Abstract
In their fundamental paper, Luce, Steingrimsson, and Narens (2010, Psychological Review, 117, 1247-1258) proposed that ratio productions constituting a generalization of cross-modality matching may be represented on a single scale of subjective intensity, if they meet “cross-dimensional commutativity.” The present experiment is the first to test this axiom by making truly cross-modal adjustments of the type: “Make the sound three times as loud as the light appears bright!” Twenty participants repeatedly adjusted the level of a burst of noise to result in the desired sensation ratio (e.g., to be three times as intense) compared to the brightness emanating from a grayscale square, and vice versa. Cross-modal commutativity was tested by comparing a set of successive ×2×3 productions with a set of ×3×2 productions. When this property was individually evaluated for each of 20 participants and for two possible directions, i.e., starting out with a noise burst or a luminous patch, only seven of the 40 tests indicated a statistically significant violation of cross-modal commutativity. Cross-modal monotonicity, i.e. checking whether ×1, ×2, and ×3 adjustments are strictly ordered, was evaluated on the same data set and found to hold. Multiplicativity, by contrast, i.e., comparing the outcome of a ×1×6 adjustment with ×2×3 sequences, irrespective of order, was violated in 17 of 40 tests, or at least once for all but six participants. This suggests that both loudness and brightness sensations may be measured on a common ratio scale of subjective intensity, but cautions against interpreting the numbers involved at face value.
Highlights
By matching sensations on one modality, for example, loudness, to equal sensation magnitudes on another modality, for example, brightness, the resulting cross-modality matching function provides an empirical consistency check for the independently determined unimodal psychophysical power functions obtained via magnitude estimation
The focus is on evaluating cross-modal commutativity, but two other conditions resulting from Narens’ (1996) theory are investigated in a cross-modal paradigm: The monotonicity of the adjustments, meaning that for p > q, a p-times production will yield a greater stimulus intensity on the target dimension than a q-times production: x fg p
Note that though Narens’ influential publication bears the title “A Theory of Ratio Magnitude Estimation,” it applies to all varieties of direct magnitude scaling, including cross-modality matching or its extension beyond producing equal sensation strength: cross-modality magnitude production
Summary
Cross-modality matching assumes a pivotal role in Stevens’ (1975) “New Psychophysics.” By matching sensations on one modality, for example, loudness, to equal sensation magnitudes on another modality, for example, brightness, the resulting cross-modality matching function provides an empirical consistency check for the independently determined unimodal psychophysical power functions obtained via magnitude estimation. By matching sensations on one modality, for example, loudness, to equal sensation magnitudes on another modality, for example, brightness, the resulting cross-modality matching function provides an empirical consistency check for the independently determined unimodal psychophysical power functions obtained via magnitude estimation. It is further stipulated that if crossmodality matches pass this test, a common underlying scale of sensory magnitude – independent of modality – may be assumed. This reasoning relies on what has been pejoratively labelled a “curve-fitting” approach, as opposed to a mathematically formulated psychophysical theory
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