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 H o the larger (more powerful) the test. Moreover, if the sample is sufficiently large, a result significant on H o at 5% or lower may represent strong evidence in support of H o , 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 H o at (say) α= 5% is more convincing evidence, ceteris paribus , against H o the larger the sample. This is a consistent finding of surveys in empirical psychology. Similarly, in accounting, see the principles for interpreting statistical tests suggested by Burgstahler (1987). In econometrics, ‘Lindley's paradox’ (as it has become known in statistics) has been explained in well known books by Zellner (1971), Leamer (1978) and Judge, Hill, Griffiths, Lutkepohl and Lee (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.