2.8. Statistical Analyses
EVENTS, SECONDARY, SIDE EFFECT
The primary outcome measures included cognitive focus and attention (i.e., total score, accuracy, average time per score, and time to completion), determined by neuropsychological testing (Stroop and TMT-B) to assess objective changes in mental processing, cognitive flexibility, and attention, with VASs assessing subjective changes in energy, sustained energy, mental stamina, focus, concentration, motivation to accomplish difficult tasks, drive, vigor, positive outlook, mood, feelings of well-being, and resilience to stress. The secondary outcome measures included vital signs (blood pressure and heart rate) and side effect profile/adverse events monitoring. Data are presented as means ± standard deviation and the primary statistical approach employed was a mixed factorial ANOVA with repeated measures on time to assess group (methylliberine vs. PLA), time, and group × time interaction effects. The primary analysis compared the acute effects at all timepoints within visits 3 and 5, while the secondary analysis compared baseline (values that were averaged) at visits 2 and 4 to the baseline/pre timepoint (prior to the 4th dose ingestion of the study product) at visits 3 and 5 (examining whether an accumulation over 3 daily doses had any effect on the primary outcomes). An a priori power analysis was conducted for the primary analyses’ main outcome measures using G*Power (i.e., specifically energy). The results for the mixed factorial ANOVA with repeated measures, with two groups and four time points, within-between interaction, and a small effect of 0.25, was a sample size of 24 to achieve 80% power. All the variables were tested for normality using the results from a Shapiro–Wilk test. When a deviation from normality was identified, natural log transformations were employed. As such, transformations were employed for the Stroop accuracy scores. In the case of scale (ratio) data, transformations were not possible. Factorial ANOVAs with repeated measures on time were used to examine changes from baseline (the first testing session on visits 3 and 5) within each group, with Bonferroni corrections applied to all pairwise comparisons. Changes from baseline (deltas) were calculated and independent 