Problem Set 1b .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# HM 878 Applied Biostatistics Problem Set #1b\n",
    "\n",
    "## T-tests, ANOVA, Chi-Square, Correlation, Simple and Multivariate Linear Regression\n",
    "\n",
    "*This Problem Set will provide students with the opportunity to learn how to use R to conduct basic statistical tests, replicating many tests that were already done in HM 802. The main goal is to make\n",
    "sure you are familiar with R as a system for statistical analysis. Again, output from SPSS from HM 802 is included for comparison.*\n",
    "\n",
    "Analyses include:\n",
    "\n",
    "-   Independent t-test\n",
    "-   ANOVA\n",
    "-   Chi-square\n",
    "-   Correlation\n",
    "-   Simple and multivariate linear regression\n",
    "\n",
    "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "*Setting up the code environment*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'car' was built under R version 4.2.3\"\n",
      "Loading required package: carData\n",
      "\n",
      "\n",
      "Attaching package: 'dplyr'\n",
      "\n",
      "\n",
      "The following object is masked from 'package:car':\n",
      "\n",
      "    recode\n",
      "\n",
      "\n",
      "The following objects are masked from 'package:stats':\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "\n",
      "The following objects are masked from 'package:base':\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n",
      "\n",
      "── \u001b[1mAttaching core tidyverse packages\u001b[22m ──────────────────────── tidyverse 2.0.0 ──\n",
      "\u001b[32m✔\u001b[39m \u001b[34mforcats  \u001b[39m 1.0.0     \u001b[32m✔\u001b[39m \u001b[34mreadr    \u001b[39m 2.1.4\n",
      "\u001b[32m✔\u001b[39m \u001b[34mggplot2  \u001b[39m 3.4.1     \u001b[32m✔\u001b[39m \u001b[34mstringr  \u001b[39m 1.5.0\n",
      "\u001b[32m✔\u001b[39m \u001b[34mlubridate\u001b[39m 1.9.2     \u001b[32m✔\u001b[39m \u001b[34mtibble   \u001b[39m 3.1.8\n",
      "\u001b[32m✔\u001b[39m \u001b[34mpurrr    \u001b[39m 1.0.1     \u001b[32m✔\u001b[39m \u001b[34mtidyr    \u001b[39m 1.3.0\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[31m✖\u001b[39m \u001b[34mdplyr\u001b[39m::\u001b[32mrecode()\u001b[39m masks \u001b[34mcar\u001b[39m::recode()\n",
      "\u001b[31m✖\u001b[39m \u001b[34mpurrr\u001b[39m::\u001b[32msome()\u001b[39m   masks \u001b[34mcar\u001b[39m::some()\n",
      "\u001b[36mℹ\u001b[39m Use the conflicted package (\u001b[3m\u001b[34m<http://conflicted.r-lib.org/>\u001b[39m\u001b[23m) to force all conflicts to become errors\n"
     ]
    }
   ],
   "source": [
    "library(car) \n",
    "library(dplyr)\n",
    "library(tidyverse)\n",
    "library(rstatix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "## Question 1\n",
    "\n",
    "Is there a difference in knowledge scores between groups based on sex? Data: COVID-19 Knowledge.csv. Variables: Male and Knowledge Score. Use R to conduct an independent samples t-test using \"Male\" as\n",
    "the grouping variable, and \"Knowledge Score\" as the dependent variable. Calculate and report the appropriate descriptive statistics, and include the Levene's test for equality of variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df = read.csv(\"C:\\\\Users\\\\ljens\\\\Downloads\\\\COVID-19 Knowledge, Attitudes, and Behaviors.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df$Male <- factor(df$Male)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "  0.000   9.000  10.000   9.517  11.000  12.000 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[df$Male == 'Male','KnowledgeScore'] |> summary(KnowledgeScore)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
       "   4.00    9.00   10.00   10.01   11.00   12.00 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[df$Male == 'Female','KnowledgeScore'] |> summary(KnowledgeScore)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "ggplot(data = df, aes(x=Male, y=KnowledgeScore)) + \n",
    "  geom_boxplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Levene’s Test is performed to check for homogeneity of KnowledgeScore variances between Males and Females.\n",
    "\n",
    "Null hypothesis: KnowledgeScore variance is equal between the groups.\n",
    "\n",
    "Alt hypothesis: KnowledgeScore variance is different between the groups.\n",
    "\n",
