ht_single_prop_theo <- function(y, success, null, alternative, y_name,
show_var_types, show_summ_stats, show_res,
show_eda_plot, show_inf_plot){
# calculate sample size
n <- length(y)
# calculate p-hat
p_hat <- sum(y == success) / n
# calculate SE
se <- sqrt(p_hat * (1 - p_hat) / n)
# calculate test statistic
z <- (p_hat - null) / se
# shading cutoffs
if(alternative == "greater"){ x_min = p_hat; x_max = Inf }
if(alternative == "less"){ x_min = -Inf; x_max = p_hat }
if(alternative == "twosided"){
if(p_hat >= null){
x_min = c(null - (p_hat - null), p_hat)
x_max = c(-Inf, Inf)
}
if(p_hat <= null){
x_min = c(p_hat, null + (null - p_hat))
x_max = c(-Inf, Inf)
}
}
# calculate p-value
if(alternative == "greater"){ p_value <- pnorm(z, lower.tail = FALSE) }
if(alternative == "less"){ p_value <- pnorm(z, lower.tail = TRUE) }
if(alternative == "twosided"){
p_value <- 2 * pnorm(abs(z), lower.tail = FALSE)
}
# print variable types
if(show_var_types == TRUE){
cat(paste0("Single categorical variable, success: ", success,"\n"))
}
# print summary statistics
if(show_summ_stats == TRUE){
cat(paste0("n = ", n, ", p-hat = ", round(p_hat, 4), "\n"))
}
# print results
if(show_res == TRUE){
if(alternative == "greater"){
alt_sign <- ">"
} else if(alternative == "less"){
alt_sign <- "<"
} else {
alt_sign <- "!="
}
cat(paste0("H0: p = ", null, "\n"))
cat(paste0("HA: p ", alt_sign, " ", null, "\n"))
p_val_to_print <- ifelse(round(p_value, 4) == 0, "< 0.0001", round(p_value, 4))
cat(paste0("z = ", round(z, 4), "\n"))
cat(paste0("p_value = ", p_val_to_print))
}
# eda_plot
d_eda <- data.frame(y = y)
eda_plot <- ggplot2::ggplot(data = d_eda, ggplot2::aes(x = y), environment = environment()) +
ggplot2::geom_bar(fill = "#8FDEE1") +
ggplot2::xlab(y_name) +
ggplot2::ylab("") +
ggplot2::ggtitle("Sample Distribution")
# inf_plot
d_for_plot <- data.frame(x = c(null - 4*se, null + 4*se))
inf_plot <- ggplot2::ggplot(d_for_plot, ggplot2::aes_string(x = 'x')) +
ggplot2::stat_function(fun = dnorm, args = list(mean = null, sd = se), color = "#999999") +
ggplot2::annotate("rect", xmin = x_min, xmax = x_max, ymin = 0, ymax = Inf,
alpha = 0.3, fill = "#FABAB8") +
ggplot2::ggtitle("Null Distribution") +
ggplot2::xlab("") +
ggplot2::ylab("") +
ggplot2::geom_vline(xintercept = p_hat, 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(SE = se, z = z, p_value = p_value))
}
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