= Crossover criterion for learning-style matching
Let $\mu_{p,f}$ be the expected score for learner-preference group $p$ under randomly assigned format $f$. A two-style visual/auditory matching claim requires $\mu_{V,V}>\mu_{V,A}$ and $\mu_{A,A}>\mu_{A,V}$. Thus the within-group format contrast changes sign. An <interaction> contrast $I=(\mu_{V,V}-\mu_{V,A})-(\mu_{A,V}-\mu_{A,A})$ is positive under this pattern, but $I>0$ alone is insufficient: one format might remain better in both groups. With preference group on the horizontal axis and format as the plotted line, the matching prediction is a crossover. This is a criterion for the stated hypothesis, not evidence that fixed styles exist.
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