One Number, Many Mechanisms: Decomposing Metrics into Position and Dispersion

Researchers often compress “closeness” constructs such as accuracy, similarity, and extremity into a single distance score by taking either the absolute deviation or mean squared error. That convenience comes with an interpretive trap because these operations fold the data around zero. The same improvement in a folded deviation metric can arise because responses shift toward a benchmark (position) or because responses become less spread out around their typical level (dispersion). These channels imply different mechanisms, yet they are routinely bundled into one headline effect. We offer a simple, theory-facing decomposition that keeps both signals visible. We then reanalyze three influential literatures to show what changes when the channels are separated. In within-person averaging (“wisdom of the inner crowd”), the apparent accuracy gain is largely dispersion reduction. In ideological similarity judgments, a key moderation on a folded predictor does not attach to either channel once unpacked. In anchoring, deviation-score moderation can mask, cancel, or even reverse directional pull when dispersion shifts dominate.