Problem Set 2 MANOVA .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Set 2 - MANOVA\n",
    "Lillian Jensen\n",
    "\n",
    "Goal: Students will use R to conduct a Multivariate Analysis of Variance (MANOVA) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Background: An investigator is interested in determining if several outcome measures are differently influenced by sex, being a veteran, and rural residence. They have outcome data related to Adverse Childhood Experience (ACES), BMI, and self-reports of the number of poor physical health days in the last month, which they believe are correlated with each other, and therefore, they would be similarly influenced by sex, veteran status, and location of residence. They want to find out if ACES, BMI, and poor health days, as a group of characteristics are different among different groups (i.e., sex, veteran, and residence), and if interactions of these groups influence these characteristics. You’ve decided to tun a MANOVA to answer these questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'comprehenr' was built under R version 4.2.3\"\n"
     ]
    }
   ],
   "source": [
    "suppressPackageStartupMessages(library(tidyverse))\n",
    "suppressPackageStartupMessages(library(dplyr))\n",
    "suppressPackageStartupMessages(library(comprehenr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "df <- read.csv(\"C:\\\\Users\\\\ljens\\\\Downloads\\\\HM 878 730 Clements - 2019 BRFSS R Data File.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "# recoding missing values\n",
    "df$VETERAN[df$VETERAN == 7] <- NA\n",
    "df$VETERAN[df$VETERAN == 9] <- NA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1: Describe how the data for this project meets/or does not meet the following assumptions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *Two or more dependent variables*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dependent variables: ACES, BMI, and poor health days"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *At least one independent variable with two or more levels*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Independent variables: sex (2 levels), veteran (2 levels), and residence (2 levels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *Adequate sample size*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Sample size: \" \"418268\"       \n"
     ]
    }
   ],
   "source": [
    "print(c('Sample size: ', nrow(df)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample size is adequate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *No outliers in dependent variables*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of ACE Score by Sex\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$ACES_Score ~ df$SEX, main='Spread of ACE Score by Sex')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of ACE Score by Veteran Status\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$ACES_Score ~ df$VETERAN, main='Spread of ACE Score by Veteran Status')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of ACE Score by Location\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$ACES_Score ~ df$URBAN_RURAL, main='Spread of ACE Score by Location')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of BMI by Sex\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$BMI ~ df$SEX, main='Spread of BMI by Sex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of BMI by Veteran Status\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$BMI ~ df$VETERAN, main='Spread of BMI by Veteran Status')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of BMI by Location\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$BMI ~ df$URBAN_RURAL, main='Spread of BMI by Location')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title \"Spread of Poor Health Days by Sex\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    " boxplot(df$PHYSHLTH_DAYS ~ df$SEX, main='Spread of Poor Health Days by Sex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of Poor Health Days by Veteran Status\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$PHYSHLTH_DAYS ~ df$VETERAN, main='Spread of Poor Health Days by Veteran Status')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Spread of Poor Health Days by Location\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "boxplot(df$PHYSHLTH_DAYS ~ df$URBAN_RURAL, main='Spread of Poor Health Days by Location')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each view of the spread of the dependent variables shows significant outliers. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *Multivariate normality*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "# Replacing NA with variable means\n",
    "# This method overwrites the original dataframe - remember this for later analyses\n",
    "# Might need to reload the dataframe later on\n",
    "\n",
    "df$PHYSHLTH_DAYS[is.na(df$PHYSHLTH_DAYS)] <- mean(df$PHYSHLTH_DAYS, na.rm=T)\n",
    "df$BMI[is.na(df$BMI)] <- mean(df$BMI, na.rm=T)\n",
    "df$URBAN_RURAL[is.na(df$URBAN_RURAL)] <- mean(df$URBAN_RURAL, na.rm=T)\n",
    "df$ACES_Score[is.na(df$ACES_Score)] <- mean(df$ACES_Score, na.rm=T)\n",
    "df$SEX[is.na(df$SEX)] <- mean(df$SEX, na.rm=T)\n",
    "df$VETERAN[is.na(df$VETERAN)] <- mean(df$VETERAN, na.rm=T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in ks.test.default(df$PHYSHLTH_DAYS, \"pnorm\", mean(df$PHYSHLTH_DAYS), :\n",
