Abstract

Maximum likelihood (ML), which is commonly used to estimate structural equation models, is based on the assumption of normality in the data. However, violations of the normality assumption are frequently reported in psychology and the social sciences, which can lead to biased estimation results and undermine the validity of statistical inferences. Although alternative methods that can provide reliable results under non-normal conditions have been explored, the performance of these methods has shown inconsistent patterns across studies, making it difficult to establish clear criteria for selecting appropriate methods. This study aims to address the problems posed by violations of the normality assumption and to explore alternative methods for dealing effectively with such violations. By integrating studies from the last 30 years of research, the study attempts to provide practical guidelines for researchers confronted with non-normality in their data. It first discusses the importance of the normality assumption in ML and examines the impact of its violation on estimation results. It then presents several alternative methods that are applicable under non-normal conditions and analyses the principles by which these methods deal with non-normality. Furthermore, previously published studies are systematically reviewed and categorized according to specific conditions, with the results visualized through tables and figures to compare the performance of different methods. Finally, the study integrates these discussions to propose guidelines for researchers and highlight their implications and limitations.