTpk2blpOTo/9Vbm7uX/7y\nl8cff7z+4++5556OHTvKqBQA0ADBDkAT+vbt+9hjjzX5VwsWLOjcufPTTz+9b9++7t27T58+\nferUqSEuDwDQJIIdgJaJioryhjn9igoAQJjgHDsAAIBWcrtFkVX8tEeUHpFdihCCGTsAAIBj\nsjvE4RKRVyLySkR+iThU7Pm6oFTYnUII8dAk8YczZVdJsAMAAPAqKRd5JSKvVOSViMPFIr82\nzJUca0IuryQk9R0LwQ5tiNvtNhgMsqsAAEhmd4qCUk9i0+fe9AB3uETYHa18ToIdECKFhYX3\n3Xff22+/XV5e3q9fv7lz51500UWyiwIABJ210pPeDteunOaXisPForhcuN1+PXNcjMhOEx0s\ndX965gSoaP8Q7KA4u91+0UUXee9/+u233/7hD394//33R40aJbcwAEBAOF2ioEzklYi8YnG4\npG7x9FCxqLb79cwGg0hrJ7LSRGaqJ71l1Ya5ZHOAqg80gh0Ut2rVqsZ3tZ8xY8auXbuk1AMA\naJ0jVZ75tsMl9RZPi0VRudA0v545JlpkWUQHi8i0iA6Wuqm4jFQRE2lBKdLqBVpo8+bNjQd3\n795dWVlpNofrBy4AaKs0TRSUGayHPbNu3rm3/BJRWe3vk1uSPIkt0zv3lio6WISlXSBKDw8E\nOyiuyfQWHR0dGxsb+mLU89577y1YsGDXrl1ZWVlXX331jBkz9FvKAkDzqmp8V04Pl4jDxVGF\nZekuP6ffokRG7cqpPvemz8NlWURMGzg+EeyguMsvv3zRokU+g5deemlUFG9+f73xxhuTJk3S\nvy4oKPjxxx+3bNny8ssvy60KQPjQm/fWb//mvYihvKrJf9GCxgXJ5rqV0/rnwKW1E225/wG/\n26C4wYMHz5kzZ+7cud6RHj16LFu2TGJJarDb7TNnzvQZfOWVV2644YahQ4dKKQmALDWOBped\nHiqqbd5bJhxOv545yiQyUkQHi+iQJrJq59706bd41l2aQrCD+h588MFRo0atWbOmpKTk1FNP\nve666+Li4mQXFfF+/fXX0tLSxuNff/01wQ5QVXF5g5Zvh4tFfqnIKwnA3bQS4/XE5k4112Sn\nGzt3iNHTW3qyMHL305Yg2KFNOPPMM888Mwxu9SKEEMLpdO7YscNqtfbt2zc1NVV2Oa0UExPT\n5DgnLwKRzu5scN5bXrHnNgx5fjTv1RmNon1yXdMQff00O110sAhznBBCOBxOq7UiPj7ebG76\nCINjItgBIbVhw4bJkyfv3r1bCBEbG3vnnXfOmzcvEu+H0b179549e+o74hUXFzdy5EhZJQFo\nkbIKz3ybdxVV/1Nk9feZE2I9i6ee5r2pniSXkSpMTL8FGcEOCJ1Dhw796U9/Kioq0jdramoe\nfvjh9PT022+/XW5hrWAwGFasWHHRRRdVVlZ6Bx9++OGePXtKrAqAD6fLc++swzfHFfoAACAA\nSURBVPWiW36AmvemJzdo/5aV5uke0o5eUvIQ7IDQWblypTfVeS1cuDASg50Q4rTTTtu1a9dT\nTz21ffv27Ozsa665ZvDgwbKLAtqoI1X1Fk+9f4pFkVVo/t07Kza6iZXTDhaRkSKiCRHhh/8T\nIHT27dvXeDAvL6+6ujpCr+fo2LHjo48+KrsKoK1waaKgVPz6e9SRGs/1p4Fs3tvOM99Wdw6c\nRXSwCEtSIEpHqBDsgNDJyspqPJiWlhahqQ5AkFRVN5h701dO80pEYZlwaUYhElv9zDFRDTqG\n1N2GoW00720LCHZA6EycOPHJJ5+sqKioP3jLLbfIqgeARJpbFFtrL1wo9aycNtu8twWSzb43\nrdf/pCcHonSEMYIdEDo9evT4xz/+MXXq1MLCQn3kuuuuu//+++VWBSCoahyehr3eS1D1qbjC\ngDTvTRUdUmneizoEOyCkLrvssuHDh3/55ZclJSUDBw7kGlJAGUVWT3TzXMRQ7Alz/jfvTUoQ\nmakiS09vqe7keFu3TglZaSI9WRgjr1cSgotgB4Rau3btLrzwQtlVAGgNu6OuW6/PPezt/k2/\nmYwiPVlkpYmshnc+9Tbv1Wmau7zcnpKS4OeOQFUEO0Amt9u9d+9es9mckZEhu5bmaJpm5LY+\naEtKj3jm27wrp3qAKy7395kTYj0rp97LTrPTRAeLaJ9C814EAMEOkObVV1+988478/LyhBD9\n+/d/9tlnzzjjDNlFNfDrr7/eddddH3/8scPhOPPMMxcuXDho0CDZRcFf33777WOPPfb77793\n6tRpypQpo0aNkl2RNA6nKChrsHLq/brGz3tnGURacsPLTtM892CgeS+CimAHyPHBBx9cffXV\n3s3NmzdfdNFFP/74Y05OjsSq6isqKho2bNjBgwf1zU8++eTcc8/95ptv+vbtK7cw+OOf//zn\nmDFj9K+//vrrf/3rXwsXLpw1a5bcqoKtvNKzfnq4uHbltFQcLhbFgWjeqzfs1RdPs2ovYqB5\nL2ThfQfI8eCDD/qMlJaWLl68+IknnpBRThMee+wxb6rTVVVVzZ49+z//+Y+skuAnm812ww03\n+Azef//9Y8aM6datm5SSAkhv3ptfKnbviym0mqw2kV97D/uqGn+fPK1dvRtnWepOg0uleS/C\nDMEOkOPnn39uPLhr167QV3I0mzdvbjz4ww8/hL4SBMrmzZtLS0t9Bu12+xdffBFBwa6yusHK\nqec0uGJRaBWapj+klf17Y6Lrbr3QoIFIKs17ETEIdoAcaWlpJSUlPoPt27eXUkyTzOYmTgVK\nTGx9y3tI53b7t+4YQppbFNU2782vvQXq4WKRXyqO+N28NzXJ97JT/U9au0CUDkhFsAPkmDRp\n0r333uszOHHiRCnFNGn06NGrV6/2Gfzzn/8spRgERP/+/ZOTk61Wq8/40KFDpdQjhKi2e26W\n5U1vecUir1QUlAqny69njo4SGSm+6S0zVWSni1im36Augh0gx6xZs3788cc33nhD34yNjZ03\nb97w4cPlVlXfNddc89FHH73yyivekSFDhjzwwAMSS4KfEhISnnnmmfHjx9cfnD9/fvfu3YP6\num63KC73zLfp66eHai9isFb6++TtEuoWT/UvEkzlmalabpcUmveiDSLYAXKYTKbXX3/9jjvu\n+Prrr+Pi4kaMGJGbmyu7KF8vv/zy+PHj161bV11dPWTIkCuvvJJudpFu3LhxnTt3XrRo0Z49\ne7p06TJlypTLLrssUE9udzRo2HuoNsnlB6J5b/uUupZvmfXuYZ8Q5/vgkhKnENySAW0UwQ6Q\n6Ywzzgi33nU+Ro0a1Zb7nClpyJAhJ510UlJSUqtjesmRupZv3vvW55WKEv+b98bVS2/eBiJp\non2y4DMFcDwIdgCAJjictfNtpZ572OfVngZn97t5r37vrA4N71vfwSKSuFEW4B+CHQC0aeWV\ndQ1782rvnXW4RBRZhZ8X0cbFiOy0htEtTXRIFRmpIsoUoOoBNESwAwD1OV2isKyu/dv+/Pji\nIwb9ZDg/m/caDJ7mvd4/WbULqSn0xgFCjmAHAOrQm/fqK6f5tTfR0qffapv36mJa+swx0Q3T\nW727oMbwmwQIG/w4AkCE0TRRZBWHS+pdwVA7FVdh8/fJU5OaTm807wUiAsEOAMKUraauYa83\nveWXiIKyADTvzUz1XHaane75gua9gAIIdggvO3bs+Oyzz1wu11lnnTVgwADZ5QBB53aLImvd\nbU/19m/6FQwBaN5r9tz8tO7WCxaRZRHRwtquXevbnQAIWwQ7hJEHHnhg4cKFdrtd35w8efLy\n5csNBtqMQgV6816flVM9zDn8bt6bkeq7cqpfgpoQ2/Q/aXRTMQCKINghXLzzzjvz5s2rP7Jy\n5cr+/fvfeuutskoCWqGk3NM9xLtyqge4kiP+PrM5zrNy2qB5r0Wk07wXQC2CHcLFSy+91Hjw\nxRdfJNghDNmdnsSWX+pZOfW2f/O3ea9RpLfzXTnNShOZqTTvDQxN01asWLF48eI9e/Z07tz5\nhhtuuP3226OjObUQijjOYLfzX/PfsV9807j+ST5/UfLv2y59ImX+hnnnBroytDVFRUXHOQiE\njLWyiZXTw8WiuNzf5r3xsXUrp972b5kWkZFC897geuSRR+6//379619++WXWrFl79+59+umn\n5VYFBMpxBrut/3f/7H898tK6FauXje9Z/5wN+6GfNm5M53cv/NezZ88vvvjCZ7BXr15SikGb\n4nSJgjLPbU/10+AOFcbllcTll5mq7X49s968V59vq9+8t4NFJJsDVD1aorCwcO7cuT6Dy5Yt\nu/nmm/v27SulJCCwjn8p1pCZUvLihNO3ff/avxf+IZsPlAi0WbNmvfHGGxUVFfUH58yZI6se\nqOdIlWe+7XDtyqk+FVdkFZrv9FvLjnEx0Q2m37zpLSOV5r3h5aeffnI6m7hW5fvvvyfYQQ3H\nf8gxnr/02zGfX37145cM3DLvX6/fO9gSxLLQBvXs2fM///nPzTffvH37diFE586dlyxZMmTI\nENl1IcJomii0isPF4nCxp3uI3kAkv0RUVvv75JZ2nu4hmfXSW4dUYaF5b4RISGj6RMWjjQMR\npyWfJaNyLlv6xf9OnnTZLfcNH/TD31e/dMPJZlpRIICGDRu2bdu2w4cP2+32Ll26yC4HYa2q\nxrNy6r3s9FCxyC8VBaXCpR37nzcjJkq0T9HS27k6tjd1am/UY5zeTCSGM+wj3IABA3Jycn7/\n/ff6gykpKcOHD5dVEhBYLV0kSDh56hvf9DrpiivmTDtr5/cvvTMv9ihdkoDWysrKkl0CwoXm\nFsU+986qvYihvMrfJ082exJbdlqDBiJp7URVlc1msyUnJ0dH00dEKTExMf/4xz8uvvjiI0c8\n7Wfi4uJWrlxpsbAIBUW05uyP9HPu/+ibk2679Jrnxp6xY2i6EH0CXhaANqXGIQ4VeVZO80s9\n97DPKxEFZf42740yiYwU0cEiOqSJrNq5N336LZ6PpZHParVu3rzZZDL169cvKcm3b0OTzjnn\nnJ07d65cufKXX37p3Lnzddddl5ubG+w6gZBp5Wm90V3/9Oz/Np5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G33vvvcrKSrPZLKUkAEBE++abb77//vvk5ORhw4ZlZ2fLLgcRg2AX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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PDanqz7778/Ly/vm2++cW2GhoY+8sgj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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(tidyverse)\n",
    "\n",
    "ggplot(data=dat.tutorial, mapping=aes(x,y)) + \n",
    "geom_point() + \n",
    "geom_smooth(method = \"lm\",  se = FALSE) + \n",
    "theme_bw()\n",
    "\n",
    "ggplot(data=dat.tutorial, mapping=aes(x,z)) + \n",
    "geom_point() + \n",
    "geom_smooth(method = \"lm\",  se = FALSE) + \n",
    "theme_bw()\n",
    "\n",
    "ggplot(data=dat.tutorial, mapping=aes(y,z)) + \n",
    "geom_point() + \n",
    "geom_smooth(method = \"lm\",  se = FALSE) + \n",
    "theme_bw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e80f17bc",
   "metadata": {},
   "source": [
    "As we can see, it seems that the strongest correlation occurs between the variables \"x\" and \"y\". But is this correlation significant if we adopt, for example, the usual Type I error rate of $\\alpha=0.05$?\"\n",
    "\n",
    "Let's address this using the `cor.test` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4978b2e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  x and y\n",