      "\"ties should not be present for the Kolmogorov-Smirnov test\"\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in ks.test.default(df$BMI, \"pnorm\", mean(df$BMI), sd(df$BMI)):\n",
      "\"ties should not be present for the Kolmogorov-Smirnov test\"\n",
      "Warning message in ks.test.default(df$URBAN_RURAL, \"pnorm\", mean(df$URBAN_RURAL), :\n",
      "\"ties should not be present for the Kolmogorov-Smirnov test\"\n"
     ]
    }
   ],
   "source": [
    "ks_healthdays <- ks.test(df$PHYSHLTH_DAYS, 'pnorm',mean(df$PHYSHLTH_DAYS),sd(df$PHYSHLTH_DAYS))\n",
    "ks_bmi <- ks.test(df$BMI, 'pnorm',mean(df$BMI),sd(df$BMI))\n",
    "ks_loc <- ks.test(df$URBAN_RURAL, 'pnorm',mean(df$URBAN_RURAL),sd(df$URBAN_RURAL))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tAsymptotic one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df$PHYSHLTH_DAYS\n",
       "D = 0.33295, p-value < 2.2e-16\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ks_healthdays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tAsymptotic one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df$BMI\n",
       "D = 0.11948, p-value < 2.2e-16\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ks_bmi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tAsymptotic one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df$URBAN_RURAL\n",
       "D = 0.49594, p-value < 2.2e-16\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ks_loc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in ks.test.default(df$ACES_Score, \"pnorm\", mean(df$ACES_Score), :\n",
      "\"ties should not be present for the Kolmogorov-Smirnov test\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tAsymptotic one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df$ACES_Score\n",
       "D = 0.41052, p-value < 2.2e-16\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ACEs Score KS Test\n",
    "ks.test(df$ACES_Score, 'pnorm',mean(df$ACES_Score),sd(df$ACES_Score))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in ks.test.default(df$SEX, \"pnorm\", mean(df$SEX), sd(df$SEX)):\n",
      "\"ties should not be present for the Kolmogorov-Smirnov test\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tAsymptotic one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df$SEX\n",
       "D = 0.36514, p-value < 2.2e-16\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sex KS Test\n",
    "ks.test(df$SEX, 'pnorm',mean(df$SEX),sd(df$SEX))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in ks.test.default(df$VETERAN, \"pnorm\", mean(df$VETERAN), sd(df$VETERAN)):\n",
      "\"ties should not be present for the Kolmogorov-Smirnov test\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tAsymptotic one-sample Kolmogorov-Smirnov test\n",
       "\n",
       "data:  df$VETERAN\n",
       "D = 0.5166, p-value < 2.2e-16\n",
       "alternative hypothesis: two-sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Veteran Status KS Test\n",
    "ks.test(df$VETERAN, 'pnorm',mean(df$VETERAN),sd(df$VETERAN))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each KS test had significant p-values, which means that the null hypothesis of normality is rejected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *No multicollinearity between dependent variables*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  df$BMI and df$PHYSHLTH_DAYS\n",
       "t = 45.096, df = 418266, p-value < 2.2e-16\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 0.06654328 0.07257504\n",
       "sample estimates:\n",
       "      cor \n",
       "0.0695598 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor.test(df$BMI, df$PHYSHLTH_DAYS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  df$URBAN_RURAL and df$PHYSHLTH_DAYS\n",
       "t = -14.894, df = 418266, p-value < 2.2e-16\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -0.02605255 -0.01999467\n",
       "sample estimates:\n",
       "        cor \n",
       "-0.02302382 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor.test(df$URBAN_RURAL, df$PHYSHLTH_DAYS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  df$BMI and df$URBAN_RURAL\n",
       "t = -18.612, df = 418266, p-value < 2.2e-16\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -0.03179376 -0.02573768\n",
       "sample estimates:\n",
       "        cor \n",
       "-0.02876598 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor.test(df$BMI, df$URBAN_RURAL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  df$ACES_Score and df$URBAN_RURAL\n",
       "t = 13.295, df = 418266, p-value < 2.2e-16\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 0.01752267 0.02358121\n",
       "sample estimates:\n",
       "       cor \n",
       "0.02055213 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor.test(df$ACES_Score, df$URBAN_RURAL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's product-moment correlation\n",
       "\n",
       "data:  df$ACES_Score and df$BMI\n",
       "t = 24.674, df = 418266, p-value < 2.2e-16\n",
       "alternative hypothesis: true correlation is not equal to 0\n",
       "95 percent confidence interval:\n",
       " 0.03509794 0.04115022\n",
       "sample estimates:\n",
       "       cor \n",
