Advanced circular statistics in biology: Multiple factors, interactions and repeated measures

Abstract Circular data is common across biology and the wider sciences, but presents unique analytical challenges due to their wrapped structure, where endpoints coincide (e.g. 360° = 0°). This requires the use of specific statistical methods. Traditional tests like the Rayleigh and Watson U 2 tests remain widely used, but lack flexibility in handling multiple linear and categorical factors or repeated measures. This study aims to fill this gap by leveraging trigonometric transformations of a circular response variable to enable the use of Multivariate Analysis of Variance (MANOVA) and linear mixed models (LMMs) with circular data. Approach and Methods . We compared the performance of MANOVA and LMM against traditional methods across various simulated and real‐world scenarios, including data with multiple co‐factors and repeated measures. Simulations were conducted using different circular distributions, sample sizes and configurations to evaluate type 1 error rates, and statistical power to detect group differences, overall non‐uniform orientation and interactions. In practical examples, we re‐analysed published data of shark predatory approaches and Emlen funnel experiments on bird orientation. Main Results . The MANOVA and LMM demonstrated robust control of type 1 errors across scenarios. The MANOVA consistently exhibited higher power than traditional methods for detecting non‐uniform orientation and group interactions in complex designs, particularly for directional differences. LMMs showed strengths in detecting deviations from uniformity, especially for unimodal distributions or symmetrical group differences. Practical examples highlighted the superiority of these methods over traditional tests in identifying nuanced effects, such as the combined influences of sun and wind direction on shark predatory angles and the effects of the test sequence on bird orientation. Conclusions and Implications . This study provides evidence supportive of a transformative expansion of the circular statistical toolkit by adapting linear statistical frameworks for circular data. MANOVA and LMMs enable researchers to model multiple random factors, covariates and grouping variables, offering substantial improvements over traditional methods. These advancements hold promise for broader applications, enhancing the power and versatility of circular data analysis in diverse biological and ecological contexts.