On the bisection operation

For two perceived sensory magnitudes, A and B, the bisection operation yields a perceived sensory magnitude, C, equally different from A and B. Available data do not resolve whether this operation is equivalent to a linear or a nonlinear mean. We tested these alternatives, using the evidence of functional measurement research that ratings are linear sensory measures. With A and B varied factorially, linear means predict that the curves relating rated C to rated A for each B are parallel straight lines, and nonlinear means predict that these curves are nonlinear and nonparallel. Using brightness and perceived size as sensory attributes, the present experiments confirm the first of these predictions, indicating that the bisection operation is equivalent to a linear mean.