Three Threats to Validity of Choice-based and Matched-Sample Studies in Accounting Research

We consider three technical errors in the statistical analysis of choice-based and matched-sample studies in accounting research. These problems constitute threats both to the internal and external validity of the research. First, we note that researchers have often failed to control for the effects of matching variables used in sample selection. Commonly, researchers believe that the selection of a matched sample already controls for the matching variables and hence controlling for them in analyses would not be necessary; but in fact it is. Typically, an unconditional analysis is performed, rather than the conditional one that is justified. Thus, failure to account for industry, size, and other matching variables may have driven incorrect findings in many research studies or may have suppressed results waiting to be revealed. Second, where matching is by "closest" size or other continuous measures, the matching is imperfect, and there remains the possibility that case versus control differences in this matching variable could be the cause of differences in outcome, so researchers must evaluate that possibility and perhaps control for it. Third, the disproportionate sampling for different population strata that is implicit in the choice-based and matched-sample selection would usually necessitate weighting data in statistical analyses by the sampling rates in each stratum, but reweighting or other appropriate adjustment to the analysis is often not implemented. A "logit exemption" to the need for reweighting has been noted in the literature but has been claimed to apply in settings where it does not. We provide a simulation example to demonstrate problems and provide suggestions for more precise ways to analyze choice-based and matched samples.