Statistical Power Analysis and Sample Size Estimation

Statistical Power Analysis and Sample Size Estimation

One common approach to statistical inference makes assertions about the truth or falsity of hypotheses. A null hypothesis asserts that in the whole population there is no difference between groups or no correlation between variables, and any apparent differences or correlations are merely the results of sampling error. A Type I error occurs when the Null hypothesis is true but the investigator wrongly rejects it because the sampling error happens to be unusually large in one experiment. The probability of making this kind of error is the significance level of the test of the hypothesis. A test that yields P < .001, for example, asserts that the probability of rejecting the Null when it is actually true is less than one chance in a thousand. A Type II error, on the other hand, occurs when the Null really is false but the statistical test fails to reject it. The power of the test is the probability that the Null will indeed be rejected when some alternative hypothesis is true. Unfortunately, for many experiments done in psychology and neuroscience, Type II error probability often exceeds 50% and power is less than 50%. The principal reason for this unhappy situation is that researchers often study too few subjects. Larger sample sizes confer greater power on statistical tests. This problem is especially severe for tests of hypotheses about interactions between heredity and environment in factorial designs.

The chapter in the Crusio & Gerlai volume explains these matters for continuous variables, whereas the chapter in the Mormede and Jones book focuses on dichotomous variables.

Wahlsten, D. Experimental design and statistical inference. In W.E. Crusio and R. T. Gerlai (eds.), Molecular-genetic Techniques for Behavioral Neuroscience. Amsterdam: Elsevier, in press.

Wahlsten, D. Planning genetic experiments: power and sample size. In P. Mormede and B Jones (Eds.), Cellular and Quantitative Methods in Neurogenetics. CRC Press, in press.

Wahlsten, D. Sensitivity of the t test to different models of interaction. Cahiers de Psychologie Cognitive, 1995, 14, 205-213.

Wahlsten, D. Sample size requirements for the Capron and Duyme balanced fostering study of I.Q. International Journal of Psychology, 1993, 28, 509-516.

Wahlsten, D. Sample size to detect a planned contrast and a one degree-of-freedom interaction effect. Psychological Bulletin, 1991, 110, 587-595.

Wahlsten, D. Insensitivity of the analysis of variance to heredity-environment interaction. Behavioral and Brain Sciences, 1990, 13, 109-161.