R/corr.os.R

In cwendorf/DGB: DGB

# DGB
## Correlations

ci.corr.os <- function(alpha, corr, n) {
 # Computes a confidence interval for a Pearson correlation
 # Arguments: 
 #   alpha: alpha level for 1-alpha confidence
 #   corr:  sample value of correlation 
 #   n:     sample size
 # Values:
 #   lower limit, upper limit
 z <- qnorm(1 - alpha/2)
 se <- sqrt(1/((n - 3)))
 zr <- log((1 + corr)/(1 - corr))/2
 LL0 <- zr - z*se
 UL0 <- zr + z*se
 LL <- (exp(2*LL0) - 1)/(exp(2*LL0) + 1)
 UL <- (exp(2*UL0) - 1)/(exp(2*UL0) + 1)
 CI <- c(LL, UL)
 return(CI)
}

size.ci.corr.os <- function(alpha, corr, w) {
 # Computes sample size required to estimate a correlation with desired precision
 # Arguments: 
 #   alpha: alpha level for 1-alpha confidence
 #   corr:  planning value of correlation
 #   w:     desired confidence interval width
 # Values:
 #          required sample size
 z <- qnorm(1 - alpha/2)
 n1 <- ceiling(4*(1 - corr^2)^2*(z/w)^2 + 3)
 zr <- log((1 + corr)/(1 - corr))/2
 se <- sqrt(1/(n1 - 3))
 LL0 <- zr - z*se
 UL0 <- zr + z*se
 LL <- (exp(2*LL0) - 1)/(exp(2*LL0) + 1)
 UL <- (exp(2*UL0) - 1)/(exp(2*UL0) + 1)
 n <- ceiling((n1 - 3)*((UL - LL)/w)^2 + 3)
 return(n)
}

size.test.corr.os <- function(alpha, power, s, cor, b) {
 # Computes sample size required to test a (partial) correlation with desired power
 # Arguments: 
 #   alpha: alpha value for test
 #   power: desired power of test
 #   s:     number of control variables
 #   cor:   planning value of (partial) correlation 
 #   b:     hypothesized value of correlation
 # Values:
 #   required sample size
 za <- qnorm(1 - alpha/2)
 zb <- qnorm(power)
 zr <- log((1 + cor)/(1 - cor))/2
 zo <- log((1 + b)/(1 - b))/2
 es <- zr - zo
 n <- ceiling((za + zb)^2/es^2 + s + 3)
 return(n)
}