       "t = 5.4891, df = 48, p-value = 1.497e-06\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 0.4142598 0.7668035\n",
       "sample estimates:\n",
       "     cor \n",
       "0.621001 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.xy<-cor.test(x, y)\n",
    "res.xy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e6aca9e",
   "metadata": {},
   "source": [
    "As you can see, running this test is very simple as we just need to use as arguments in this function the variables whose association we want to test.\n",
    "\n",
    "Alternatively, you can achieve the same result using the formulas syntax as follows (Note how the formula needs to be used in this case):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7cc60acd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  x and y\n",
       "t = 5.4891, df = 48, p-value = 1.497e-06\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 0.4142598 0.7668035\n",
       "sample estimates:\n",
       "     cor \n",
       "0.621001 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.xy<-cor.test(formula = ~ x + y, data = dat.tutorial)\n",
    "res.xy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc9305c0",
   "metadata": {},
   "source": [
    "As usual, whenever we run a statistical test and save its outputs to a variable, this will store a bunch of important results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "56f0df82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'statistic'</li><li>'parameter'</li><li>'p.value'</li><li>'estimate'</li><li>'null.value'</li><li>'alternative'</li><li>'method'</li><li>'data.name'</li><li>'conf.int'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'statistic'\n",
       "\\item 'parameter'\n",
       "\\item 'p.value'\n",
       "\\item 'estimate'\n",
       "\\item 'null.value'\n",
       "\\item 'alternative'\n",
       "\\item 'method'\n",
       "\\item 'data.name'\n",
       "\\item 'conf.int'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'statistic'\n",
       "2. 'parameter'\n",
       "3. 'p.value'\n",
       "4. 'estimate'\n",
       "5. 'null.value'\n",
       "6. 'alternative'\n",
       "7. 'method'\n",
       "8. 'data.name'\n",
       "9. 'conf.int'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"statistic\"   \"parameter\"   \"p.value\"     \"estimate\"    \"null.value\" \n",
       "[6] \"alternative\" \"method\"      \"data.name\"   \"conf.int\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "names(res.xy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2947e2a5",
   "metadata": {},
   "source": [
    "In particular, here the \"estimate\" refers to the observed Pearson correlation *r*, and \"statistic\" the t-statistic built to generate our p-value, as we saw in the lectures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "59b36d0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>cor:</strong> 0.621001002293932"
      ],
      "text/latex": [
       "\\textbf{cor:} 0.621001002293932"
      ],
      "text/markdown": [
       "**cor:** 0.621001002293932"
      ],
      "text/plain": [
       "     cor \n",
       "0.621001 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<strong>t:</strong> 5.48911396127289"
