The shape of the latent trait distribution can be of considerable theoretical and methodological importance. A simulation study was performed to examine the distribution of the likelihood ratio statistic that was used to test for normality via Johnson curves, the power to detect deviations from normality, and the estimation properties of the item and latent trait distribution parameters. Except in conditions in which all items had high-difficulty parameters or were dichotomous, the distribution of the statistic used to test for normality could be approximated with a chi-square distributed with 2 degrees of freedom. In a variety of situations, the power was good enough to detect even small deviations from normality. Compared to assuming a normal distribution, allowing for Johnson curve latent trait distributions increased the standard errors of the marginal maximum likelihood item parameter estimates but reduced their bias in situations in which the latent trait was nonnormal.
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