The appropriateness of the use of the standardized residual (SR) to assess congruence between sample test item responses and the one parameter latent trait (Rasch) item characteristic curve is investigated. Latent trait theory is reviewed, as well as theory of the SR, the apparent error in calculating the expected distribution of the SR, and implications of using the SR for item analysis. Empirical results using actual data are presented to support the theoretical anlaysis, as well as a demonstration of the practical implications of the failure to reject items which do not fit the model. Conclusions based on the findings include: (1) discriminations of all the items in a test must be very similar in order for Rasch model analyses to work in practice; (2) the SR mean square fit statistic does not detect unacceptable variation in discrimination; and (3) item discrimination needs to be monitored and controlled using more exact tests of fit than the residual mean square. Finally, an alternate linear model is described which may provide a practical solution to problems encountered in the construction of item banks and tailored testing. (RL)