Power of the different methodologies for comparing groups on subjective measurements controlling the type I error, for different simulation parameters; the difficulties are considered unknown, the latent traits are normally distributed.

CTT: Classical Test Theory, IRT: Item Response Theory, CML: conditional maximum likelihood, MML: marginal maximum likelihood, MML-Cov: MML with group covariate, : items difficulties distribution, : number of items, : sample size, : difference between the latent traits means, WML: weighted maximum likelihood, EAP: expected a posteriori, PV: plausible values, MI: multiple imputations of PV, Norm: normal distribution, Mixt: equiprobable mixture of two normal distributions.