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 2 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Df</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></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>group</th><td>   1</td><td>10.79294</td><td>0.001053159</td></tr>\n",
       "\t<tr><th scope=row> </th><td>1032</td><td>      NA</td><td>         NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 2 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & Df & F value & Pr(>F)\\\\\n",
       "  & <int> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tgroup &    1 & 10.79294 & 0.001053159\\\\\n",
       "\t  & 1032 &       NA &          NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 2 × 3\n",
       "\n",
       "| <!--/--> | Df &lt;int&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| group |    1 | 10.79294 | 0.001053159 |\n",
       "| <!----> | 1032 |       NA |          NA |\n",
       "\n"
      ],
      "text/plain": [
       "      Df   F value  Pr(>F)     \n",
       "group    1 10.79294 0.001053159\n",
       "      1032       NA          NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "leveneTest(KnowledgeScore ~ Male, df)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Levene’s test returned p = 0.001, so null is rejected. Mean variances are not homogeneous. We proceed to the t-test.\n",
    "\n",
    "Null hypothesis: There’s no difference in KnowledgeScore means between the two measured genders\n",
    "\n",
    "Alt hypothesis: Mean KnowledgeScore differs between the two measured genders.\n",
    "\n",
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "t = t.test(df$KnowledgeScore ~ df$Male, var.equal=FALSE)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWelch Two Sample t-test\n",
       "\n",
       "data:  df$KnowledgeScore by df$Male\n",
       "t = 4.1835, df = 1014.3, p-value = 3.119e-05\n",
       "alternative hypothesis: true difference in means between group Female and group Male is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 0.2603405 0.7203258\n",
       "sample estimates:\n",
       "mean in group Female   mean in group Male \n",
       "           10.006944             9.516611 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Female Mean:  10.0069444444444\"\n"
     ]
    }
   ],
   "source": [
    "print(paste('Female Mean: ',as.character(t$estimate)[1]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Male Mean:  9.51661129568106\"\n"
     ]
    }
   ],
   "source": [
    "print(paste('Male Mean: ',as.character(t$estimate)[2]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"p-value:  3.11851265227345e-05\"\n"
     ]
    }
   ],
   "source": [
    "print(paste('p-value: ',as.character(t$p.value)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The p-value is lower than alpha, so the null is rejected and we assume that there is a significant difference in mean knowledge scores between the two measured genders."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "## Question 2\n",
    "\n",
    "Is there a difference in knowledge scores among groups based on generational categories? Data: COVID-19 Knowledge.csv. Variables: Generations and Knowledge Score. Use R to conduct an ANOVA using\n",
    "\"Generations\" as the grouping variable, and \"Knowledge Score\" as the dependent variable. Generate appropriate descriptive stats, and if applicable, generate and interpret post hoc tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 4 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Generations</th><th scope=col>KnowledgeScore</th></tr>\n",
       "\t<tr><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl[,2]&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>Baby Boomers</td><td>11, 1</td></tr>\n",
       "\t<tr><td>Gen X       </td><td>10, 2</td></tr>\n",
       "\t<tr><td>Gen Z       </td><td> 9, 2</td></tr>\n",
       "\t<tr><td>Millenials  </td><td>10, 2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 4 × 2\n",
       "\\begin{tabular}{ll}\n",
       " Generations & KnowledgeScore\\\\\n",
       " <chr> & <dbl{[},2{]}>\\\\\n",
       "\\hline\n",
       "\t Baby Boomers & 11, 1\\\\\n",
       "\t Gen X        & 10, 2\\\\\n",
       "\t Gen Z        &  9, 2\\\\\n",
       "\t Millenials   & 10, 2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 4 × 2\n",
       "\n",
       "| Generations &lt;chr&gt; | KnowledgeScore &lt;dbl[,2]&gt; |\n",
       "|---|---|\n",
       "| Baby Boomers | 11, 1 |\n",
