A Lilliefors test of normality has been applied to data from precision and accuracy studies. Most data sets tested as non-normal. Simulation studies showed that the test is extremely sensitive to the rounded, narrowly distributed data that are typical of method performance studies in clinical chemistry. The Lilliefors test can be modified to be applicable to rounded data so that it gives fewer indications of non-normality. The authors conclude that the selection of a test of normality requires careful study of the properties of the test. Otherwise, the subsequent choice between parametric and nonparametric statistics may not be meaningful.