Effects of Compounded Nonnormality of Residuals in Hierarchical Linear Modeling

Examining the normality assumption of a design-comparable effect size in single-case designs

What Works Clearinghouse (WWC, 2022) recommends a design-comparable effect size (D-CES; i.e., gAB) to gauge an intervention in single-case experimental design (SCED) studies, or to synthesize findings in meta-analysis. So far, no research has examined gAB's performance under non-normal distributions. This study expanded Pustejovsky et al. (2014) to investigate the impact of data distributions, number of cases (m), number of measurements (N), within-case reliability or intra-class correlation (ρ), ratio of variance components (λ), and autocorrelation (ϕ) on gAB in multiple-baseline (MB) design. The performance of gAB was assessed by relative bias (RB), relative bias of variance (RBV), MSE, and coverage rate of 95% CIs (CR). Findings revealed that gAB was unbiased even under non-normal distributions. gAB's variance was generally overestimated, and its 95% CI was over-covered, especially when distributions were normal or nearly normal combined with small m and N. Large imprecision of gAB occurred when m was small and ρ was large. According to the ANOVA results, data distributions contributed to approximately 49% of variance in RB and 25% of variance in both RBV and CR. m and ρ each contributed to 34% of variance in MSE. We recommend gAB for MB studies and meta-analysis with N ≥ 16 and when either (1) data distributions are normal or nearly normal, m = 6, and ρ = 0.6 or 0.8, or (2) data distributions are mildly or moderately non-normal, m ≥ 4, and ρ = 0.2, 0.4, or 0.6. The paper concludes with a discussion of gAB's applicability and design-comparability, and sound reporting practices of ES indices.

Cultural contributions to adults' self-rated mental health problems and strengths: 7 culture clusters, 28 societies, 16 906 adults

BACKGROUND

It is unknown how much variation in adult mental health problems is associated with differences between societal/cultural groups, over and above differences between individuals.

METHODS

To test these relative contributions, a consortium of indigenous researchers collected Adult Self-Report (ASR) ratings from 16 906 18- to 59-year-olds in 28 societies that represented seven culture clusters identified in the Global Leadership and Organizational Behavioral Effectiveness study (e.g. Confucian, Anglo). The ASR is scored on 17 problem scales, plus a personal strengths scale. Hierarchical linear modeling estimated variance accounted for by individual differences (including measurement error), society, and culture cluster. Multi-level analyses of covariance tested age and gender effects.

RESULTS

Across the 17 problem scales, the variance accounted for by individual differences ranged from 80.3% for DSM-oriented anxiety problems to 95.2% for DSM-oriented avoidant personality (mean = 90.7%); by society: 3.2% for DSM-oriented somatic problems to 8.0% for DSM-oriented anxiety problems (mean = 6.3%); and by culture cluster: 0.0% for DSM-oriented avoidant personality to 11.6% for DSM-oriented anxiety problems (mean = 3.0%). For strengths, individual differences accounted for 80.8% of variance, societal differences 10.5%, and cultural differences 8.7%. Age and gender had very small effects.

CONCLUSIONS

Overall, adults' self-ratings of mental health problems and strengths were associated much more with individual differences than societal/cultural differences, although this varied across scales. These findings support cross-cultural use of standardized measures to assess mental health problems, but urge caution in assessment of personal strengths.

Jumping of flea beetles onto inclined platforms

The flea beetle, Altica cirsicola, escapes predators by jumping and landing in a dense maze of leaves. How do they land on such varied surfaces? In this experimental study, we filmed the take-off, flight, and landing of flea beetles on a configurable angled platform. We report three in-flight behaviors: winged, wingless, and an intermediate winged mode. These modes significantly affected take-off speed, acceleration, and the duration that wings were deployed. When wings were closed, flea beetles rolled or pitched up to five times in the air. This work may help to understand how insects can jump and right themselves onto variable surfaces.