       "| Gen X        | 10, 2 |\n",
       "| Gen Z        |  9, 2 |\n",
       "| Millenials   | 10, 2 |\n",
       "\n"
      ],
      "text/plain": [
       "  Generations  KnowledgeScore\n",
       "1 Baby Boomers 11, 1         \n",
       "2 Gen X        10, 2         \n",
       "3 Gen Z         9, 2         \n",
       "4 Millenials   10, 2         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aggregate(KnowledgeScore ~ Generations, data=df, function(x) round(c(mean=mean(x), sd=sd(x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": [
    "ggplot(data = df, aes(x=Generations, y=KnowledgeScore)) + \n",
    "  geom_boxplot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "nova = aov(KnowledgeScore ~ Generations, data = df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Call:\n",
       "   aov(formula = KnowledgeScore ~ Generations, data = df)\n",
       "\n",
       "Terms:\n",
       "                Generations Residuals\n",
       "Sum of Squares      100.714  3765.069\n",
       "Deg. of Freedom           3      1030\n",
       "\n",
       "Residual standard error: 1.911912\n",
       "Estimated effects may be unbalanced"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nova"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Histogram of nova$residuals\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(nova$residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqPlot(nova$residuals, id=FALSE)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  nova$residuals\n",
       "W = 0.90133, p-value < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(nova$residuals)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "              Df Sum Sq Mean Sq F value   Pr(>F)    \n",
       "Generations    3    101   33.57   9.184 5.34e-06 ***\n",
       "Residuals   1030   3765    3.66                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(nova)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "  Tukey multiple comparisons of means\n",
       "    95% family-wise confidence level\n",
       "\n",
       "Fit: aov(formula = KnowledgeScore ~ Generations, data = df)\n",
       "\n",
       "$Generations\n",
       "                              diff        lwr         upr     p adj\n",
       "Gen X-Baby Boomers      -0.6837912 -1.3206758 -0.04690664 0.0297174\n",
       "Gen Z-Baby Boomers      -1.3562961 -2.1074952 -0.60509705 0.0000227\n",
       "Millenials-Baby Boomers -0.9204619 -1.4366902 -0.40423354 0.0000297\n",
       "Gen Z-Gen X             -0.6725049 -1.3827543  0.03774447 0.0710040\n",
       "Millenials-Gen X        -0.2366707 -0.6912538  0.21791248 0.5377678\n",
       "Millenials-Gen Z         0.4358342 -0.1685861  1.04025453 0.2481295\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TukeyHSD(nova)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"95% family-wise confidence level\n",
       "\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(TukeyHSD(nova))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Significant differences are seen between Boomers and basically every other generation. In other words, Boomers had higher Knowledge Scores than every other generation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A rstatix_test: 6 × 8</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>.y.</th><th scope=col>group1</th><th scope=col>group2</th><th scope=col>estimate</th><th scope=col>conf.low</th><th scope=col>conf.high</th><th scope=col>p.adj</th><th scope=col>p.adj.signif</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;chr&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>KnowledgeScore</td><td>Baby Boomers</td><td>Gen X     </td><td>-0.6837912</td><td>-1.2183066</td><td>-0.1492759</td><td>6.00e-03</td><td>**  </td></tr>\n",
       "\t<tr><th scope=row>2</th><td>KnowledgeScore</td><td>Baby Boomers</td><td>Gen Z     </td><td>-1.3562961</td><td>-2.1816282</td><td>-0.5309640</td><td>2.26e-04</td><td>*** </td></tr>\n",
       "\t<tr><th scope=row>3</th><td>KnowledgeScore</td><td>Baby Boomers</td><td>Millenials</td><td>-0.9204619</td><td>-1.3418489</td><td>-0.4990749</td><td>3.88e-07</td><td>****</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>KnowledgeScore</td><td>Gen X       </td><td>Gen Z     </td><td>-0.6725049</td><td>-1.4997496</td><td> 0.1547398</td><td>1.53e-01</td><td>ns  </td></tr>\n",
