#' Tusell Additivity Test
#'
#' Test for an interaction in two-way ANOVA table by the Tusell test.
#'
#' @param Y data matrix
#' @param alpha level of the test
#' @param critical.value result of \code{\link{critical.values}} function, see \code{Details}
#' @param Nsim number of simulations to be used for a critical value estimation
#'
#' @return A list with class "\code{aTest}" containing the following components:
#' test statistics \code{stat}, critical value \code{critical.value} and the result of
#' the test \code{result}, i.e. whether the additivity hypothesis has been rejected.
#'
#' @details The critical value can be computed in advance and given in the parameter \code{critical value}.
#' If not a function \code{\link{critical.values}} is called to do that.
#'
#' @references Tusell, F.: Testing for Interaction in Two-way ANOVA Tables with no Replication,
#' \emph{Computational Statistics \& Data Analysis} \bold{10}, pp. 29--45, 1990
#'
#' @seealso \code{\link{tukey.test}}, \code{\link{mtukey.test}}, \code{\link{mandel.test}},
#' \code{\link{lbi.test}}, \code{\link{johnson.graybill.test}}
#'
#' @keywords htest
#'
#' @export
#'
#' @examples
#' data(Boik)
#' tusell.test(Boik)
`tusell.test` <-
function(Y,alpha=0.05,critical.value=NA,Nsim=1000)
{
if (nrow(Y)>ncol(Y)) Y<-t(Y)
if (is.na(critical.value)) critical.value<-critical.values(nrow(Y),ncol(Y),Nsim,alpha)$t3
a<-nrow(Y)
b<-ncol(Y)
p<-a-1
q<-b-1
R<-Y-rep(apply(Y,1,mean),b)-rep(apply(Y,2,mean),each=a)+rep(mean(Y),a*b)
S<-R %*% t(R)
vl.cisla<-eigen(S / sum(diag(S)),only.values = TRUE)$values
if (prod(vl.cisla[1:p])<critical.value) out<-list(result=TRUE,stat=prod(vl.cisla[1:p]),critical.value=critical.value,alpha=alpha,name="Tusell test") # zamitame aditivitu
else out<-list(result=FALSE,stat=prod(vl.cisla[1:p]),critical.value=critical.value,alpha=alpha,name="Tusell test") # nezamitame aditivitu
class(out)<-"aTest"
return(out)
}
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