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sampleSizeWilcoxTwoSample <- function(a = 0.05, b = 0.2, c = 0.5, pxy = 0.75, two.sided = TRUE){
# Given two independent samples X_1, ..., X_m and Y_1, ..., Y_n,
# we want to test the hypothesis that the two samples come from
# the same population against that Y's tend to be larger than X's
# Taken from Nother (1987), JASA 82, 644 - 647
#
# Input:
# a: significance level
# b: desired power
# c: proportion of observations in group 1: c = m / (m + n)
# (c = 0.5 means equally sized groups)
# pxy: P(Y > X)
# two.sided: if = T --> two.sided, else one sided test
#
# Output: vector E N^2 containing
# m: number of observations in Sample 1
# n: number of observations in Sample 2
#
# Kaspar Rufibach, December 2007
#
side <- 2
if (two.sided == FALSE){side <- 1}
za <- qnorm(1 - a / side)
zb <- qnorm(1 - b)
N <- (za + zb) ^ 2 / (12 * c * (1 - c) * (pxy - 1 / 2) ^ 2)
m <- ceiling(c * N)
n <- ceiling(N * (1 - c))
return(c("m = " = m, "n = " = n))
}
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