title: Functional anatomy of the null hypothesis and of tests of it.
abstract: The author compared simulations of the "true" null hypothesis (zeta) test, in which sigma was known and fixed, with the t test, in which s, an estimate of sigma, was calculated from the sample because the t test was used to emulate the "true" test. The true null hypothesis test bears exclusively on calculating the probability that a sample distance (mean) is larger than a specified value. The results showed that the value of t was sensitive to sampling fluctuations in both distance and standard error. Large values of t reflect small standard errors when n is small. The value of t achieves sensitivity primarily to distance only when the sample sizes are large. One cannot make a definitive statement about the probability or "significance" of a distance solely on the basis of the value of t.
authors.affiliation: Department of Psychology, Louisiana State University, Baton Rouge 70803, USA. ariope@lsu.edu
authors.forename: Arthur J
authors.initials: AJ
authors.lastname: Riopelle
mesh_terms: D006801:Humans; D008960:Models, Psychological; D011582:Psychological Theory; D011584:Psychology / Q000379:methods