Exact test size and power of a Gaussian error linear model for an internalpilot study

Wittes and Brittain recommended using an 'internal pilot study' to adjust s ample size. The approach involves five steps in testing a general linear hy pothesis for a general linear univariate model, with Gaussian errors. First , specify the design, hypothesis, desired test size, power, a smallest 'cli nically meaningful' effect, and a speculated error variance. Second, conduc t a power analysis to choose provisionally a planned sample size. Third, co llect a specified proportion of the planned sample as the internal pilot sa mple, and estimate the variance (but do not test the hypothesis). Fourth, u pdate the power analysis with the variance estimate to adjust the total sam ple size. Fifth, finish the study and test the hypothesis with all data. We describe methods for computing exact test size and power under this scenar io. Our analytic results agree with simulations of Wittes and Brittain. Fur thermore,:our exact results apply to any general linear univariate model wi th fixed predictors, which is much more general than the two-sample t-test considered by Wittes and Brittain. In addition, our results allow for exami nation of the impact on test size of internal pilot studies for more compli cated designs in the framework of the general linear model. We examine the impact of (i) small samples, (ii) allowing the planned sample size to decre ase, (iii) the choice of internal pilot sample size, and (iv) the maximum a llowable size of the second sample. All affect test size, power and expecte d total sample size. We present a number of examples including one that use s an internal pilot study in a three-group analysis of variance. Copyright (C) 1999 John Wiley & Sons, Ltd.