       "0.03812443 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor.test(df$ACES_Score, df$BMI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With significant p-values for each correlation test, the 'no multicollinearity' assumption is violated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2: Based on your evaluation of the assumptions testing, is MANOVA an appropriate test in this situation? Explain."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MANOVA is not an appropriate test in this situation. Each of the dependent variables' distributions stray from the normal distribution, and each are significatly correlated with one another."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3: Run the MANOVA using sex (Male reference), veteran status (Not a veteran reference), and urban/rural location (rural reference) as the independent variables, and ACES, BMI, and number of poor physical health days as the dependent variables. Interpret the output for each of the following tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'multiUS' was built under R version 4.2.3\"\n"
     ]
    }
   ],
   "source": [
    "suppressPackageStartupMessages(library(MASS))\n",
    "suppressPackageStartupMessages(library(multiUS))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *Box's Test of Equality of Covariance Matrices*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------\n",
      "      MBox    Chi-sqr          df            P\n",
      "------------------------------------------------\n",
      "11569.1832 11569.0923           6       0.0000\n",
      "------------------------------------------------\n",
      "Covariance matrices are significantly different.\n"
     ]
    }
   ],
   "source": [
    "BoxMTest(X = cbind(df$ACES_Score, df$BMI, df$PHYSHLTH_DAYS), cl = as.factor(df$SEX))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------\n",
      "      MBox    Chi-sqr          df            P\n",
      "------------------------------------------------\n",
      "       Inf        Inf          12       0.0000\n",
      "------------------------------------------------\n",
      "Covariance matrices are significantly different.\n"
     ]
    }
   ],
   "source": [
    "BoxMTest(X = cbind(df$ACES_Score, df$BMI, df$PHYSHLTH_DAYS), cl = as.factor(df$URBAN_RURAL))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------\n",
      "      MBox    Chi-sqr          df            P\n",
      "------------------------------------------------\n",
      " 6278.7346  6277.2512          12       0.0000\n",
      "------------------------------------------------\n",
      "Covariance matrices are significantly different.\n"
     ]
    }
   ],
   "source": [
    "BoxMTest(X = cbind(df$ACES_Score, df$BMI, df$PHYSHLTH_DAYS), cl = as.factor(df$VETERAN))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------\n",
      "      MBox    Chi-sqr          df            P\n",
      "------------------------------------------------\n",
      "       Inf        Inf          24       0.0000\n",
      "------------------------------------------------\n",
      "Covariance matrices are significantly different.\n"
     ]
    }
   ],
   "source": [
    "BoxMTest(X = cbind(df$ACES_Score, df$BMI, df$PHYSHLTH_DAYS), cl = as.factor(df$VETERAN* df$URBAN_RURAL* df$SEX))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dependent variables failed the 'Equality of Covariances' assumption."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *Multivariate Tests*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "model <-manova(cbind(df$ACES_Score, df$BMI, df$PHYSHLTH_DAYS) ~ df$SEX * df$URBAN_RURAL * df$VETERAN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Call:\n",
       "   manova(cbind(df$ACES_Score, df$BMI, df$PHYSHLTH_DAYS) ~ df$SEX * \n",
       "    df$URBAN_RURAL * df$VETERAN)\n",
       "\n",
       "Terms:\n",
       "                  df$SEX df$URBAN_RURAL df$VETERAN df$SEX:df$URBAN_RURAL\n",
       "resp 1               391            200          1                     2\n",
       "resp 2              6896          13217          3                   164\n",
       "resp 3             96565          47391     100655                  1130\n",
       "Deg. of Freedom        1              1          1                     1\n",
       "                df$SEX:df$VETERAN df$URBAN_RURAL:df$VETERAN\n",
       "resp 1                        188                         5\n",
       "resp 2                          5                      1478\n",
       "resp 3                       9209                        78\n",
       "Deg. of Freedom                 1                         1\n",
       "                df$SEX:df$URBAN_RURAL:df$VETERAN Residuals\n",
       "resp 1                                         0    460525\n",
       "resp 2                                        58  15754558\n",
       "resp 3                                       477  91320097\n",
       "Deg. of Freedom                                1    418260\n",
       "\n",
       "Residual standard errors: 1.049309 6.137337 14.77611\n",
       "Estimated effects may be unbalanced"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df     Pillai approx F num Df den Df\n",
       "df$SEX                                1 0.00243326   340.07      3 418258\n",
       "df$URBAN_RURAL                        1 0.00177900   248.47      3 418258\n",
