Cross-modal matching and internal references

'Make the light as bright as the sound is loud.' This is a typical instruction in experiments dealing with the cross-modal matching of stimuli. According to Luce's (Luce, Steingrimsson, & Narens, 2010) theory of global psychophysics, in such a cross-modal task the perceived stimulus intensities are judged against respondent-generated internal reference intensities, all represented on a common psychological scale. Heller (2021) generalizes Luce's theory by distinguishing the internal references with respect to their role in the experimental setup, that is, whether they pertain to the standard or to the variable stimulus in the matching task. By testing Heller's generalization of Luce's theory of global psychophysics on cross-modal data, the present study aims at thoroughly investigating the role-sensitivity of the internal reference intensities. For achieving this, it replicates a classical experiment by Stevens and Marks (1965), who made participants adjust the brightness of a light to the perceived loudness of a noise sound and vice versa. This allows for complementing the traditional group-level analysis by evaluating the data at the individual level, and for fitting the global psychophysical model to the data in a cognitive modeling approach. We find that on the individual level, the cross-modal matching curves differ in slope, and show a regression effect as reported in the classical literature. This implies role-dependent reference intensities as suggested by Heller's model. In order to experimentally manipulate the internal references' role-(in)dependence, an alternative psychophysical method is discussed. Using an adaptive staircase procedure within the method of constant stimuli, and if instructed to choose the more intense stimulus, the subject is not aware which of the stimuli is the standard and which the variable stimulus. Under these conditions the internal references are expected to be role-independent, and the regression effect should vanish. Heller, J. (2021). Internal references in cross-modal judgments: A global psychophysical perspective. Psychological Review, 128(3), 509–524. https://doi.org/10.1037/rev0000280 Luce, R. D., Steingrimsson, R., & Narens, L. (2010). Are psychophysical scales of intensities the same or different when stimuli vary on other dimensions? Theory with experiments varying loudness and pitch. Psychological Review, 117(4), 1247–1258. https://doi.org/10.1037/a0020174 Stevens, J. C., & Marks, L. E. (1965). Cross-modality matching of brightness and loudness. Proceedings of the National Academy of Sciences of the United States of America, 54(2), 407.