Good statistical practice in pharmacology. Problem 2.

Background And Purpose: This paper is intended to assist pharmacologists to make the most of statistical analysis and in avoid common errors.

Approach: A scenario is presented where an experimenter performed an experiment to test the effects of two drugs on cultured cells. Analysis of the results, expressed as percentage of control, by a one-way ANOVA yielded P=0.058 and the experimenter concluded that neither drug was effective. The data were expressed as percentage of control because of pairing of the data within each experimental run, a common feature in cell culture experiments. Such data can be analysed with potentially more powerful ANOVA methods equivalent to the paired t-test. Monte Carlo simulations are presented to compare the power of relevant analyses.

Results: For data correlated within experimental run (i.e. paired values), transformation to percentage of control improved the power of a one-way ANOVA to detect a real effect, but a randomized block ANOVA (equivalent to a 2-way ANOVA with experiment and treatment as factors) using the raw values was substantially more powerful. The randomized block ANOVA performed well even with uncorrelated data, being only marginally less powerful than the one-way ANOVA.

Conclusions And Implications: A randomized block ANOVA is far superior to the one-way ANOVA with correlated data, and with uncorrelated data it is only marginally less powerful. Thus where there is, or might reasonably be, such a correlation (e.g. relatedness among the data within a single experimental run, or within a multi-well culture plate, or within an animal, et cetera), use the more powerful randomized block ANOVA rather than one-way ANOVA.