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#' Dunn's Test for Multiple Comparisons (Non-Parametric)
#'
#' Performs Dunn's test for pairwise comparisons following a Kruskal-Wallis test.
#' Suitable for non-parametric data (ordinal or non-normal), using rank sums.
#' Includes Holm correction by default for multiple comparisons.
#'
#' Advantages:
#' - Simple and widely used non-parametric alternative to Tukey's test.
#' - Handles unequal sample sizes.
#' - Compatible with various p-value corrections (e.g., Holm, Bonferroni).
#'
#' Disadvantages:
#' - Less powerful than DSCF or Conover when sample sizes vary widely.
#' - Requires ranking all data and can be conservative depending on adjustment.
#'
#' @param formula A formula of the form \code{y ~ group}.
#' @param data A data frame containing the variables.
#' @param alpha Significance level (default is 0.05).
#' @param method.p Method for p-value adjustment (default is "holm").
#'
#' @return An object of class \code{"dunn"} and \code{"comparaciones"}, including:
#' \itemize{
#' \item \code{Resultados}: Data frame with group comparisons, z-values, raw and adjusted p-values, and significance.
#' \item \code{Promedios}: Mean ranks of each group.
#' \item \code{Orden_Medias}: Group names ordered from highest to lowest rank.
#' \item \code{Metodo}: "Dunn (no paramétrico)".
#' }
#'
#' @references
#' Dunn, O. J. (1964). Multiple comparisons using rank sums. *Technometrics*, 6(3), 241–252. \doi{10.1080/00401706.1964.10490181}
#'
#' @seealso \code{\link{kruskal.test}}, \code{\link[dunn.test]{dunn.test}}
#'
#'@examples
#'data(d_e, package = "Analitica")
#'DunnTest(Sueldo_actual ~ labor, data = d_e)
#'
#'
#' @export
#' @importFrom stats p.adjust pnorm kruskal.test
#' @importFrom utils combn
DunnTest <- function(formula, data, alpha = 0.05, method.p = "holm") {
mf <- model.frame(formula, data)
response <- mf[[1]]
grupo <- as.factor(mf[[2]])
# Kruskal-Wallis check (opcional, pero puede ayudarte a verificar)
kruskal <- kruskal.test(formula, data = data)
# Ranks y estructura
ranks <- rank(response)
niveles <- levels(grupo)
k <- length(niveles)
n <- table(grupo)
N <- length(response)
Rj <- tapply(ranks, grupo, mean)
S2 <- (N * (N + 1)) / 12
comparaciones <- combn(niveles, 2, simplify = FALSE)
resultados <- data.frame(
Comparacion = character(),
z = numeric(),
p_value = numeric(),
p_ajustada = numeric(),
Significancia = character(),
stringsAsFactors = FALSE
)
z_vals <- numeric(length(comparaciones))
p_vals <- numeric(length(comparaciones))
for (i in seq_along(comparaciones)) {
par <- comparaciones[[i]]
g1 <- par[1]; g2 <- par[2]
dif <- abs(Rj[g1] - Rj[g2])
se <- sqrt(S2 * (1 / n[g1] + 1 / n[g2]))
z <- dif / se
p <- 2 * (1 - pnorm(abs(z)))
z_vals[i] <- z
p_vals[i] <- p
}
p_ajustada <- p.adjust(p_vals, method = method.p)
sig <- ifelse(p_ajustada < 0.001, "***",
ifelse(p_ajustada < 0.01, "**",
ifelse(p_ajustada < 0.05, "*", "ns")))
for (i in seq_along(comparaciones)) {
comp <- paste(sort(comparaciones[[i]]), collapse = " - ")
resultados[i, ] <- list(
Comparacion = comp,
z = round(z_vals[i], 4),
p_value = round(p_vals[i], 4),
p_ajustada = round(p_ajustada[i], 4),
Significancia = sig[i]
)
}
ordenado <- names(sort(Rj, decreasing = TRUE))
out <- list(
Resultados = resultados,
Promedios = Rj,
Orden_Medias = ordenado,
Metodo = "Dunn (no parametrico)"
)
class(out) <- c("comparaciones", "dunn")
return(out)
}
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