Conjoint measurement of physical size and numerical magnitude: Direct evidence that numerals do not automatically activate their semantic magnitude

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
models of the contribution of physical size and numerical magnitude to perceived size
were fit to the data using maximum likelihood. The independent and additive observer
models 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.