Most study samples show less variability in key variables than do their source populations due most often to indirect selection into study participation associated with a wide range of personal and circumstantial characteristics. Formulas exist to correct the distortions of population-level correlations created. Formula accuracy has been tested…

A sampling subspace in hypothesis testing where Type II error is made for completely illogical reasons from the standpoint of probability is described. The case of unequal probabilities of populations or conditions is also considered. (Author/BS)

The sampling errors of maximum likelihood estimates of item-response theory parameters are studied in the case where both people and item parameters are estimated simultaneously. A check on the validity of the standard error formulas is carried out. The effect of varying sample size, test length, and the shape of the ability distribution is…