# functions for power and sample size calculation for the two-sample
# t-test with equal (pooled) variances

# copy this text and paste it into an R session,
# or just type
# source("http://www.stat.ncsu.edu/people/bloomfield/courses/st516/2sample.r")
# at the R prompt.

twoSamplePower = function(alpha, deltaMu, sigma, n1, n2 = n1) {
# power of the two-sided two-sample t-test with pooled variance

# alpha   = size of test
# deltaMu = difference of means
# sigma   = standard deviation of a single measurement
# n1      = size of first sample
# n2      = size of second sample
        
        if (alpha <= 0 || alpha >= 1)
                stop("alpha must be between 0 and 1");
        if (sigma <= 0)
                stop("sigma must be positive");
        if (n1 + n2 < 3)
                stop("combined sample sizes must be at least 3");

        df = n1 + n2 - 2;
        tcrit = qt(1 - alpha / 2, df);
        ncp = abs(deltaMu) / (sigma * sqrt(1 / n1 + 1 / n2));
        1 - pt(tcrit, df, ncp) + pt(-tcrit, df, ncp);
}

twoSampleSize = function(alpha, deltaMu, sigma, targetPower) {
# required sample size in the two-sided two-sample t-test with pooled
# variance

# alpha       = size of test
# deltaMu     = difference of means
# sigma       = standard deviation of a single measurement
# targetPower = desired power

        if (alpha <= 0 || alpha >= 1)
                stop("alpha must be between 0 and 1");
        if (sigma <= 0)
                stop("sigma must be positive");
        if (targetPower <= 0 || targetPower >= 1)
                stop("target power must be between 0 and 1");

        p = 0;
        n = 1;
        while (p < targetPower) {
                n = n + 1;
                p = twoSamplePower(alpha, deltaMu, sigma, n);
        }
        list(SampleSize = n, ActualPower = p);
}