As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting…

This study investigated how population parameters representing heterogeneity of variance, skewness, kurtosis, bimodality, and outlier-proneness, drawn from normal and eleven non-normal distributions, also characterized the ranks corresponding to independent samples of scores. When the parameters of population distributions from which samples were…

U.S. state educational testing programs administer tests to track student progress and hold schools accountable for educational outcomes. Methods from item response theory, especially Rasch models, are usually used to equate different forms of a test. The most popular method for estimating Rasch models yields inconsistent estimates and relies on…

Tests of model misfit are often performed to validate the use of a particular model in item response theory. Douglas and Cohen (2001) introduced a general nonparametric approach for detecting misfit under the two-parameter logistic model. However, the statistical properties of their approach, and empirical comparisons to other methods, have not…

Through simulation, the power of the U3 statistic was compared with the power of one of the simplest person-fit statistics, the sum of the number of Guttman errors. In most cases, a weighted version of the latter statistic performed as well as the U3 statistic. (SLD)

It is well known that the two-sample Student t test fails to maintain its significance level when the variances of treatment groups are unequal, and, at the same time, sample sizes are unequal. However, introductory textbooks in psychology and education often maintain that the test is robust to variance heterogeneity when sample sizes are equal.…