       "\t<tr><th scope=row>5</th><td>KnowledgeScore</td><td>Gen X       </td><td>Millenials</td><td>-0.2366707</td><td>-0.6611437</td><td> 0.1878024</td><td>4.74e-01</td><td>ns  </td></tr>\n",
       "\t<tr><th scope=row>6</th><td>KnowledgeScore</td><td>Gen Z       </td><td>Millenials</td><td> 0.4358342</td><td>-0.3255453</td><td> 1.1972138</td><td>4.41e-01</td><td>ns  </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A rstatix\\_test: 6 × 8\n",
       "\\begin{tabular}{r|llllllll}\n",
       "  & .y. & group1 & group2 & estimate & conf.low & conf.high & p.adj & p.adj.signif\\\\\n",
       "  & <chr> & <chr> & <chr> & <dbl> & <dbl> & <dbl> & <dbl> & <chr>\\\\\n",
       "\\hline\n",
       "\t1 & KnowledgeScore & Baby Boomers & Gen X      & -0.6837912 & -1.2183066 & -0.1492759 & 6.00e-03 & **  \\\\\n",
       "\t2 & KnowledgeScore & Baby Boomers & Gen Z      & -1.3562961 & -2.1816282 & -0.5309640 & 2.26e-04 & *** \\\\\n",
       "\t3 & KnowledgeScore & Baby Boomers & Millenials & -0.9204619 & -1.3418489 & -0.4990749 & 3.88e-07 & ****\\\\\n",
       "\t4 & KnowledgeScore & Gen X        & Gen Z      & -0.6725049 & -1.4997496 &  0.1547398 & 1.53e-01 & ns  \\\\\n",
       "\t5 & KnowledgeScore & Gen X        & Millenials & -0.2366707 & -0.6611437 &  0.1878024 & 4.74e-01 & ns  \\\\\n",
       "\t6 & KnowledgeScore & Gen Z        & Millenials &  0.4358342 & -0.3255453 &  1.1972138 & 4.41e-01 & ns  \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A rstatix_test: 6 × 8\n",
       "\n",
       "| <!--/--> | .y. &lt;chr&gt; | group1 &lt;chr&gt; | group2 &lt;chr&gt; | estimate &lt;dbl&gt; | conf.low &lt;dbl&gt; | conf.high &lt;dbl&gt; | p.adj &lt;dbl&gt; | p.adj.signif &lt;chr&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | KnowledgeScore | Baby Boomers | Gen X      | -0.6837912 | -1.2183066 | -0.1492759 | 6.00e-03 | **   |\n",
       "| 2 | KnowledgeScore | Baby Boomers | Gen Z      | -1.3562961 | -2.1816282 | -0.5309640 | 2.26e-04 | ***  |\n",
       "| 3 | KnowledgeScore | Baby Boomers | Millenials | -0.9204619 | -1.3418489 | -0.4990749 | 3.88e-07 | **** |\n",
       "| 4 | KnowledgeScore | Gen X        | Gen Z      | -0.6725049 | -1.4997496 |  0.1547398 | 1.53e-01 | ns   |\n",
       "| 5 | KnowledgeScore | Gen X        | Millenials | -0.2366707 | -0.6611437 |  0.1878024 | 4.74e-01 | ns   |\n",
       "| 6 | KnowledgeScore | Gen Z        | Millenials |  0.4358342 | -0.3255453 |  1.1972138 | 4.41e-01 | ns   |\n",
       "\n"
      ],
      "text/plain": [
       "  .y.            group1       group2     estimate   conf.low   conf.high \n",
       "1 KnowledgeScore Baby Boomers Gen X      -0.6837912 -1.2183066 -0.1492759\n",
       "2 KnowledgeScore Baby Boomers Gen Z      -1.3562961 -2.1816282 -0.5309640\n",
       "3 KnowledgeScore Baby Boomers Millenials -0.9204619 -1.3418489 -0.4990749\n",
       "4 KnowledgeScore Gen X        Gen Z      -0.6725049 -1.4997496  0.1547398\n",
       "5 KnowledgeScore Gen X        Millenials -0.2366707 -0.6611437  0.1878024\n",
       "6 KnowledgeScore Gen Z        Millenials  0.4358342 -0.3255453  1.1972138\n",
       "  p.adj    p.adj.signif\n",
       "1 6.00e-03 **          \n",
       "2 2.26e-04 ***         \n",
       "3 3.88e-07 ****        \n",
       "4 1.53e-01 ns          \n",
       "5 4.74e-01 ns          \n",
       "6 4.41e-01 ns          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "games_howell_test(df, KnowledgeScore ~ Generations, conf.level = 0.95, detailed = FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "## Question 3\n",
    "\n",
    "Is there an association between political party ideology/identification and whether respondents report that COVID-19 will be successfully controlled? Data: COVID-19 Knowledge.csv. Variables: RepDemInd\n",
    "and SuccessControl. Use R to conduct a chi-square analysis to determine if there is an association between the two variables.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df = read.csv(\"C:\\\\Users\\\\ljens\\\\Downloads\\\\COVID-19 Knowledge.csv\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df = df |> mutate(RepDemInd = as.character(factor(RepDemInd)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df = df |> mutate(SuccessControl = as.character(factor(SuccessControl)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   \n",
      "      1   2   3   4   5\n",
      "  1 123 112  28  13  13\n",
      "  2 118 201 105  51  12\n",
      "  3  55 132  43  19   9\n"
     ]
    }
   ],
   "source": [