       "df$VETERAN                            1 0.00110954   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1 0.00002551     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1 0.00052273    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1 0.00010940    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1 0.00000843     1.18      3 418258\n",
       "Residuals                        418260                                  \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model, 'Pillai')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df   Wilks approx F num Df den Df\n",
       "df$SEX                                1 0.99757   340.07      3 418258\n",
       "df$URBAN_RURAL                        1 0.99822   248.47      3 418258\n",
       "df$VETERAN                            1 0.99889   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1 0.99997     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1 0.99948    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1 0.99989    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1 0.99999     1.18      3 418258\n",
       "Residuals                        418260                               \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model,'Wilks')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df        Roy approx F num Df den Df\n",
       "df$SEX                                1 0.00243920   340.07      3 418258\n",
       "df$URBAN_RURAL                        1 0.00178217   248.47      3 418258\n",
       "df$VETERAN                            1 0.00111077   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1 0.00002551     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1 0.00052300    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1 0.00010941    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1 0.00000843     1.18      3 418258\n",
       "Residuals                        418260                                  \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model, 'Roy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df Hotelling-Lawley approx F num Df den Df\n",
       "df$SEX                                1       0.00243920   340.07      3 418258\n",
       "df$URBAN_RURAL                        1       0.00178217   248.47      3 418258\n",
       "df$VETERAN                            1       0.00111077   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1       0.00002551     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1       0.00052300    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1       0.00010941    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1       0.00000843     1.18      3 418258\n",
       "Residuals                        418260                                        \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model, 'Hotelling-Lawley')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results are congruent among each of the four test statistics. Each individual independent variable had statistically significant impact on outcomes, and similarly, each linear combination of independent variables had significant impacts on outcomes; except for the combination of all three variables. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- *Tests of Between-Subjects Effects*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "nova <- summary.aov(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " Response 1 :\n",
       "                                     Df Sum Sq Mean Sq  F value  Pr(>F)    \n",
       "df$SEX                                1    391  390.70 354.8440 < 2e-16 ***\n",
       "df$URBAN_RURAL                        1    200  199.58 181.2655 < 2e-16 ***\n",
       "df$VETERAN                            1      1    0.72   0.6556 0.41813    \n",
       "df$SEX:df$URBAN_RURAL                 1      2    1.53   1.3903 0.23835    \n",
       "df$SEX:df$VETERAN                     1    188  188.20 170.9258 < 2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN             1      5    4.92   4.4715 0.03447 *  \n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1      0    0.09   0.0796 0.77782    \n",
       "Residuals                        418260 460525    1.10                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       " Response 2 :\n",
       "                                     Df   Sum Sq Mean Sq  F value    Pr(>F)    \n",
       "df$SEX                                1     6896  6896.3 183.0872 < 2.2e-16 ***\n",
       "df$URBAN_RURAL                        1    13217 13217.3 350.8993 < 2.2e-16 ***\n",
       "df$VETERAN                            1        3     2.8   0.0749   0.78440    \n",
       "df$SEX:df$URBAN_RURAL                 1      164   164.3   4.3610   0.03677 *  \n",
       "df$SEX:df$VETERAN                     1        5     4.6   0.1216   0.72734    \n",
       "df$URBAN_RURAL:df$VETERAN             1     1478  1478.0  39.2376 3.756e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1       58    58.1   1.5430   0.21418    \n",
       "Residuals                        418260 15754558    37.7                       \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       " Response 3 :\n",
       "                                     Df   Sum Sq Mean Sq  F value    Pr(>F)    \n",
       "df$SEX                                1    96565   96565 442.2817 < 2.2e-16 ***\n",
