Axiomatic evaluation of k-multiplicativity in ratio scaling: Investigating numerical distortion

Birkenbusch, Jana; Ellermeier, Wolfgang

doi:10.1016/j.jmp.2015.12.004

Cited by 2 publications

(2 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This problem has been treated in the pertinent literature as one of determining a transformation function (Ellermeier & Faulhammer, 2000 ; Narens, 1996 , Eq. 1 ; Schneider et al, 1974 ), a numerical distortion (Birkenbusch & Ellermeier, 2016 ), or a weighting function (Steingrimsson & Luce, 2007 ) relating the numerals used in judgments or instructions to their mathematical equivalent. In the present data, that kind of numerical distortion is evident in the fact that for some three quarters of the participants, the ×6 productions systematically exceed the ×2×3 and ×3×2 productions (see Fig.…”

Section: Discussionmentioning

confidence: 99%

“…The problem of reference points Different implicit reference points for assessing ratios of subjective intensities had been used as an explanatory construct to account for the often inconsistent results obtained when mixing the production of multiples and fractions to test scaling axioms in the context of Luce's theory (Birkenbusch & Ellermeier, 2016;Luce et al, 2010). Note that in the case of cross-modal productions, the situation is more complicated: When making a sound three times as loud as a light is bright, for example, the observer may use an (implicit) internal reference on the brightness continuum to determine the brightness magnitude of the reference luminance, and simultaneously a (potentially different) internal reference on the loudness continuum by which to evaluate the adjusted loudness to be three times as intense.…”

Section: Comparison With the Intramodal Cross-dimensional Casementioning

confidence: 99%

See 1 more Smart Citation

Cross-modal commutativity of magnitude productions of loudness and brightness

Ellermeier

Kattner

Raum

2021

Atten Percept Psychophys

Self Cite

View full text Add to dashboard Cite

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.

show abstract