Conjoint measurement of physical size and numerical magnitude: Numerals do not automatically activate their semantic meaning

I applied the methodology known as maximum likelihood conjoint measurement (MLCM) to diagnose how numerical magnitude affects the perception of physical size of numerals in the size congruity effect (SCE). Traditional theories of the SCE argue for automatic activation of numerical magnitude, and therefore the obligatory interaction in perception between number and size. Participants in the current study were presented with pairs of numerals varying on physical size and numerical magnitude. They judged which member of the pair was physically larger, while ignoring numerical magnitude. Three nested observer models (i.e. independent, additive, and saturated) of the contribution of physical size and numerical magnitude to perceived size were fit to the data using maximum likelihood. The independent observer model exhibited the best fit for the majority of observers. These results cast doubts on the view that numerical magnitude is activated automatically in judgments of physical size of numerals.