2.10. Statistical Analysis
Statistical analysis of data was conducted using analysis of variance (ANOVA), based on linear mixed effect models with fixed effects for trial arm, treatment and time × treatment interaction and random effects for participant, participant × trial arm and participant × time. Residuals were inspected to check that the assumptions of the model were satisfied; for many of the antioxidant and cytokine measures, data were log-transformed before analysis to stabilise the variance. For most data, raw means are presented; for antioxidant and cytokine measures, there were a few missing samples which influenced the raw data means. For these measures, predicted means were calculated, and where the data had been log-transformed, the predicted means were back-transformed. Models were fitted with the R package Imer Test, and post-hoc tests were performed using the predict means package.