       "df$URBAN_RURAL                        1    47391   47391 217.0594 < 2.2e-16 ***\n",
       "df$VETERAN                            1   100655  100655 461.0133 < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL                 1     1130    1130   5.1747   0.02292 *  \n",
       "df$SEX:df$VETERAN                     1     9209    9209  42.1766 8.349e-11 ***\n",
       "df$URBAN_RURAL:df$VETERAN             1       78      78   0.3573   0.55003    \n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1      477     477   2.1842   0.13944    \n",
       "Residuals                        418260 91320097     218                       \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nova"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "p_adjust <- p.adjust(c(nova[[1]]$\"Pr(>F)\",nova[[2]]$\"Pr(>F)\",nova[[3]]$\"Pr(>F)\"),'fdr')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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>2.82011466593676e-78</li><li>7.84968020490841e-41</li><li>0.516513367677175</li><li>0.312838989255046</li><li>1.24099957483937e-38</li><li>0.0594008836701059</li><li>0.784396745245705</li><li>&lt;NA&gt;</li><li>3.66658100801849e-41</li><li>1.52613511112026e-77</li><li>0.784396745245705</li><li>0.0594008836701059</li><li>0.784396745245705</li><li>7.88788617761231e-10</li><li>0.299845552952263</li><li>&lt;NA&gt;</li><li>4.07406113606404e-97</li><li>1.71158958123884e-48</li><li>6.90185345337992e-101</li><li>0.0437528940898088</li><li>1.94800696041556e-10</li><li>0.641697002486713</li><li>0.20915673998409</li><li>&lt;NA&gt;</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2.82011466593676e-78\n",
       "\\item 7.84968020490841e-41\n",
       "\\item 0.516513367677175\n",
       "\\item 0.312838989255046\n",
       "\\item 1.24099957483937e-38\n",
       "\\item 0.0594008836701059\n",
       "\\item 0.784396745245705\n",
       "\\item <NA>\n",
       "\\item 3.66658100801849e-41\n",
       "\\item 1.52613511112026e-77\n",
       "\\item 0.784396745245705\n",
       "\\item 0.0594008836701059\n",
       "\\item 0.784396745245705\n",
       "\\item 7.88788617761231e-10\n",
       "\\item 0.299845552952263\n",
       "\\item <NA>\n",
       "\\item 4.07406113606404e-97\n",
       "\\item 1.71158958123884e-48\n",
       "\\item 6.90185345337992e-101\n",
       "\\item 0.0437528940898088\n",
       "\\item 1.94800696041556e-10\n",
       "\\item 0.641697002486713\n",
       "\\item 0.20915673998409\n",
       "\\item <NA>\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2.82011466593676e-78\n",
       "2. 7.84968020490841e-41\n",
       "3. 0.516513367677175\n",
       "4. 0.312838989255046\n",
       "5. 1.24099957483937e-38\n",
       "6. 0.0594008836701059\n",
       "7. 0.784396745245705\n",
       "8. &lt;NA&gt;\n",
       "9. 3.66658100801849e-41\n",
       "10. 1.52613511112026e-77\n",
       "11. 0.784396745245705\n",
       "12. 0.0594008836701059\n",
       "13. 0.784396745245705\n",
       "14. 7.88788617761231e-10\n",
       "15. 0.299845552952263\n",
       "16. &lt;NA&gt;\n",
       "17. 4.07406113606404e-97\n",
       "18. 1.71158958123884e-48\n",
       "19. 6.90185345337992e-101\n",
       "20. 0.0437528940898088\n",
       "21. 1.94800696041556e-10\n",
       "22. 0.641697002486713\n",
       "23. 0.20915673998409\n",
       "24. &lt;NA&gt;\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  2.820115e-78  7.849680e-41  5.165134e-01  3.128390e-01  1.241000e-38\n",
       " [6]  5.940088e-02  7.843967e-01            NA  3.666581e-41  1.526135e-77\n",
       "[11]  7.843967e-01  5.940088e-02  7.843967e-01  7.887886e-10  2.998456e-01\n",
       "[16]            NA  4.074061e-97  1.711590e-48 6.901853e-101  4.375289e-02\n",
       "[21]  1.948007e-10  6.416970e-01  2.091567e-01            NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_adjust"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "nova[[1]]$\"Adjusted P\" <- c(p_adjust[1:7],NA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "nova[[2]]$\"Adjusted P\" <- c(p_adjust[9:15],NA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "nova[[3]]$\"Adjusted P\" <- c(p_adjust[17:23],NA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " Response 1 :\n",
       "                                     Df Sum Sq Mean Sq  F value  Pr(>F)\n",
       "df$SEX                                1    391  390.70 354.8440 0.00000\n",
       "df$URBAN_RURAL                        1    200  199.58 181.2655 0.00000\n",
       "df$VETERAN                            1      1    0.72   0.6556 0.41813\n",
       "df$SEX:df$URBAN_RURAL                 1      2    1.53   1.3903 0.23835\n",
       "df$SEX:df$VETERAN                     1    188  188.20 170.9258 0.00000\n",
       "df$URBAN_RURAL:df$VETERAN             1      5    4.92   4.4715 0.03447\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1      0    0.09   0.0796 0.77782\n",
       "Residuals                        418260 460525    1.10                 \n",
       "                                 Adjusted P\n",
       "df$SEX                              0.00000\n",
       "df$URBAN_RURAL                      0.00000\n",
       "df$VETERAN                          0.51651\n",
       "df$SEX:df$URBAN_RURAL               0.31284\n",
       "df$SEX:df$VETERAN                   0.00000\n",
