The Standardized S-X 2 Statistic for Assessing Item Fit
Zhuangzhuang Han1, Sandip Sinharay1, Matthew S Johnson1
1Educational Testing Service, Princeton NJ, USA.
Abstract:
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.
Related Concept Videos
Testing a Claim about Standard Deviation
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
Test for Homogeneity
Goodness-of-Fit Test
One-Way ANOVA: Unequal Sample Sizes
Calculating Standard Deviation
The standard deviation value is small when all the data is concentrated close to the mean. Here the data exhibits low variation. The standard deviation value is larger when the data values are more spread out from the mean. Here, the data displays high...
Chi-square Distribution