    "print(table(df$RepDemInd, df$SuccessControl))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Null hypothesis: No association between political ideology and predicted COVID control.\n",
    "\n",
    "Alt hypothesis: Political ideology and predicted COVID control are associated.\n",
    "\n",
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Number of cases in table: 1034 \n",
       "Number of factors: 2 \n",
       "Test for independence of all factors:\n",
       "\tChisq = 58.87, df = 8, p-value = 7.777e-10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(table(df$RepDemInd, df$SuccessControl))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's Chi-squared test\n",
       "\n",
       "data:  df$RepDemInd and df$SuccessControl\n",
       "X-squared = 58.866, df = 8, p-value = 7.777e-10\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chisq.test(x=df$RepDemInd, y=df$SuccessControl, correct=FALSE)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "P-value is lower than alpha, so we reject the null and assume that the two variables are associated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "## Question 4\n",
    "\n",
    "Is there a correlation between the number of cigarettes smoked per day and BMI? Data: Cigarettes Smoked_BMI.csv. Variable: CigarettesSmoked and BMI. Using R, calculate a correlation coefficient and\n",
    "determine statistical significance. Second, using R, conduct a simple linear regression to predict BMI using CigarettesSmoked."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df = read.csv(\"C:\\\\Users\\\\ljens\\\\Downloads\\\\Cigarettes Smoked_BMI.csv\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing normality of CigarettesSmoked (not normal).\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  df$CigarettesSmoked\n",
       "W = 0.95968, p-value = 0.816\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(df$CigarettesSmoked)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing normality of BMI (not normal)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tShapiro-Wilk normality test\n",
       "\n",
       "data:  df$BMI\n",
       "W = 0.94087, p-value = 0.6466\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "shapiro.test(df$BMI)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using Pearson’s test to test for correlation between CigarettesSmoked and BMI\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  df$CigarettesSmoked and df$BMI\n",
       "t = 4.3126, df = 5, p-value = 0.007624\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 0.4063894 0.9833888\n",
       "sample estimates:\n",
       "      cor \n",
       "0.8877615 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor.test(x=df$CigarettesSmoked, y=df$BMI, method=\"pearson\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Pearson Correlation Coefficient:  0.887761545248006\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"Pearson Correlation Coefficient: \", as.character(cor.test(x=df$CigarettesSmoked, y=df$BMI, method=\"pearson\")$estimate)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Pearson P-Value:  0.00762398969022782\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"Pearson P-Value: \", as.character(cor.test(x=df$CigarettesSmoked, y=df$BMI, method=\"pearson\")$p.value)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As stated, the two variables have statistically significant correlation.\n",
    "\n",
    "Let’s see how the relationship looks in a chart.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[1m\u001b[22m`geom_smooth()` using method = 'loess' and formula = 'y ~ x'\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(df, aes(x=CigarettesSmoked, y=BMI)) +\n",
    "  geom_point() +\n",
    "  stat_smooth()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "model = lm(BMI ~ CigarettesSmoked, data = df)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "corr.coef = model$coefficients[2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "corr.incpt = model$coefficients[1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Linear Model: BMI =  0.345375218150087 * CigarettesSmoked +  19.9602094240838\"\n"
     ]
    }
   ],
   "source": [
    "print(paste('Linear Model: BMI = ', corr.coef, '* CigarettesSmoked + ', corr.incpt ))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each (daily?) cigarette smoked increased BMI by 0.35\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "## Question 5\n",
