**1. Introduction**

Hypothesis testing and *p*-values are routinely used in applied, empirically oriented research. However, practitioners of statistics often misinterpret *p*-values, particularly in settings where hypothesis tests are used for model comparisons. Riedle, Neath and Cavanaugh [1] attempt to address this issue by providing an alternate conceptualization of the *p*-value. The authors introduce and investigate the concept of the discrepancy comparison probability (DCP) and its bootstrapped estimator, called the bootstrap discrepancy comparison probability (BDCP). The authors establish a clear connection between the BDCP based on the Kullback–Leibler discrepancy (KLD) and the *p*-values derived from likelihood ratio tests. However, this connection only exists when using the bootstrap discrepancy (BD) that arises from the "plug-in" principle, which yields a biased approximation to the KLD. Similarly to complexity penalization of the Akaike Information Criterion (AIC), we establish that an intuitive bias correction to the BD is the addition of *k*, the number of functionally independent parameters in the candidate model. We also propose utilizing a bootstrap-based correction, which can be justified under less stringent assumptions. We analyze how well the bootstrap approach corrects the bias of the BDCP and the BD, and we show that, in most settings, its performance is comparable to simply adding *k*.
