Hutchinson, Susan R.

Committee Member

Lalonde, Trent

Committee Member

Pulos, Steven

Committee Member

Ku, Heng-Yu


Applied Statistics & Research Methods


University of Northern Colorado

Type of Resources


Place of Publication

Greeley (Colo.)


University of Northern Colorado

Date Created



298 pages

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Born digital


To understand the role of fit statistics in Rasch measurement, it is necessary to comprehend why fit is important in measurement. The answer to this question is simple: applied researchers can only benefit from the desirable properties of the Rasch model when the data fit the model; however, the currently available fit statistics are flawed. A problem with fit statistics which are based on residuals is that they are based on unknown distributional properties (Masters & Wright, 1997; Ostini & Nering, 2006). Rost and von Davier (1994) developed the Q-Index. The Q-Index makes use of the statistical properties of the Rasch model, namely, parameter separability and conditional inference. Ostini and Nering, as early as 2006, called attention to the fact that little research has been performed on the Q-Index and thus there is little knowledge regarding the fit statistic’s robustness. To assess the Q-Index robustness, its performance was compared, in the present study, to the currently popular fit statistics known as Infit, Oufit, and standardized Infit and Oufit (ZSTDs) under varying conditions of test length, sample size, item difficulty (normal and uniform), and Rasch model (dichotomous and rating scale). The simulation consisted of 128 conditions that varied in sample size, test length, item difficulty distribution, and dimensionality. A series of factorial ANOVAs were conducted to examine the effect of sample size, test length, item difficulty distribution, and dimensionality on the fit statistics of interest. The results showed the Q-Index had a large effect size for dimensionality and for the dichotomous model a medium effect size for test length. Factorial ANOVAs for Infit, ZSTD Infit, Outfit, and ZSTD Infit resulted in trivial effect sizes for all the variables of interest. Parameter recovery was also examined, these findings suggest that the correlation between true and estimated parameters were high (r > .930) for both the dichotomous Rasch and the rating scale Rasch model indicating good pameter recovery despite the manipulation of test length, sample size, item difficulty distribution and dimensionality. Future research may explore the Q-Index under different measurement disturbances such as local independence or the robustness of the person Q-Index. Overall more research is needed regarding the robustness of the Q-Index.

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Available for download on Friday, April 16, 2021