title: Two-way ANOVA for scalar trajectories, with experimental evidence of non-phasic interactions.
abstract: Kinematic and force trajectories are often normalized in time, with mean and variance summary statistic trajectories reported. It has been shown elsewhere, for simple one-factor experiments, that statistical testing can be conducted directly on those summary statistic trajectories using Random Field Theory (RFT). This technical note describes how RFT extends to two-factor designs, and how bizarre "non-phasic interactions" can occur in multi-factor experiments. We reanalyzed a public dataset detailing stance phase knee flexion during walking in (a) patellofemoral pain vs. controls, and (b) females vs. males using both a full model (with interaction effect) and a main-effects-only model. In both models the main effect of PAIN failed to reach significance at α=0.05. The main effect of GENDER reached significance over 5-40% stance (p=0.0005), but only for the full model. The interaction effect (in the full model) reached significance over 0-15% of stance (p=0.030), and resulted from greater flexion in females but decreased flexion in males in PFP vs. controls. Thus there was a non-phasic interaction in which a non-significant interaction (over 20-40% stance) suppressed the main effect of GENDER. Similarly, if we had only analyzed 20-40% stance, we would have committed Type II error by failing to reject the null PAIN-GENDER interaction hypothesis. The possible presence of non-phasic interactions implies that trajectory analyses must be conducted at the whole-trajectory level, because a failure to do so will generally miss non-phasic interactions if present.
authors.affiliation: Department of Bioengineering, Shinshu University, Japan. Electronic address: tpataky@shinshu-u.ac.jp.
authors.forename: Todd C
authors.initials: TC
authors.lastname: Pataky
authors.affiliation: Research Institute for Sport and Exercise Sciences, Liverpool John Moores University, UK.
authors.forename: Jos
authors.initials: J
authors.lastname: Vanrenterghem
authors.affiliation: Research Institute for Sport and Exercise Sciences, Liverpool John Moores University, UK.
authors.forename: Mark A
authors.initials: MA
authors.lastname: Robinson
mesh_terms: D000704:Analysis of Variance; D001696:Biomechanical Phenomena; D001703:Biophysics / Q000379:methods*; D005260:Female; D006801:Humans; D007719:Knee Joint / Q000502:physiology*; D008297:Male; D010146:Pain; D046788:Patellofemoral Pain Syndrome / Q000503:physiopathology; D012727:Sex Characteristics; D016138:Walking / Q000502:physiology*
keywords: Kinematics; Random field theory; Statistical parametric mapping; Time series analysis