Abstract Regardless of whether one is analyzing quantitative data from research involving generative artificial intelligence (GenAI) or more classical methods, testing for normality remains a necessary step in statistical analysis. Although over 60 methods have been proposed for assessing univariate normality, previous systematic reviews show that normality testing remains underreported in L2 research. This paper addresses this gap by first reviewing the concept of normality and its role in parametric statistical inference. We then examine 12 normality assessment methods including five graphical and seven analytical methods selected based on their prominence in statistical literature and availability in commonly used software. Each method is explained in terms of its underlying mechanism and sensitivity to specific forms of nonnormality, such as skewness, tail heaviness, and multimodality. In the second part of the study, we review 237 empirical articles published between 2020 and 2025 in ten selected L2-focused Q1 journals, using AI-assisted annotation. Our findings reveal inconsistencies in how graphical tests are reported, a tendency to rely on tests such as the Kolmogorov-Smirnov without explicit attention to sample size constraints, and limited justification provided for critical values of skewness and kurtosis. These results indicate some divergence between recommended statistical practices and the procedures for normality testing reported in the L2 publications examined. The paper concludes with actionable recommendations for selecting and interpreting normality tests in L2 research contexts.
Aryadoust et al. (2026) studied this question.