R/lc.prop.bs.R

In cwendorf/dgb: DGB

# DGB
## Linear Contrast of Proportions (Between Subjects)

ci.lc.prop.bs <- function(alpha, f, n, c) {
 # Computes adjusted Wald confidence interval for a linear contrast 
 # of population proportions in a between-subjects design
 # Arguments:
 #   alpha:  alpha level for 1-alpha confidence
 #   f:      vector of sample frequency counts
 #   n:      vector of sample sizes
 #   c:      vector of contrast coefficients
 # Values:
 #   estimate, standard error, lower limit, upper limit
 z <- qnorm(1 - alpha/2)
 m <- length(c) - length(which(c==0))
 p <- (f + 2/m)/(n + 4/m)
 est <- t(c)%*%p
 se <- sqrt(t(c)%*%diag(p*(1 - p))%*%solve(diag(n + 4/m))%*%c)
 t <- est/se
 pval <- 2*(1 - pnorm(abs(t)))
 LL <- est - z*se
 UL <- est + z*se
 CI <- c(LL, UL)
 out <- t(c(est, se, LL, UL))
 colnames(out) <- c("Estimate", "SE", "LL", "UL")
 return(out)
}

size.ci.lc.prop.bs <- function(alpha, p, c, w) {
 # Computes sample size per group required to estimate a linear contrast
 # of proportions in between-subjects design with desired precision
 # Arguments: 
 #   alpha:  alpha level for 1-alpha confidence 
 #   p:      vector of proportion planning values
 #   c:      vector of contrast coefficients
 #   w:      desired confidence interval width
 # Values:
 #   required sample size
 z <- qnorm(1 - alpha/2)
 n <- ceiling((4*t(c)%*%diag(p*(1 - p))%*%c)*(z/w)^2)
 return(n)
}

size.test.lc.prop.bs <- function(alpha, power, p, c, es) {
 # Computes sample size per group required to test a linear contrast
 # of proportions in between-subjects design with desired power
 # Arguments: 
 #   alpha:  alpha level for 1-alpha confidence 
 #   power:  desired power of test
 #   p:      vector of proportion planning values
 #   c:      vector of contrast coefficients
 #   es:     expected effect size
 # Values:
 #   required sample size
 za <- qnorm(1 - alpha/2)
 zb <- qnorm(power)
 n <- ceiling((t(c)%*%diag(p*(1 - p))%*%c)*(za + zb)^2/es^2)
 return(n)
}