| Direct ratio scaling techniques have been plagued by threshold curvature and the regression effect, two sources of systematic error. They produce functions which depart from the simple, unique, log-log linearity posited by Stevens' power law and obscure the relationship between sensory magnitude and stimulus intensity.;Two experiments were conducted to examine the regression-reducing effectiveness of two forms of cross-modality matching, a free and a fixed method of presentation. Thirty subjects in Experiment 1 performed alternating matches of duration to loudness and vice versa. They were free to adjust both the matched and matching continua. Thirty-two subjects in Experiment 2 also performed alternating matches but only adjusted the matching continua to fixed stimulus levels.;The regression angle with the free technique was 79% smaller than that angle previously found with traditional interchanged methods. Further, the curvature present appeared more random than systematic since upward and downward curvature occurred about equally. Average amount of function curvature, assessed via the additive constant, was not significantly greater than zero. Correlations indicated low amounts of regression and curvature were associated with better goodness-of-fit; low regression was correlated with low curvature.;The fixed technique did not lead to regression reduction. Curvature in these functions was greater and more systematic than in Experiment 1 with 75% of the functions curving downwards at low intensities. This experiment revealed that reductions in regression and curvature can occur with practice--both decreased significantly over repetitions. Importantly, many of the relationships between regression and curvature in Experiment 1 also occurred here--low regression being significantly correlated with low curvature.;Further correction for regression still is necessary, since regression, although reduced considerably with the free technique, was not eliminated. The study supports the Stevens and Greenbaum (1966) correction which takes the geometric mean of the two exponents obtained in an interchanged design as the best estimate of true exponent. Average geometric-mean exponents for Experiment 1 and 2 were not significantly different. The findings suggest threshold mechanisms are not the sole explanations for curvature and that curvature may result from subjects' response patterns such as the tendency to regress. |
