A Note on Accepting the Null Hypothesis

Models are sometimes developed on the premise that there are no differences between two or more conditions regardless of experimental manipulation. This article argues that unless a very sensitive experiment (or series of experiments) was conducted, such conclusions are often premature. Design and statistical factors such as alpha level, variability, sample size, and treatment effect are all determinants of the sensitivity of the experiment. It is sometimes the case that an experiment produces differences between means and yet the null hypothesis is not rejected because of high variability within experimental conditions or because too few subjects were used. Unless the probability of detecting a difference between groups is known, it would seem unwise to conclude that no difference exists. Judgment on the model should be suspended. Examples are taken from the mass-spring and pulse-step models for voluntary movement control to illustrate the problem.