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
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.