       "df$URBAN_RURAL:df$VETERAN           0.05940\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN    0.78440\n",
       "Residuals                                  \n",
       "\n",
       " Response 2 :\n",
       "                                     Df   Sum Sq Mean Sq  F value  Pr(>F)\n",
       "df$SEX                                1     6896  6896.3 183.0872 0.00000\n",
       "df$URBAN_RURAL                        1    13217 13217.3 350.8993 0.00000\n",
       "df$VETERAN                            1        3     2.8   0.0749 0.78440\n",
       "df$SEX:df$URBAN_RURAL                 1      164   164.3   4.3610 0.03677\n",
       "df$SEX:df$VETERAN                     1        5     4.6   0.1216 0.72734\n",
       "df$URBAN_RURAL:df$VETERAN             1     1478  1478.0  39.2376 0.00000\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1       58    58.1   1.5430 0.21418\n",
       "Residuals                        418260 15754558    37.7                 \n",
       "                                 Adjusted P\n",
       "df$SEX                              0.00000\n",
       "df$URBAN_RURAL                      0.00000\n",
       "df$VETERAN                          0.78440\n",
       "df$SEX:df$URBAN_RURAL               0.05940\n",
       "df$SEX:df$VETERAN                   0.78440\n",
       "df$URBAN_RURAL:df$VETERAN           0.00000\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN    0.29985\n",
       "Residuals                                  \n",
       "\n",
       " Response 3 :\n",
       "                                     Df   Sum Sq Mean Sq  F value  Pr(>F)\n",
       "df$SEX                                1    96565   96565 442.2817 0.00000\n",
       "df$URBAN_RURAL                        1    47391   47391 217.0594 0.00000\n",
       "df$VETERAN                            1   100655  100655 461.0133 0.00000\n",
       "df$SEX:df$URBAN_RURAL                 1     1130    1130   5.1747 0.02292\n",
       "df$SEX:df$VETERAN                     1     9209    9209  42.1766 0.00000\n",
       "df$URBAN_RURAL:df$VETERAN             1       78      78   0.3573 0.55003\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1      477     477   2.1842 0.13944\n",
       "Residuals                        418260 91320097     218                 \n",
       "                                 Adjusted P\n",
       "df$SEX                              0.00000\n",
       "df$URBAN_RURAL                      0.00000\n",
       "df$VETERAN                          0.00000\n",
       "df$SEX:df$URBAN_RURAL               0.04375\n",
       "df$SEX:df$VETERAN                   0.00000\n",
       "df$URBAN_RURAL:df$VETERAN           0.64170\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN    0.20916\n",
       "Residuals                                  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nova"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As evident in the \"Adjusted P\" columns, there are significant between-subjects effects, further supporting our theory that MANOVA is not appropriate here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4: Select a random sample of approximately 400 cases, redo the MANOVA (not the assumptions tests) of the analyses above. Compare and contrast the same tables/questions from #2. Also comment on the impact of sample size on your results. Why does this matter?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "sdf <- df[sample(nrow(df), size=400), ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "   Subject_ID          ACES_Score          BMI        PHYSHLTH_DAYS   \n",
       " Min.   :2.019e+09   Min.   : 0.000   Min.   :16.46   Min.   : 0.000  \n",
       " 1st Qu.:2.019e+09   1st Qu.: 1.703   1st Qu.:24.69   1st Qu.: 0.000  \n",
       " Median :2.019e+09   Median : 1.703   Median :28.06   Median : 0.000  \n",
       " Mean   :2.019e+09   Mean   : 1.702   Mean   :28.73   Mean   : 6.112  \n",
       " 3rd Qu.:2.019e+09   3rd Qu.: 1.703   3rd Qu.:32.09   3rd Qu.: 4.000  \n",
       " Max.   :2.019e+09   Max.   :10.000   Max.   :55.36   Max.   :99.000  \n",
       "      SEX        URBAN_RURAL        VETERAN      \n",
       " Min.   :0.00   Min.   :0.0000   Min.   :0.0000  \n",
       " 1st Qu.:0.00   1st Qu.:1.0000   1st Qu.:0.0000  \n",
       " Median :1.00   Median :1.0000   Median :0.0000  \n",
       " Mean   :0.57   Mean   :0.8421   Mean   :0.1356  \n",
       " 3rd Qu.:1.00   3rd Qu.:1.0000   3rd Qu.:0.0000  \n",
       " Max.   :1.00   Max.   :1.0000   Max.   :1.0000  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(sdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Call:\n",
       "   manova(cbind(sdf$ACES_Score, sdf$BMI, sdf$PHYSHLTH_DAYS) ~ sdf$SEX * \n",
       "    sdf$URBAN_RURAL * sdf$VETERAN)\n",
       "\n",
       "Terms:\n",
       "                 sdf$SEX sdf$URBAN_RURAL sdf$VETERAN sdf$SEX:sdf$URBAN_RURAL\n",
       "resp 1              0.02            1.30        1.12                    3.79\n",
       "resp 2             80.86          160.45       26.80                    1.73\n",
       "resp 3            519.36          153.90      123.36                  371.52\n",
       "Deg. of Freedom        1               1           1                       1\n",
       "                sdf$SEX:sdf$VETERAN sdf$URBAN_RURAL:sdf$VETERAN Residuals\n",
