The S-X 2 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-X 2 statistic that is based on the modified Rao-Robson χ 2 statistic (Rao & Robson, 1974). A simulation study and a real data analyses demonstrate that the use of the modified statistic instead of the S-X 2 statistic would lead to fewer items being flagged for misfit.
Keywords: Orlando-Thissen statistic; Pearson’s; Rao-Robson’s modified; item response theory model fit; statistic.
© The Author(s) 2022.