Global field trials show the advantages of beta regression compared with logit transformation and quasi‐likelihood for the analysis of percentage plant disease severity

Abstract Disease severity in crop protection field trials is commonly assessed as a proportion represented as a percentage. Traditional statistical analysis uses transformation to logit or angle (arcsine). This study compares analyses based on the beta distribution and the quasi‐likelihood method with the logit transform using a large global data set of field trials. A beta regression model fits better than logit‐normal. Both beta regression and quasi‐likelihood have a better distribution of residuals, beta regression being slightly better. These advantages are particularly marked for skewed data, which are common in field trials including very effective standard products and untreated controls. A result of using these better models is lower p‐values for the F or LR test of the treatment effect and thus more statistical power using beta regression to distinguish between treatment effects. The authors conclude that the distribution‐based beta regression can be usefully recommended as a method for the analysis of disease severity data, and as a method of reference for inclusion into official crop protection product registration guidelines.