       "resp 1                         0.18                        0.02    455.81\n",
       "resp 2                       597.80                       57.02  15578.82\n",
       "resp 3                       109.51                      588.67  75071.61\n",
       "Deg. of Freedom                   1                           1       393\n",
       "\n",
       "Residual standard errors: 1.076951 6.296092 13.82107\n",
       "1 out of 8 effects not estimable\n",
       "Estimated effects may be unbalanced"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "smodel <-manova(\n",
    "                cbind(sdf$ACES_Score, sdf$BMI, sdf$PHYSHLTH_DAYS) ~ \n",
    "                sdf$SEX * sdf$URBAN_RURAL * sdf$VETERAN\n",
    "                )\n",
    "smodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df     Pillai approx F num Df den Df\n",
       "df$SEX                                1 0.00243326   340.07      3 418258\n",
       "df$URBAN_RURAL                        1 0.00177900   248.47      3 418258\n",
       "df$VETERAN                            1 0.00110954   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1 0.00002551     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1 0.00052273    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1 0.00010940    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1 0.00000843     1.18      3 418258\n",
       "Residuals                        418260                                  \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "                             Df   Pillai approx F num Df den Df    Pr(>F)    \n",
       "sdf$SEX                       1 0.010441   1.3751      3    391 0.2499243    \n",
       "sdf$URBAN_RURAL               1 0.014077   1.8609      3    391 0.1356684    \n",
       "sdf$VETERAN                   1 0.006353   0.8333      3    391 0.4761533    \n",
       "sdf$SEX:sdf$URBAN_RURAL       1 0.013754   1.8176      3    391 0.1433855    \n",
       "sdf$SEX:sdf$VETERAN           1 0.041730   5.6756      3    391 0.0008193 ***\n",
       "sdf$URBAN_RURAL:sdf$VETERAN   1 0.010093   1.3288      3    391 0.2645718    \n",
       "Residuals                   393                                              \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model, 'Pillai')\n",
    "summary(smodel, 'Pillai')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df   Wilks approx F num Df den Df\n",
       "df$SEX                                1 0.99757   340.07      3 418258\n",
       "df$URBAN_RURAL                        1 0.99822   248.47      3 418258\n",
       "df$VETERAN                            1 0.99889   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1 0.99997     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1 0.99948    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1 0.99989    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1 0.99999     1.18      3 418258\n",
       "Residuals                        418260                               \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "                             Df   Wilks approx F num Df den Df    Pr(>F)    \n",
       "sdf$SEX                       1 0.98956   1.3751      3    391 0.2499243    \n",
       "sdf$URBAN_RURAL               1 0.98592   1.8609      3    391 0.1356684    \n",
       "sdf$VETERAN                   1 0.99365   0.8333      3    391 0.4761533    \n",
       "sdf$SEX:sdf$URBAN_RURAL       1 0.98625   1.8176      3    391 0.1433855    \n",
       "sdf$SEX:sdf$VETERAN           1 0.95827   5.6756      3    391 0.0008193 ***\n",
       "sdf$URBAN_RURAL:sdf$VETERAN   1 0.98991   1.3288      3    391 0.2645718    \n",
       "Residuals                   393                                             \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model,'Wilks')\n",
    "summary(smodel,'Wilks')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df        Roy approx F num Df den Df\n",
       "df$SEX                                1 0.00243920   340.07      3 418258\n",
       "df$URBAN_RURAL                        1 0.00178217   248.47      3 418258\n",
       "df$VETERAN                            1 0.00111077   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1 0.00002551     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1 0.00052300    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1 0.00010941    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1 0.00000843     1.18      3 418258\n",
       "Residuals                        418260                                  \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "                             Df      Roy approx F num Df den Df    Pr(>F)    \n",
       "sdf$SEX                       1 0.010551   1.3751      3    391 0.2499243    \n",
       "sdf$URBAN_RURAL               1 0.014278   1.8609      3    391 0.1356684    \n",
       "sdf$VETERAN                   1 0.006394   0.8333      3    391 0.4761533    \n",
       "sdf$SEX:sdf$URBAN_RURAL       1 0.013945   1.8176      3    391 0.1433855    \n",
       "sdf$SEX:sdf$VETERAN           1 0.043547   5.6756      3    391 0.0008193 ***\n",
       "sdf$URBAN_RURAL:sdf$VETERAN   1 0.010196   1.3288      3    391 0.2645718    \n",
       "Residuals                   393                                              \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model, 'Roy')\n",
