Fit indices are widely used in order to test the model fit for structural equation models. In a highly influential study, Hu and Bentler (1999) showed that certain cutoff values for these indices could be derived, which, over time, has led to the reification of these suggested thresholds as "golden rules" for establishing the fit or other aspects of structural equation models. The current study shows how differences in unique variances influence the value of the global chi-square model test and the most commonly used fit indices: Root-mean-square error of approximation, standardized root-mean-square residual, and the comparative fit index. Using data simulation, the authors illustrate how the value of the chi-square test, the root-mean-square error of approximation, and the standardized root-mean-square residual are decreased when unique variances are increased although model misspecification is present. For a broader understanding of the phenomenon, the authors used different sample sizes, number of observed variables per factor, and types of misspecification. A theoretical explanation is provided, and implications for the application of structural equation modeling are discussed.

Empirical evidence to the robustness of the analysis of variance (ANOVA) concerning violation of the normality assumption is presented by means of Monte Carlo methods. High-quality samples underlying normally, rectangularly, and exponentially distributed basic populations are created by drawing samples which consist of random numbers from respective generators, checking their goodness of fit, and allowing only the best 10% to take part in the investigation. A one-way fixed-effect design with three groups of 25 values each is chosen. Effect-sizes are implemented in the samples and varied over a broad range. Comparing the outcomes of the ANOVA calculations for the different types of distributions, gives reason to regard the ANOVA as robust. Both, the empirical type I error α and the empirical type II error β remain constant under violation. Moreover, regression analysis identifies the factor “type of distribution” as not significant in explanation of the ANOVA results.

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