      ],
      "text/latex": [
       "\\textbf{t:} 5.48911396127289"
      ],
      "text/markdown": [
       "**t:** 5.48911396127289"
      ],
      "text/plain": [
       "       t \n",
       "5.489114 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This is the Pearson correlation\n",
    "res.xy$estimate\n",
    "\n",
    "# This is the t-statistic\n",
    "res.xy$statistic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83baf736",
   "metadata": {},
   "source": [
    "As we can see, assuming $\\alpha=0.05$, we can indeed reject the null hypothesis that there is no association between \"x\" and \"y\". \n",
    "\n",
    "In the above example, keep in mind that by default, `cor.test` uses $r\\neq 0$ as the alternative hypothesis, but we can change this to test either side of the correlation (r>0 or r<0) by setting the argument *alternative* in `cor.test`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "14f8614b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  x and y\n",
       "t = 5.4891, df = 48, p-value = 7.484e-07\n",
       "alternative hypothesis: true correlation is greater than 0\n",
       "95 percent confidence interval:\n",
       " 0.4515983 1.0000000\n",
       "sample estimates:\n",
       "     cor \n",
       "0.621001 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  x and y\n",
       "t = 5.4891, df = 48, p-value = 1\n",
       "alternative hypothesis: true correlation is less than 0\n",
       "95 percent confidence interval:\n",
       " -1.0000000  0.7471884\n",
       "sample estimates:\n",
       "     cor \n",
       "0.621001 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here the alternative hypothesis is that r > 0\n",
    "cor.test(formula = ~ x + y, data = dat.tutorial, alternative = \"greater\")\n",
    "\n",
    "# Here the alternative hypothesis is that r < 0\n",
    "cor.test(formula = ~ x + y, data = dat.tutorial, alternative = \"less\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c873260",
   "metadata": {},
   "source": [
    "Finally, for this particular dataset that we have created, we can also confirm that there is no significant statistical association between the other pairs of variables, as suggested by the scatterplots above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "94f6f465",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  dat.tutorial$x and dat.tutorial$z\n",
       "t = 0.71378, df = 48, p-value = 0.4788\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -0.1810290  0.3702683\n",
       "sample estimates:\n",
       "      cor \n",
       "0.1024828 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  y and z\n",
       "t = 1.5008, df = 48, p-value = 0.14\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -0.07080536  0.46279026\n",
       "sample estimates:\n",
       "      cor \n",
       "0.2117149 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This tests the association between x and z\n",
    "res.xz<-cor.test(dat.tutorial$x, dat.tutorial$z)\n",
    "res.xz\n",
    "\n",
    "# This tests the association between y and z\n",
    "res.yz<-cor.test(formula = ~ y + z, data = dat.tutorial)\n",
    "res.yz"
   ]
  }
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