Sample Size Determination

Sample Size to Achieve a Given Variance or Relative Variance

One may want to estimate a parameter θ by an estimator $\hat{\theta }$ based on a sample of size n. Often the variance of $\hat{\theta },$ $\mbox{ var}(\hat{\theta }),$ will have the form $\mbox{ var}(\hat{\theta }) = b/n$ for some known constant b. To achieve a variance of $\hat{\theta }$ no larger than a specified amount A, one simply sets A = b ∕ n and solves for n: n = b ∕ A. The value of n must be an integer, so one takes n to be the smallest integer no smaller than b ∕ A. Note that nis...