New invariant and consistent chi-squared type goodness-of-fit tests for multivariate normality and a related comparative simulation study

ABSTRACT

New invariant and consistent goodness-of-fit tests for multivariate normality are introduced. Tests are based on the Karhunen–Loève transformation of a multidimensional sample from a population. A comparison of simulated powers of tests and other well-known tests with respect to some alternatives is given. The simulation study demonstrates that power of the proposed McCull test almost does not depend on the number of grouping cells. The test shows an advantage over other chi-squared type tests. However, averaged over all of the simulated conditions examined in this article, the Anderson–Darling type and the Cramer–von Mises type tests seem to be the best.     

Physiological Regulation and Fearfulness as Predictors of Young Children's Empathy‐related Reactions

Indices of physiological regulation (i.e., resting respiratory sinus arrhythmia [RSA] and RSA suppression) and observed fearfulness were tested as predictors of empathy‐related reactions to an unfamiliar person's simulated distress within and across 18 (T1, N = 247) and 30 (T2, N = 216) months of age. Controlling for T1 helping, high RSA suppression and low fearfulness at T1 predicted T2 helping. In a structural model, empathic concern was marginally positively related to resting RSA at both assessments whereas personal distress was related to RSA suppression within time (marginally positively at T1 and significantly negatively at T2). Fearfulness was associated with self‐oriented, distress‐related reactions within time. Comfort seeking (an index of personal distress) declined in mean level with age whereas helping increased, and both behaviors exhibited differential continuity (as did resting RSA). Individual, as well as developmental, differences in the types of reactions that young children exhibit when witnessing others' suffering and distress were discussed.