Sample Size and the Strength of Evidence: A Bayesian Interpretation of Binomial Tests of the Information Content of Qualified Audit Reports

Lindley (1957) demonstrated that from a Bayesian standpoint a given level of statistical significance P, carries less evidence against the null hypothesis H0 the larger (more powerful) the test. Moreover, if the sample is sufficiently large, a result significant on H0 at 5% or lower may represent strong evidence in support of H0, not against it. Contrary to Lindley's argument, a great many applied researchers, trained exclusively in orthodox statistics, feel intuitively that to "reject" the null hypothesis H0 at (say) a=5% is more convincing evidence, ceteris paribus, against H0 the larger the sample. This is a consistent finding of surveys in empirical psychology. Similarly, in accounting, see Burgstahler (1987). In econometrics, "Lindley's paradox" (as it has become known statistics) has been explained in well known books by Zellner (1971), Leamer (1978) and Judge et al. (1982), but is not widely appreciated. The objective of this paper is to reiterate the Bayesian argument in an applied context familiar to empirical researchers in accounting.