Sampling distribution of the SAM statistic

1 Background We derive the sampling distribution of the SAM (significance analysis for microarrays) statistic introduced by Tusher et al. (2001). The statistic resembles the t-statistic, but has an additional regularizing term in the denominator, which is a constant for a given dataset. We first introduce some notation and the SAM statistic, and then proceed to derive an approximate sampling distribution. Notation Consider log-transformed microarray data D in two classes: X i and Y j are taken to be i.i.d. random variables drawn according to Normal distributions N (µ X , σ 2 X) and N (µ Y , σ 2 Y) respectively. That is, µ X and µ Y are the true (or population) class means and σ 2 X and σ 2 Y the corresponding variances. Let ¯ X and ¯ Y represent the sample means of data in the two classes: ¯ X = 1 m m i=1