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# Project: 2 * t Contingency Table
# adapted from Angie Zhu's getTable2xtNull.R
# Filename: Contingency2xt.R
# Last modified: 03.23.2012
# This function computes or simulates the null distribution of
# the Kruskal-Wallis statistics in a 2 x t contingency table.
# Treatment | 1 2 ... t | Total
# ---------------------------------------
# Response | |
# a | A_1 A_2 ... A_t | m
# b | B_1 B_2 ... B_t | n
# ---------------------------------------
# Total | d_1 d_2 ... d_t | N
# Arguments:
# Avec: integer vector of length tnum, containing the
# "a" reponses
# Bvec: integer vector of length tnum, containing the
# "b" reponses
# method: "asymptotic", "simulated", "exact",
# indicating the method of p-value calculation,
# dist: FALSE (default) means that the exact or
# estimated null distribution is not requested,
# otherwise it is.
# tab0: TRUE (default), when method = "simulated",
# the null distribution is given in tabular form,
# when tab0 = FALSE and method = "simulated", the
# null distribution is given as a single vector
# of all simulated values.
# Nsim: number of simulations to run, default 10^6
#
#
# Output: a list of class "kSamples" with components
# test.name = "2 x t Contingency Table"
# t = number of columns in the table
# KW.cont = 2 (or 3 vector) containing the observed KW
# value, its asymptotic (and the simulated
# or exact) P-value
# null.dist = a 2 x M matrix giving the M unique
# ordered KW values of the null
# distribution in the first column, and
# the corresponding probabilities
# (simulated or exact) in the second
# column. When method = "simulated" and
# tab0 = FALSE null.dist consists of a
# single vector of all simulated values.
# When dist = NULL or method = "asymptotic", only
# NULL is returned.
# method = the method used
# Nsim = number of simulations employed
contingency2xt <- function(Avec, Bvec, method=c("asymptotic","simulated","exact"),
dist = FALSE, tab0 = TRUE, Nsim=1e6) {
method <- match.arg(method)
m <- sum(Avec)
n <- sum(Bvec)
tnum <- length(Avec)
N <- m + n
dvec <- Avec + Bvec
KW.obs <- (N * (N - 1) / (m * n)) * (sum(Avec^2 / dvec) -
m^2/N )
pValue.asy <- 1 - pchisq(KW.obs,tnum-1)
if(dist == TRUE) Nsim <- min(Nsim,1e8)
# limits the size of null.dist
# whether method = "exact" or = "simulated"
if(method == "asymptotic"){
KW.cont <- c(KW.obs,pValue.asy)
null.dist <- NULL
}else{
ncomb <- choose(m + tnum - 1, tnum - 1)
if (ncomb <= Nsim && method == "exact") {
if(dist){
ans <- numeric(2+2*ncomb)
}else{
ans <- numeric(2)
}
out <- .C("contingency2xtExact0",
Avec = as.integer(Avec), Bvec = as.integer(Bvec),
tnum = as.integer(tnum),
ncomb = as.integer(ncomb),
getDist = as.integer(dist),
ans = as.double(ans), PACKAGE = "kSamples")
KW.obs <- out$ans[1]
KW.obs <- (N * (N - 1) / (m * n)) * (KW.obs -
m^2 / N)
KW.obs <- round(KW.obs, 6)
pValue <- out$ans[2]
if(dist){
out <- out$ans[-(1:2)]
out <- matrix(out, nrow=ncomb, ncol=2, byrow=FALSE)
out <- out[out[, 2] > 0, ]
prob <- out[ , 2]
KW <- (N * (N - 1) / (m * n)) * (
out[ , 1] - m^2 / N)
KW <- round(KW, 6)
KW.u <- sort(unique(KW))
k.u <- length(KW.u)
prob.u <- sapply(1:k.u, function(j) {
sum( prob[KW == KW.u[j]] ) })
null.dist <- cbind(KW.u,prob.u)
dimnames(null.dist) <- list(NULL,c("KW","prob"))
}else{
null.dist <- NULL
}
KW.cont <- c(KW.obs,pValue.asy,pValue)
}else{
method <- "simulated"
}
if( method == "simulated" ){
if( Nsim < 100) Nsim <- 100
if(dist){
ans <- numeric(2+Nsim)
}else{
ans <- numeric(2)
}
out <- .C("contingency2xtSim0",
Avec = as.integer(Avec), Bvec = as.integer(Bvec),
tnum = as.integer(tnum),
Nsim = as.integer(Nsim),
getDist = as.integer(dist),
ans = as.double(ans))
KW.obs <- out$ans[1]
KW.obs <- (N * (N - 1) / (m * n)) * (KW.obs - m^2 / N)
KW.obs <- round(KW.obs, 6)
pValue <- out$ans[2]
if(dist){
KW <- (N * (N - 1) / (m * n)) *
(round(out$ans[3:(Nsim+2)],6) - m^2 / N)
if(tab0==TRUE){
tab <- table(KW)/Nsim
null.dist <-
cbind(as.numeric(names(tab)),
as.vector(tab))
dimnames(null.dist) <-
list(NULL,c("KW","prob"))}else{
null.dist <- KW
}
}else{
null.dist <- NULL
}
KW.cont <- c(KW.obs,pValue.asy,pValue)
}
}
if(method=="asymptotic"){
names(KW.cont) <- c("observed KW",
" asympt. P-value")
}
if(method=="exact"){
names(KW.cont) <- c("observed KW",
" asympt. P-value","exact P-Value")
}
if(method=="simulated"){
names(KW.cont) <- c("observed KW",
" asympt. P-value","sim. P-Value")
}
object <- list(test.name =paste("2 x t Contingency Table"),
t = tnum, KW.cont = KW.cont,
null.dist = null.dist,
method = method, Nsim = Nsim)
class(object) <- "kSamples"
object
}
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