To compensate for a power analysis based on a poor estimate of variance, in
ternal pilot designs use some fraction of the planned observations to reest
imate error variance and modify the final sample size. Ignoring the randomn
ess of the final sample size may bias the final variance estimate and infla
te test size. We propose and evaluate three different tests that control te
st size for an internal pilot in a general linear univariate model with fix
ed predictors and Gaussian errors. Test 1 uses the first sample plus those
observations guaranteed to be collected in the second sample for the final
variance estimate. Test 2 depends mostly on the second sample for the final
variance estimate. Test 3 uses the unadjusted variance estimate and modifi
es the critical value to bound test size. We also examine three sample-size
modification rules. Only test 2 can control conditional test sire. align w
ith a modification rule, and provide simple power calculations. We recommen
d it if the minimum second (incremental) sample is at least moderate (perha
ps 20). Otherwise, the bounding test appears to have the highest power in s
mall samples. Reanalyzing published data highlights some advantages and dis
advantages of the various tests.