    "summary(smodel, 'Roy')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                     Df Hotelling-Lawley approx F num Df den Df\n",
       "df$SEX                                1       0.00243920   340.07      3 418258\n",
       "df$URBAN_RURAL                        1       0.00178217   248.47      3 418258\n",
       "df$VETERAN                            1       0.00111077   154.86      3 418258\n",
       "df$SEX:df$URBAN_RURAL                 1       0.00002551     3.56      3 418258\n",
       "df$SEX:df$VETERAN                     1       0.00052300    72.92      3 418258\n",
       "df$URBAN_RURAL:df$VETERAN             1       0.00010941    15.25      3 418258\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN      1       0.00000843     1.18      3 418258\n",
       "Residuals                        418260                                        \n",
       "                                    Pr(>F)    \n",
       "df$SEX                           < 2.2e-16 ***\n",
       "df$URBAN_RURAL                   < 2.2e-16 ***\n",
       "df$VETERAN                       < 2.2e-16 ***\n",
       "df$SEX:df$URBAN_RURAL              0.01365 *  \n",
       "df$SEX:df$VETERAN                < 2.2e-16 ***\n",
       "df$URBAN_RURAL:df$VETERAN        6.379e-10 ***\n",
       "df$SEX:df$URBAN_RURAL:df$VETERAN   0.31747    \n",
       "Residuals                                     \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "                             Df Hotelling-Lawley approx F num Df den Df\n",
       "sdf$SEX                       1         0.010551   1.3751      3    391\n",
       "sdf$URBAN_RURAL               1         0.014278   1.8609      3    391\n",
       "sdf$VETERAN                   1         0.006394   0.8333      3    391\n",
       "sdf$SEX:sdf$URBAN_RURAL       1         0.013945   1.8176      3    391\n",
       "sdf$SEX:sdf$VETERAN           1         0.043547   5.6756      3    391\n",
       "sdf$URBAN_RURAL:sdf$VETERAN   1         0.010196   1.3288      3    391\n",
       "Residuals                   393                                        \n",
       "                               Pr(>F)    \n",
       "sdf$SEX                     0.2499243    \n",
       "sdf$URBAN_RURAL             0.1356684    \n",
       "sdf$VETERAN                 0.4761533    \n",
       "sdf$SEX:sdf$URBAN_RURAL     0.1433855    \n",
       "sdf$SEX:sdf$VETERAN         0.0008193 ***\n",
       "sdf$URBAN_RURAL:sdf$VETERAN 0.2645718    \n",
       "Residuals                                \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(model, 'Hotelling-Lawley')\n",
    "summary(smodel, 'Hotelling-Lawley')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The decreased sample size caused the MANOVA's failure to perform every test. Additionally, the p-values differed significantly, with some significant interactions in the larger group failing to reach significance at the 0.01 level in the smaller group. This comparison underscores the importance of power and sample size in statistical tests like the MANOVA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5: The data in this assignment has been modified from the original BRFSS data in order to highlight some issues over others. In the original PRFSS, the codebook presents information about how data about sex and sexual orientation and gender identity are asked of participants. See information from the tables below. Thinking about these from a data equity perspective, reflect on the ways these questions are asked, the responses that are available, and how this may or may not present consequences for processing, analyzing, interpreting, and reporting results using this data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Alt text](assets/image-1.png)\n",
    "![Alt text](assets/image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are issues with the wording in both of these questions. The 'sex' question limits participants' choices to Male/Female, excluding transgender, nonbinary, and intersex folks. Similarly, the question about sexuality also has weird and exclusionary language. Something about \"Straight, that is, not gay\" implies an expectation that the participants will hold negative attitudes towards gay folks by default. Perhaps it was written that way to capture straight folks who don't know what 'straight' means.\n",
    "\n",
    "The sexuality question also limits participant choices. Overall, the impact of these questions is undoubtably significant. By excluding specific, already minoritized communities, the questions erase their existence in the eyes of science. These communities may have differing health outcomes compared to the normative gender and sexuality groups, which may muddy the study's results for majority groups, and what's more, fail to identify disparities in minority groups. \n",
    "\n",
    "As public health researchers, we must remain open to the idea that our study designs might inadvertantly exclude minoritized groups. Even the researcher with the most DEI training is vulnerable to these kinds of mistakes. Only by being willing to listen to the communities' experiences will we be able to correct our mistakes. "
   ]
  }
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