Many nonnormalities, one simulation: Do different data generation algorithms affect study results?

Monte Carlo simulation studies are among the primary scientific outputs contributed by methodologists, guiding application of various statistical tools in practice. Although methodological researchers routinely extend simulation study findings through follow-up work, few studies are ever replicated. Simulation studies are susceptible to factors that can contribute to replicability failures, however. This paper sought to conduct a meta-scientific study by replicating one highly cited simulation study (Curran et al., Psychological Methods, 1, 16-29, 1996) that investigated the robustness of normal theory maximum likelihood (ML)-based chi-square fit statistics under multivariate nonnormality. We further examined the generalizability of the original study findings across different nonnormal data generation algorithms. Our replication results were generally consistent with original findings, but we discerned several differences. Our generalizability results were more mixed. Only two results observed under the original data generation algorithm held completely across other algorithms examined. One of the most striking findings we observed was that results associated with the independent generator (IG) data generation algorithm vastly differed from other procedures examined and suggested that ML was robust to nonnormality for the particular factor model used in the simulation. Findings point to the reality that extant methodological recommendations may not be universally valid in contexts where multiple data generation algorithms exist for a given data characteristic. We recommend that researchers consider multiple approaches to generating a specific data or model characteristic (when more than one is available) to optimize the generalizability of simulation results.

How to think clearly about the central limit theorem.

The central limit theorem (CLT) is one of the most important theorems in statistics, and it is often introduced to social sciences researchers in an introductory statistics course. However, the recent replication crisis in the social sciences prompts us to investigate just how common certain misconceptions of statistical concepts are. The main purposes of this article are to investigate the misconceptions of the CLT among social sciences researchers and to address these misconceptions by clarifying the definition and properties of the CLT in a manner that is approachable to social science researchers. As part of our article, we conducted a survey to examine the misconceptions of the CLT among graduate students and researchers in the social sciences. We found that the most common misconception of the CLT is that researchers think the CLT is about the convergence of sample data to the normal distribution. We also found that most researchers did not realize that the CLT applies to both sample means and sample sums, and that the CLT has implications for many common statistical concepts and techniques. Our article addresses these misconceptions of the CLT by explaining the preliminaries needed to understand the CLT, introducing the formal definition of the CLT, and elaborating on the implications of the CLT. We hope that through this article, researchers can obtain a more accurate and nuanced understanding of how the CLT operates as well as its role in a variety of statistical concepts and techniques. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

The National Standard of Psychological Health and Safety in the Workplace: A Psychometric and Descriptive Study of the Nursing Workforce in British Columbia Hospitals.

BACKGROUND: In 2013, the Mental Health Commission of Canada created a National Standard that includes 13 workplace factors associated with employee mental health. PURPOSE: This study (a) examined the psychometric properties of Guarding Minds at Work (GMW), the instrument used to measure the Standard's 13 workplace factors and (b) assessed BC nurses' workplace risk factors. METHODS: A province-wide survey study of 3,077 direct care nurses working in acute care settings was conducted. RESULTS: Subscale internal consistencies were acceptable. For most items, the original alphas were greater than the alpha-if-item-deleted. All corrected item-subtotal correlations were moderate to high. The 13-factor structure showed an adequate model fit based on absolute fit indices (SRMR = 0.057 and RMSEA = 0.054) but the relative fit indices were lower than the recommended cutoff (CFI = 0.827 and TLI = 0.815). Nurses identified nine of the 13 GMW factors as serious or significant concern in their workplace. CONCLUSIONS: The findings were consistent with a plethora of evidence pointing to shortcomings in nurses' work environments. This was the first study partially supporting the reliability and validity of the GMW. More work is required to refine the GMW and gain a better understanding of its psychometric properties.

Population models and simulation methods: The case of the Spearman rank correlation.

The purpose of this paper is to highlight the importance of a population model in guiding the design and interpretation of simulation studies used to investigate the Spearman rank correlation. The Spearman rank correlation has been known for over a hundred years to applied researchers and methodologists alike and is one of the most widely used non-parametric statistics. Still, certain misconceptions can be found, either explicitly or implicitly, in the published literature because a population definition for this statistic is rarely discussed within the social and behavioural sciences. By relying on copula distribution theory, a population model is presented for the Spearman rank correlation, and its properties are explored both theoretically and in a simulation study. Through the use of the Iman-Conover algorithm (which allows the user to specify the rank correlation as a population parameter), simulation studies from previously published articles are explored, and it is found that many of the conclusions purported in them regarding the nature of the Spearman correlation would change if the data-generation mechanism better matched the simulation design. More specifically, issues such as small sample bias and lack of power of the t-test and r-to-z Fisher transformation disappear when the rank correlation is calculated from data sampled where the rank correlation is the population parameter. A proof for the consistency of the sample estimate of the rank correlation is shown as well as the flexibility of the copula model to encompass results previously published in the mathematical literature.