Weighted Answer Similarity Analysis

Romero et al. (2015; see also Wollack, 1997) developed the <i>ω</i> statistic as a method for detecting unusually similar answers between pairs of examinees. For each pair, the <i>ω</i> statistic considers whether the observed number of similar answers is significantly larger than the expected number of similar answers. However, one limitation of <i>ω</i> is that it does not account for the particular items on which similar answers are observed. Therefore, in this study, we propose a weighted version of the <i>ω</i> statistic that takes this information into account. We compare the performance of the new and existing statistics using detailed simulations in which several factors are manipulated. Results show that while both the new and existing statistics are able to control the Type I error rate, the new statistic is more powerful, on average.