Drasgow, Levine, and Zickar (1996) suggested a statistic based on the Neyman-Pearson lemma (e.g., Lehmann & Romano, 2005, p. 60) for detecting preknowledge on a known set of items. The statistic is a special case of the optimal appropriateness indices of Levine and Drasgow (1988) and is the most powerful statistic for detecting item preknowledge when the assumptions underlying the statistic hold for the data (e.g., Belov, 2016; Drasgow et al., 1996). This paper demonstrated using real data analysis that one assumption underlying the statistic of Drasgow et al. (1996) is often likely to be violated in practice. This paper also demonstrated, using simulated data, that the statistic is not robust to realistic violations of its underlying assumptions. Together, the results from the real data and the simulations demonstrate that the statistic of Drasgow et al. (1996) may not always be the optimum statistic in practice and occasionally has smaller power than another statistic for detecting preknowledge on a known set of items, especially when the assumptions underlying the former statistic do not hold. The findings of this paper demonstrate the importance of keeping in mind the assumptions underlying and the limitations of any statistic or method. [This paper will be published in "Applied Psychological Measurement."]