Measuring Loudness of Long and Short Tones Using Magnitude Estimation

McFadden (1975) questioned the accuracy and reliability of the method of magnitude estimation for the measurement of loudness of tones that vary both in duration and level. He suggested that it produced unreliable results and should not be used to assess how loudness depends on stimulus duration. To examine this issue further, the present study obtained loudness functions for 5and 200-ms tones in nine listeners using magnitude estimation. Loudness matches between the short and long tones were also obtained using an adaptive 2IFC procedure. The average amounts of temporal integration (defined as the level difference between equally loud short and long tones) obtained with the two procedures show good agreement. However, this may not apply to individual listeners. Some listeners show poor agreement, whereas others show good agreement. These results indicate that magnitude estimation provides a rapid and accurate means for assessing group-average loudness functions for tones of different durations. Nonetheless, it appears that magnitude estimation often is too susceptible to judgment biases and variability to reveal detailed features of individual listeners’ loudness functions for tones of various durations, even if it does reveal their general form. Magnitude estimation has frequently been used to measure the growth of loudness. As a procedure, it has received its share of criticism (e.g., McFadden, 1975; Poulton, 1989) as well as praise (e.g., Stevens, 1975; Hellman and Zwislocki, 1964). Previous experiments using magnitude estimation to assess temporal integration have had mixed success. Stevens and Hall (1966) attempted to obtain information about the growth of loudness for bursts of white noise with different durations using magnitude estimation. They measured loudness across a relatively wide range of levels (36 to 109 dB SPL) and assumed a simple power-function representation. They found that the average slope of the loudness functions were nearly the same for noise bursts ranging in duration from 5 to 500 ms. They did not report on the variability, but the reported data appear to be internally consistent. On the other hand, McFadden (1975) found magnitude estimation to be unsuitable for obtaining loudness functions for pure tones that varied both in duration and level. His data showed very large variability and his results were inconsistent with other measures of loudness as a function of duration. It is unclear why the results of these two studies differ so dramatically. The purpose of the present study is to evaluate the suitability of magnitude estimation as a method for measuring loudness functions for pure tones of different durations. In order to assess this, magnitude estimation data are compared with loudness matches to examine their internal consistency. Procedure All stimuli were presented monaurally via headphones. Listeners were seated in a double-wall sound-attenuating booth. 1. Absolute Thresholds Absolute thresholds were measured monaurally for 1-kHz tones with 5and 200-ms durations. Measurements were performed using a three-down, one-up adaptive staircase method and a two-interval, two-alternative, forced-choice paradigm with feedback. 2. Absolute Magnitude Estimation Each listener was asked to rate the loudness of individual tones by assigning a number whose magnitude matched the tone’s loudness. The number was typed on a computer-microterminal keypad. No reference or range was given as a basis for this judgment. The 5and 200-ms tones were presented in mixed order at levels ranging from 5 dB SL to 100 dB SPL for the 200ms tones and 110 dB SPL for the 5-ms tones. Ten magnitude estimates were obtained for each level and duration. The trials were chosen by selecting each new stimulus level and duration randomly from the set of possibilities that met the following criteria: The SL needed to be within 30 dB of the level in the previous trial for tones of the same duration and within 25 dB for the other duration. The final estimates were obtained as the geometric mean of the ten estimates completed for each duration and level. 3. Loudness Matching The final part of the experiment consisted of loudness matches between 5and 200-ms stimuli. This was performed using a roving-level two-alternative forced-choice adaptive procedure similar to that used by Buus et al. (1999). This procedure obtains ten concurrent loudness matches by randomly interleaving ten adaptive tracks. Five of these tracks varied the 5-ms tone and five varied the 200-ms tone. The fixed stimulus for each of the five tracks was set to different SLs between 5 and 85 dB in 20-dB steps. On each trial, the listener heard two tones separated by a 600-ms interstimulus interval. The fixed-level tone followed the variable tone or the reverse with equal a priori probability. The listener’s task was to indicate which sound was louder by pressing a key on the response terminal. The level of the variable tone was adjusted according to a simple up-down method. If the listener indicated that the variable tone was the louder one, its level was reduced; otherwise it was increased. The step size was 5 dB until the second reversal, after which it was 2 dB. Each track ended after nine reversals and the average level of the last four reversals was used as an estimate of the point of subjective equality. This procedure made the variable tone converge towards a level at which it was judged louder than the fixed tone in 50% of the trials (Levitt, 1971). Results and Discussion Figure 1 shows the geometric mean of nine listeners’ loudness functions obtained using magnitude estimation for long and short tones. The loudness functions have a mid-to-high-level slope of about 0.18. This is lower than the frequently reported slope of 0.3 (Hellman, 1991), but it is within the range of previously reported slopes (cf. Viemeister and Bacon, 1988).