Extensions of the Significance Test for One-Parameter Signal Detection Hypotheses

Abstract

The basic models of signal detection theory involve the parametric measure, d ′, generally interpreted as a detectability index. Given two observers, one might wish to know whether their detectability indices are equal or unequal. Gourevitch and Galanter (1967) proposed a large sample statistical test that could be used to test the hypothesis of equal d ′ values. In this paper, their large two sample test is extended to a K -sample detection test. If the null hypothesis d 1 ′ = d 2 ′ = ... = d K ′ is rejected, one can employ the post hoc confidence interval procedure described in this paper to locate possible statistically significant sources of variance and differences. In addition, it is shown how one can use the Gourevitch and Galanter statistics to test d ′ = 0 for a single individual.