Academic journal article Perception and Psychophysics

Examining the Validity of Numerical Ratios in Loudness Fractionation

Academic journal article Perception and Psychophysics

Examining the Validity of Numerical Ratios in Loudness Fractionation

Article excerpt

Direct psychophysical scaling procedures presuppose that observers are able to directly relate a numerical value to the sensation magnitude experienced. This assumption is based on fundamental conditions (specified by Luce, 2002), which were evaluated experimentally. The participants' task was to adjust the loudness of a 1-kHz tone so that it reached a certain prespecified fraction of the loudness of a reference tone. The results of the first experiment suggest that the listeners were indeed able to make adjustments on a ratio scale level. It was not possible, however, to interpret the nominal fractions used in the task as "true" scientific numbers. Thus, Stevens's (1956, 1975) fundamental assumption that an observer can directly assess the sensation magnitude a stimulus elicits did not hold. In the second experiment, the possibility of establishing a specific, strictly increasing transformation function that related the overt numerals to the latent mathematical numbers was investigated. The results indicate that this was not possible for the majority of the 7 participants.

Scaling constitutes the assignment of numbers to sensations. In most applications, direct estimation (or production) procedures are employed, for which observers are asked to relate a numerical value to the sensation magnitude a stimulus elicits. The number words used in this straightforward assessment are then considered to correspond to the proper (mathematical) numbers they signify, which in turn are interpreted as scale values on the sensation scale in question.

A typical task involves presenting the listeners with two sounds. The loudness of the first sound, the standard, is given a prespecified modulus value, often 10 or 100. The listener is then asked to evaluate the loudness of the second sound by assigning a number that reflects the ratio of loudnesses of the two sounds. Thus, if the second sound is judged to be twice as loud as the standard, it will be assigned the number 20 (or 200); if it is one fourth as loud, the number given is 2.5 (or 25). If the observer assigns the numbers, the method is called magnitude estimation; if number words are presented and the corresponding stimulus levels are sought, the procedure is called magnitude production. A classical variant of magnitude production, also used in this study, asks observers to adjust fractions, such as ½ or 1/3 of magnitudes, and has been termed fractionation, or ratio production (e.g., Gescheider, 1997). Because observers are asked to judge the magnitude ratio of two sounds, it is presumed, furthermore, that the numbers assigned (or matched with an appropriate sound level) are valid on a ratio scale.

These procedures were first used to study brightness perception ("Methode der doppelten Reize"; Merkel, 1888) and to describe the strength of auditory imagery and the loudness of sine tones (Richardson, 1929; Richardson & Ross, 1930), and they have been widespread ever since Stevens (e.g., 1956, 1975) propagated them in his seminal work. Assessments obtained by procedures of direct scaling are generally reliable and consistent (for investigations in loudness scaling, see, e.g., Collins & Gescheider, 1989; Hellman, 1976; Teghtsoonian & Teghtsoonian, 1971). Their validity, however, rests on two fundamental assumptions first laid out by Narens (1996)-namely, (1) that observers are able to estimate (or produce) sensation magnitudes that are meaningful on a ratio scale level and (2) that the number words the observers use can be taken "at face value" (i.e., that they are identical to the mathematical numbers they denote).

Narens's (1996) theory of magnitude scaling specifies the fundamental conditions, or axioms, that have to be met in order for these substantial assumptions to hold. The theory covers magnitude estimations or productions with a standard (modulus). It is based on a behavioral axiomatization that relates the number words used to mathematical numbers and on a cognitive axiomatization connecting the mathematical numbers to the observer's sensations. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.