日時：2026年3月27日(金) 10:00 ~　90分

場所：webのみ　（※ 対象は特に限定しない）

講演者：Wolfgang Wiedermann 先生（University of Missouri）　

題目： Tackling a classical problem in Classical Test Theory: Cumulant-based approaches for testing the independent error assumption in non-Gaussian parallel and congeneric measures.

In classical test theory, independence of measurement errors
constitutes a central assumption when estimating the reliability of
measures. Further, it is well known that this assumption cannot be
tested with standard methods that rely on second-order moments
(variances, covariances). The present study, therefore, explores
properties of non-Gaussian parallel and congeneric measures with
respect to their capabilities of identifying violations of the error
independence assumption. It is shown that, under non-Gaussianity and
inequality of hidden confounding effects, third and fourth
cumulant-based test statistics can be derived which enable researchers
to detect non-independent error structures. Identifiability conditions
under which the proposed test statistics can be expected to have
adequate statistical power in parallel and congeneric measures are
described, and results of Monte-Carlo simulation experiments are
presented. Simulation results suggest that third-order tests
adequately protect the nominal significance level. However,
fourth-order tests can produce inflated Type I error rates, in
particular, when error variances are unequal. In general, the power to
detect non-independent errors increases with the sample size, the
magnitude of non-Gaussianity, the degree of inequality of hidden
confounding effects, and the degree of error non-independence. A
real-world data example is presented for illustrative purposes.

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