#' Analysis of Variance for Equality of Means
#'
#' Given univariate samples \eqn{X_1~,\ldots,~X_k}, it tests
#' \deqn{H_0 : \mu_1^2 = \cdots \mu_k^2\quad vs\quad H_1 : \textrm{at least one equality does not hold.}}
#'
#' @param dlist a list of length \eqn{k} where each element is a sample vector.
#'
#' @return a (list) object of \code{S3} class \code{htest} containing: \describe{
#' \item{statistic}{a test statistic.}
#' \item{p.value}{\eqn{p}-value under \eqn{H_0}.}
#' \item{alternative}{alternative hypothesis.}
#' \item{method}{name of the test.}
#' \item{data.name}{name(s) of provided sample data.}
#' }
#'
#' @examples
#' \donttest{
#' ## test when k=5 (samples)
#' ## empirical Type 1 error
#' niter = 1000
#' counter = rep(0,niter) # record p-values
#' for (i in 1:niter){
#' mylist = list()
#' for (j in 1:5){
#' mylist[[j]] = rnorm(50)
#' }
#'
#' counter[i] = ifelse(meank.anova(mylist)$p.value < 0.05, 1, 0)
#' }
#'
#' ## print the result
#' cat(paste("\n* Example for 'meank.anova'\n","*\n",
#' "* number of rejections : ", sum(counter),"\n",
#' "* total number of trials : ", niter,"\n",
#' "* empirical Type 1 error : ",round(sum(counter/niter),5),"\n",sep=""))
#' }
#'
#' @concept mean_univariate
#' @export
meank.anova <- function(dlist){
##############################################################
# PREPROCESSING
check_dlist1d(dlist)
##############################################################
# COMPUTATION : PRELIMINARY FOR USING ANOVA
K = length(dlist)
if (K < 2){
stop("* meank.anova : we need at least 2 sets of data.")
}
labellist = list()
for (i in 1:K){
labellist[[i]] = rep(i,length(dlist[[i]]))
}
data = unlist(dlist)
group = as.factor(unlist(labellist))
##############################################################
# COMPUTATION : USE AOV INTERFACE
aovout = unlist(summary(aov(data~group)))
##############################################################
# REPORT
hname = "Analysis of Variance for Equality of Means"
Ha = "at least one of equalities does not hold."
thestat = as.double(aovout[7])
pvalue = as.double(aovout[9])
# if (pvalue < alpha){
# conclusion = "Reject Null Hypothesis"
# } else {
# conclusion = "Not Reject Null Hypothesis"
# }
DNAME = deparse(substitute(dlist))
names(thestat) = "statistic"
res = list(statistic=thestat, p.value=pvalue, alternative = Ha, method=hname, data.name = DNAME)
class(res) = "htest"
return(res)
}
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