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#' Multiple comparison: Least Significant Difference test
#'
#' \code{lsd} Performs the t test (LSD) for multiple comparison
#' of means.
#' @param y Numeric or complex vector containing the response
#' variable.
#' @param trt Numeric or complex vector containing the
#' treatments.
#' @param DFerror Error degrees of freedom.
#' @param SSerror Error sum of squares.
#' @param alpha Significance level.
#' @param group TRUE or FALSE.
#' @param main Title.
#' @return Returns the multiple comparison of means according
#' to the LSD test.
#' @author Eric B Ferreira,
#' \email{eric.ferreira@@unifal-mg.edu.br}
#' @author Denismar Alves Nogueira
#' @author Portya Piscitelli Cavalcanti
#' @seealso \code{\link{snk}}, \code{\link{duncan}},
#' \code{\link{ccboot}}, \code{\link{lsdb}},
#' \code{\link{scottknott}}, \code{\link{tukey}},
#' \code{\link{ccF}}.
#' @examples
#' data(ex1)
#' attach(ex1)
#' crd(trat, ig, quali = TRUE, mcomp = "lsd", sigT = 0.05)
#' @importFrom "stats" "AIC" "coef" "dnorm" "fitted"
#' "fitted.values" "nls" "ppoints" "pt" "qnorm" "qt"
#' "residuals"
#' @export
lsd <-
function (y, trt, DFerror, SSerror, alpha = 0.05, group = TRUE, main = NULL)
{
MSerror <- SSerror/DFerror
name.y <- paste(deparse(substitute(y)))
name.t <- paste(deparse(substitute(trt)))
junto <- subset(data.frame(y, trt), is.na(y) == FALSE)
means <- tapply.stat(junto[, 1], junto[, 2], stat = "mean")
sds <- tapply.stat(junto[, 1], junto[, 2], stat = "sd")
nn <- tapply.stat(junto[, 1], junto[, 2], stat = "length")
means <- data.frame(means, std.err = sds[, 2]/sqrt(nn[, 2]),
replication = nn[, 2])
names(means)[1:2] <- c(name.t, name.y)
ntr <- nrow(means)
#Tprob <- qtukey(1 - alpha, ntr, DFerror)
Tprob <- qt(1-(alpha/2),DFerror)*sqrt(2)
nr <- unique(nn[, 2])
nfila <- c("Alpha", "Error Degrees of Freedom", "Error Mean Square",
"Critical Value of Studentized Range")
nvalor <- c(alpha, DFerror, MSerror, Tprob)
#cat("\nStudy:", main)
#cat("\n\nHSD Test for", name.y, "\n")
xtabla <- data.frame(...... = nvalor)
row.names(xtabla) <- nfila
#print(xtabla)
#cat("\nTreatment Means\n")
#print(data.frame(row.names = NULL, means))
if (group) {
if (length(nr) == 1) {
HSD <- Tprob * sqrt(MSerror/nr)
#cat("\nHonestly Significant Difference", HSD)
}
else {
nr1 <- 1/mean(1/nn[, 2])
HSD <- Tprob * sqrt(MSerror/nr1)
#cat("\nHonestly Significant Difference", HSD)
#cat("\nHarmonic Mean of Cell Sizes ", nr1)
#cat("\n\nDifferent HSD for each comparison")
}
cat("\nT test (LSD)\n------------------------------------------------------------------------")
cat("\nGroups Treatments Means\n")
output <- order.group(means[, 1], means[, 2], means[,4], MSerror, Tprob, means[, 3], parameter = 0.5)
cat('------------------------------------------------------------------------\n')
}
if (!group) {
comb <- combn(ntr, 2)
nn <- ncol(comb)
dif <- rep(0, nn)
pvalue <- rep(0, nn)
for (k in 1:nn) {
i <- comb[1, k]
j <- comb[2, k]
dif[k] <- abs(means[i, 2] - means[j, 2])
sdtdif <- sqrt(MSerror * (1/means[i, 4] + 1/means[j,
4]))
pvalue[k] <- round(1 - ptukey(dif[k] * sqrt(2)/sdtdif,
ntr, DFerror), 4)
}
tr.i <- comb[1, ]
tr.j <- comb[2, ]
#cat("\nComparison between treatments means\n\n")
#print(data.frame(row.names = NULL, tr.i, tr.j, diff = dif, pvalue = pvalue))
output <- data.frame(trt = means[, 1], means = means[,2], M = "", N = means[, 4], std.err = means[, 3])
}
# return(output)
}
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