Description

This Master Prompt provides a comprehensive framework for designing, analyzing, interpreting and reporting factorial experiments in which multiple factors are varied simultaneously to reveal not only their individual effects but also the interactions that govern complex experimental systems. It covers two-level and multi-level full factorial designs, fractional factorial designs, factorial treatment structures, effect coding, contrasts, main effects, two-factor and higher-order interactions, factorial regression models, ANOVA, sums of squares, degrees of freedom, F-tests, effect sizes, residual variance, model hierarchy, design resolution, aliasing, confounding, minimum-aberration reasoning and model adequacy.