Power and Sample Size Calculations for Association Studies
Review of Errors:
Type II error is represented by beta and type I error as alpha
Where Z1 - (alpha /2)is the Z-value that creates the target value of alpha in the tail of the distribution. Power decreases as alpha increases.
Power also has a direct relationship with sample size. Sometimes we choose sample sized based on the desired power for a specific alternative hypothesis of interest, and other times we used a fixed sample size and significance level.
A Z-test of differences in proportions with 2 groups with different sample sizes:
C is the mean of the distribution under the alternative hypothesis:
And the power can be calculated by taking the cdf of C minus the one sided Z-value