A Comparison of the Power of Rasch Total and Between-Item Fit Statistics to Detect Measurement Disturbances

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Abstract
This study investigates the properties of the total and between fit statistics commonly used in Rasch model calibration and analysis programs to assess the fit of items to various Rasch models. There are two aspects of the study: an examination of the distributional properties of the item between fit statistics when the data fit the dichotomous model and a comparison of the power of the item between and total fit statistics to detect various types of simulated measurement disturbances in dichotomous data. The results indicate that the distributional properties of the between fit statistic are approximate unit normals and stable over a wide variety of testing conditions. In the presence of measurement disturbances, the between fit statistic appears to be more sensitive to systematic measurement disturbances and the total fit statistic is more sensitive to random measurement disturbances.

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