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akp.effect <- function(formula, data, EQVAR = TRUE, tr = 0.2, nboot = 200, alpha = 0.05, ...){
#
# Computes the robust effect size suggested by
#Algina, Keselman, Penfield Psych Methods, 2005, 317-328
if (missing(data)) {
mf <- model.frame(formula)
} else {
mf <- model.frame(formula, data)
}
cl <- match.call()
xy <- split(model.extract(mf, "response"), mf[,2])
faclevels <- names(xy)
x <- xy[[1]]
y <- xy[[2]]
x<-elimna(x)
y<-elimna(y)
n1<-length(x)
n2<-length(y)
## effect size computation
s1sq=winvar(x,tr=tr)
s2sq=winvar(y,tr=tr)
spsq<-(n1-1)*s1sq+(n2-1)*s2sq
sp<-sqrt(spsq/(n1+n2-2))
cterm=1
if(tr>0)cterm=area(dnormvar,qnorm(tr),qnorm(1-tr))+2*(qnorm(tr)^2)*tr
cterm=sqrt(cterm)
if(EQVAR)dval<-cterm*(tmean(x,tr)-tmean(y,tr))/sp
if(!EQVAR) dval<-cterm*(tmean(x,tr)-tmean(y,tr))/sqrt(s1sq)
## bootstrap CI
be.f=NA
for(i in 1:nboot){
X=sample(x,n1,replace=TRUE)
Y=sample(y,n2,replace=TRUE)
s1sq=winvar(X,tr=tr)
s2sq=winvar(Y,tr=tr)
spsq<-(n1-1)*s1sq+(n2-1)*s2sq
sp<-sqrt(spsq/(n1+n2-2))
cterm=1
if(tr>0)cterm=area(dnormvar,qnorm(tr),qnorm(1-tr))+2*(qnorm(tr)^2)*tr
cterm=sqrt(cterm)
if(EQVAR)dval_b<-cterm*(tmean(X,tr)-tmean(Y,tr))/sp
if(!EQVAR)dval_b<-cterm*(tmean(X,tr)-tmean(Y,tr))/sqrt(s1sq)
be.f[i] <- dval_b
}
L=alpha*nboot/2
U=nboot-L
be.f=sort(be.f)
ci=be.f[L+1]
ci[2]=be.f[U]
## output
result <- list(AKPeffect = dval, AKPci = ci, alpha = alpha, call = cl)
class(result) = "AKP"
result
}
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