    "\n",
    "Run a Multiple Linear Regression. Data: Multiple Linear Regression Data, with Dependent variable: BMI5. Independent variables: HLTHPLN1, RFSMOK3, VEGESU1, and SEX. Remember to test for assumptions for\n",
    "doing a linear regression: equality of variances, multicollinearity, and outliers in the dependent variables. When doing the linear regression remember to also generate Collinearity Statistics and\n",
    "VIF, as well as a Normal P-P Plot to test for normality of residuals.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df <- read.csv(\"C:\\\\Users\\\\ljens\\\\Downloads\\\\Multiple Linear Regression Data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "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>'BMI5'</li><li>'SEX'</li><li>'VEGESU1'</li><li>'RFSMOK3'</li><li>'HLTHPLN1'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'BMI5'\n",
       "\\item 'SEX'\n",
       "\\item 'VEGESU1'\n",
       "\\item 'RFSMOK3'\n",
       "\\item 'HLTHPLN1'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'BMI5'\n",
       "2. 'SEX'\n",
       "3. 'VEGESU1'\n",
       "4. 'RFSMOK3'\n",
       "5. 'HLTHPLN1'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"BMI5\"     \"SEX\"      \"VEGESU1\"  \"RFSMOK3\"  \"HLTHPLN1\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colnames(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "m <- lm(BMI5 ~ HLTHPLN1 + RFSMOK3 + VEGESU1 + SEX, data = df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = BMI5 ~ HLTHPLN1 + RFSMOK3 + VEGESU1 + SEX, data = df)\n",
       "\n",
       "Coefficients:\n",
       "(Intercept)     HLTHPLN1      RFSMOK3      VEGESU1          SEX  \n",
       "   28.33762     -0.16289     -0.21248     -0.05257      0.36618  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = BMI5 ~ HLTHPLN1 + RFSMOK3 + VEGESU1 + SEX, data = df)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-16.522  -4.237  -1.102   3.050  71.403 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error  t value Pr(>|t|)    \n",
       "(Intercept) 28.337621   0.026376 1074.390  < 2e-16 ***\n",
       "HLTHPLN1    -0.162886   0.022378   -7.279 3.37e-13 ***\n",
       "RFSMOK3     -0.212477   0.014747  -14.409  < 2e-16 ***\n",
       "VEGESU1     -0.052570   0.003251  -16.171  < 2e-16 ***\n",
       "SEX          0.366175   0.019228   19.043  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 6.277 on 379010 degrees of freedom\n",
       "  (71001 observations deleted due to missingness)\n",
       "Multiple R-squared:  0.002334,\tAdjusted R-squared:  0.002324 \n",
       "F-statistic: 221.7 on 4 and 379010 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HLTHPLN1  RFSMOK3  VEGESU1      SEX \n",
      "1.001096 1.001178 1.000677 1.000928 \n"
     ]
    }
   ],
   "source": [
    "print(vif(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Call:\n",
      "   aov(formula = m)\n",
      "\n",
      "Terms:\n",
      "                HLTHPLN1  RFSMOK3  VEGESU1      SEX Residuals\n",
      "Sum of Squares      1994     7749    10913    14291  14935139\n",
      "Deg. of Freedom        1        1        1        1    379010\n",
      "\n",
      "Residual standard error: 6.277393\n",
      "Estimated effects may be unbalanced\n",
      "71001 observations deleted due to missingness\n"
     ]
    }
   ],
   "source": [
    "print(aov(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                Df   Sum Sq Mean Sq F value   Pr(>F)    \n",
       "HLTHPLN1         1     1994    1994    50.6 1.14e-12 ***\n",
       "RFSMOK3          1     7749    7749   196.6  < 2e-16 ***\n",
       "VEGESU1          1    10913   10913   276.9  < 2e-16 ***\n",
       "SEX              1    14291   14291   362.7  < 2e-16 ***\n",
       "Residuals   379010 14935139      39                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "71001 observations deleted due to missingness"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(aov(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "nova <- aov(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title \"Histogram of nova$residuals\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(nova$residuals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqPlot(nova$residuals, id=FALSE)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
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