This paper is concerned with supplementing statistical tests for the Rasch model so that additionally to the probability of the error of the first kind (Type I probability) the probability of the error of the second kind (Type II probability) can be controlled at a predetermined level by basing the test on the appropriate number of observations. An approach to determining a practically meaningful extent of model deviation is proposed, and the approximate distribution of the Wald test is derived under the extent of model deviation of interest. (Contains 2 tables.)