The Standardized S-X2 Statistic for Assessing Item Fit

The S-X2 statistic (Orlando & Thissen, 2000) is popular among researchers and practitioners who are interested in the assessment of item fit. However, the statistic suffers from the Chernoff–Lehmann problem (Chernoff & Lehmann, 1954) and hence does not have a known asymptotic null distribution. This paper suggests a modified version of the S-X2 statistic that is based on the modified Rao–Robson χ2 statistic (Rao & Robson, 1974). A simulation study and a real data analyses demonstrate that the use of the modified statistic instead of the S-X2 statistic would lead to fewer items being flagged for misfit.