Statistical hypothesis testing is commonly used to assess the fit of data to the Rasch models. Such tests of fit are problematical as they are sensitive to sample size and the number of parameters in the model. Furthermore, the null distributions of the statistical test may deviate from a distribution with a known parametric shape. Accordingly, in this study, a number of descriptive fit statistics for the Rasch model, based on the tenets of Andersen’s LR test and Fischer-Scheiblechner’s S test, are suggested and compared using simulation studies. The results showed that some of the measures were sensitive to sample size while some were insensitive to model violations. Andersen’s χ2/df measure was found to be the best measure of fit.