R/lc.stdmean.ws.R

In cwendorf/dgb: DGB

# DGB
## Standardized Linear Contrast of Means (Within Subjects)

ci.lc.stdmean.ws <- function(alpha, m, sd, cor, n, h) {
 # Computes confidence interval for a population standardized linear 
 # contrast of means in a within-subjects design (assumes equal
 # correlations)
 # Arguments: 
 #   alpha: alpha level for 1-alpha confidence
 #   m:     vector of sample means
 #   sd:    vector of sample standard deviations
 #   cor:   average of sample correlations
 #   n:     sample size
 #   h:     vector of contrast coefficients
 # Values:
 #   estimate, SE, lower limit, upper limit
 z <- qnorm(1 - alpha/2)
 a <- length(m)
 df <- n - 1
 s <- sqrt(sum(sd^2)/a)
 est <- (t(h)%*%m)/s
 se1 <- sqrt(est^2*(1 + (a - 1)*cor^2)/(2*a*df) + (1 - cor)*t(h)%*%h/n)
 v1 <- est^2/(2*a^2*s^4*df)
 v2 <- sum(sd^4)
 v3 <- cor^2*t(sd^2)%*%sd^2 
 v4 <- sum(h^2*sd^2)
 v5 <- cor*t(h*sd)%*%(h*sd)
 se2 <- sqrt(v1*(v2 + v3) + (v4 - v5)/(df*s^2))
 ll1 <- est - z*se1
 ul1 <- est + z*se1
 ll2 <- est - z*se2
 ul2 <- est + z*se2
 out1 <- t(c(est, se1, ll1, ul1))
 out2 <- t(c(est, se2, ll2, ul2))
 out <- rbind(out1, out2)
 colnames(out) <- c("Estimate", "SE", "LL", "UL")
 rownames(out) <- c("Equal Var & Cor Assumed:", "Only Equal Cor Assumed:")
 return(out)
}

size.ci.lc.stdmean.ws <- function(alpha, d, cor, w, h) {
 # Computes sample size required to estimate a standardized linear contrast of 
 # population means with desired precision in a within-subjects design 
 # Arguments: 
 #   alpha: alpha level for 1-alpha confidence
 #   d:     planning value of standardized linear contrast  
 #   cor:   planning value of smallest correlation
 #   w:     desired confidence interval width
 #   h:     vector of contrast coefficients 
 # Values:
 #   required sample size
 z <- qnorm(1 - alpha/2)
 a <- length(h)
 n <- ceiling(4*(d^2*(1 + (a - 1)*cor^2)/(2*a) + (1 - cor)*(t(h)%*%h))*(z/w)^2)
 return(n)
}