Derivations based on the kernel method’s standard error formulas are given for computing the standard errors of the root mean square difference (RMSD) and of the simple difference between two subpopulations’ equated scores. An investigation of popular invariance for the equivalent groups design is discussed. The accuracy of the derived standard errors is evaluated with respect to empirical standard errors. This evaluation shows that the accuracy of the standard error estimates for the equated score differences is better than for the RMSD, and that accuracy for both standard error estimates is best when sample sizes are large.