R/ht_two_median_sim.R

In andrewpbray/reed-oilabs: R Package Companion to OpenIntro Labs

ht_two_median_sim <- function(y, x, null, alternative, nsim, seed,
                              y_name, x_name, 
                              show_var_types, show_summ_stats, show_res,
                              show_eda_plot, show_inf_plot){

  # set seed
  if(!is.null(seed)){ set.seed(seed) }

  # calculate n1 and n2
  ns <- by(y, x, length)
  n1 <- as.numeric(ns[1])
  n2 <- as.numeric(ns[2])
  n <- n1 + n2

  # calculate y-med1 and y-med2
  y_meds <- by(y, x, median)
  y_med1 <- as.numeric(y_meds[1])
  y_med2 <- as.numeric(y_meds[2])
  
  # calculate difference in y-meds
  y_med_diff <- y_med1 - y_med2

  # create null distribution
  sim_dist <- rep(NA, nsim)
  for(i in 1:nsim){
    y_sim <- sample(y, size = n, replace = FALSE)
    y_sim_meds <- by(y_sim, x, median)
    y_sim_med1 <- as.numeric(y_sim_meds[1])
    y_sim_med2 <- as.numeric(y_sim_meds[2])
    sim_dist[i] <- y_sim_med1 - y_sim_med2
  }
  
  # shading cutoffs
  if(alternative == "greater"){ 
    x_min <- y_med_diff
    x_max <- Inf 
    }
  if(alternative == "less"){ 
    x_min <- -Inf
    x_max <- y_med_diff
    }
  if(alternative == "twosided"){
    if(y_med_diff >= null){
      x_min <- c(null - (y_med_diff - null), y_med_diff)
      x_max <- c(-Inf, Inf)
    }
    if(y_med_diff <= null){
      x_min <- c(y_med_diff, null + (null - y_med_diff))
      x_max <- c(-Inf, Inf)
    }    
  }
  
  # calculate p-value
  if(alternative == "greater"){ p_value <- sum(sim_dist >= y_med_diff) / nsim }
  if(alternative == "less"){ p_value <- sum(sim_dist <= y_med_diff) / nsim }
  if(alternative == "twosided"){
    if(y_med_diff > null){
      p_value <- min(2 * (sum(sim_dist >= y_med_diff) / nsim), 1)
    }
    if(y_med_diff < null){
      p_value <- min(2 * (sum(sim_dist <= y_med_diff) / nsim), 1)
    }
    if(y_med_diff == null){ p_value <- 1 }
  }
  
  # print variable types
  if(show_var_types == TRUE){
    n_x_levels <- length(levels(x))
    cat(paste0("Response variable: numerical\n"))
    cat(paste0("Explanatory variable: categorical (", n_x_levels, " levels) \n"))
  }
  
  # print summary statistics
  if(show_summ_stats == TRUE){
    gr1 <- levels(x)[1]
    gr2 <- levels(x)[2]
    iqrs <- by(y, x, IQR)
    iqr1 <- iqrs[1]
    iqr2 <- iqrs[2]
    cat(paste0("n_", gr1, " = ", n1, ", y_med_", gr1, " = ", round(y_med1, 4), 
               ", IQR_", gr1, " = ", iqr1, "\n"))
    cat(paste0("n_", gr2, " = ", n2, ", y_med_", gr2, " = ", round(y_med2, 4), 
               ", IQR_", gr2, " = ", iqr2, "\n"))
  }
  
  # print results
  if(show_res == TRUE){
    if(alternative == "greater"){
      alt_sign <- ">"
    } else if(alternative == "less"){
      alt_sign <- "<"
    } else {
      alt_sign <- "!="
    }
    cat(paste0("H0: mu_", gr1, " =  mu_", gr2, "\n"))
    cat(paste0("HA: mu_", gr1, " ", alt_sign, " mu_", gr2, "\n"))
    p_val_to_print <- ifelse(round(p_value, 4) == 0, "< 0.0001", round(p_value, 4))
    cat(paste0("p_value = ", p_val_to_print))
  }
  
  # eda_plot
  d_eda <- data.frame(y = y, x = x)

  eda_plot <- ggplot2::ggplot(data = d_eda, ggplot2::aes(x = x, y = y), environment = environment()) +
    ggplot2::geom_boxplot(color = "#1FBEC3", fill = "#8FDEE1", outlier.colour = "#1FBEC3") +
    ggplot2::xlab(x_name) +
    ggplot2::ylab(y_name) +
    ggplot2::ggtitle("Sample Distribution")
    
  # inf_plot
  d_inf <- data.frame(sim_dist = sim_dist)
  
  inf_plot <- ggplot2::ggplot(data = d_inf, ggplot2::aes(x = sim_dist), environment = environment()) +
    ggplot2::geom_histogram(fill = "#CCCCCC", binwidth = diff(range(sim_dist)) / 20) +
    ggplot2::annotate("rect", xmin = x_min, xmax = x_max, ymin = 0, ymax = Inf, 
             alpha = 0.3, fill = "#FABAB8") +
    ggplot2::xlab("simulated difference in medians") +
    ggplot2::ylab("") +
    ggplot2::ggtitle("Null Distribution") +
    ggplot2::geom_vline(xintercept = y_med_diff, color = "#F57670", lwd = 1.5)
  
  # print plots
  if(show_eda_plot & !show_inf_plot){ 
    print(eda_plot)
  }
  if(!show_eda_plot & show_inf_plot){ 
    print(inf_plot)
  }
  if(show_eda_plot & show_inf_plot){
    gridExtra::grid.arrange(eda_plot, inf_plot, ncol = 2)
  }
  
  # return
  return(list(sim_dist = sim_dist, p_value = p_value))
}