Acoust. Sci. & Tech. 26, 5 (2005)
PAPER
Statistical distribution of normal hearing thresholds under free-field listening conditions Kenji Kurakata1; , Tazu Mizunami1 , Kazuma Matsushita2 and Kaoru Ashihara1 1
National Institute of Advanced Industrial Science and Technology, AIST Central 6, 1–1–1 Higashi, Tsukuba, 305–8566 Japan 2 National Institute of Technology and Evaluation, 1–2 Namiki, Tsukuba, 305–0044 Japan ( Received 1 September 2004, Accepted for publication 25 January 2005 ) Abstract: The statistical distribution of normal hearing thresholds for pure tones of frontal incidence under binaural, free-field listening conditions was estimated as a function of frequency. First, the form of threshold distribution was investigated with threshold measurement data of the present study and those of other studies. Analytical results indicate that the threshold distribution has a form of normal distribution for the frequency range from 25 Hz to 16 kHz. Second, under the assumption of normality, standard deviations of thresholds were calculated for the frequency range from 25 Hz to 18 kHz by combining available threshold data of different studies. A supplementary experiment showed that thresholds at frequencies above 16 kHz were measurable with high reliability. These results illustrate the profile of our auditory sensitivity more accurately because they account for individual differences. Keywords: Hearing threshold, Individual difference, Statistical distribution, Free-field listening PACS number: 43.66.Cb
1.
[DOI: 10.1250/ast.26.440]
INTRODUCTION
The absolute threshold for pure tones in a free field as a function of frequency has attracted the interest of hearing researchers and acoustic engineers over many decades. Threshold measurement has been conducted in different laboratories using a variety of methods [1–13]. The results show remarkably good agreement if they are obtained under common listening conditions using a similar procedure. The great effort of those studies [1–12] established the average threshold curve of otologically normal persons as an ISO standard [14] for which measurement data of 15 studies were integrated to produce normative threshold values from 20 Hz to 18 kHz. Those studies also reveal vast differences of threshold values among individual listeners. Such differences are observable even among young listeners with normal hearing. Furthermore, the differences are not negligible, especially in the high-frequency region. For example, Kurakata et al. [13] demonstrated that the inter-quartile range of threshold values was greater than 20 dB at 16 kHz: four or more times larger than that at 1 kHz. For that reason, the entire profile of hearing thresholds cannot be
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clarified without considering such large variability of thresholds among listeners. In addition to audiological interest, individual differences in sensitivity to sounds near thresholds hold practical importance with regard to machine-induced or environmental noise problems. Some people complain about sounds that are considered inaudible by people with average hearing ability. Such cases have been reported frequently, especially when the noises contain highfrequency components for which individual differences in sensitivity are relatively large [15]. A normative threshold distribution should be determined to establish a noise criterion so that better-than-average ears would not suffer from such low-level noises. This paper is intended to describe the statistical distribution of normal absolute thresholds for pure tones of frontal incidence under binaural free-field listening conditions. The form of threshold distribution was first estimated based on threshold measurement data of individual listeners and statistical indices of thresholds reported in other studies to achieve this aim. Then, normative standard deviations (SDs) of hearing thresholds were estimated over the frequency range of 25 Hz to 18 kHz. In this estimation, measurement data in the present study and those in other studies were combined to enhance the
K. KURAKATA et al.: STATISTICAL DISTRIBUTION OF NORMAL HEARING THRESHOLDS
estimation accuracy. In the Appendix, a supplementary experiment was conducted to verify the measurement reliability and to search for possible artifacts in threshold measurements at high frequencies.
2.
ESTIMATION OF THE FORM OF THRESHOLD DISTRIBUTION
It is convenient to assume that the threshold variation should follow a certain statistical distribution because the entire form of distribution can be expressed by a small number of parameters such as mean and SD. In addition, it is advantageous that the threshold variation can be reasonably estimated, even when threshold data are unobtainable from some listeners at very high frequencies, as described in Section 3. The distribution of individual differences in human psychological characteristics has been known to fit a normal distribution. It would be natural to assume that auditory threshold variability fits a similar form. However, for the following reasons, the normality of threshold variation on the scale of sound pressure level is not guaranteed a priori. The decibel scale is a physical scale. Consequently, it may not correlate directly with psychological processes of tone detection. Moreover, hearing ability easily worsens, but has a certain limit in improvement. Accordingly, its distribution may not be symmetrical; instead, it may have a long tail to higher sound pressure levels. This study tested the normal-distribution hypothesis of hearing threshold using threshold data of individual listeners and statistical indices that have been reported in previous studies. The former is described in Section 2.1 and the latter in Section 2.2. 2.1. Threshold Measurement The hearing threshold in the free field was measured as a function of frequency in accordance with the preferred test conditions [16]. Frequencies measured were 1 kHz and higher: in that range, individual differences are relatively large. 2.1.1. Measurement method The frequency of pure tone was 1, 2, 4, 5, 6.3, 8, 10, 12.5, 16, 18, or 20 kHz. Tone duration was 1,000 ms with a rise/fall time of 50 ms. Signals were calculated digitally using a PC with 24-bit resolution and 48-kHz sampling. Then they were generated using a D/A converter (Roland, UA-5). Output signals were fed into a control amplifier (Technics, SU-C1010) and a power amplifier (Technics, SE-A1010). Then they were presented to listeners via a two-way, concentric loudspeaker (Tannoy, i8). Maximum output levels were between 83.4 and 87.9 dB SPL, depending on the tone frequency. Measurement was conducted in an anechoic room that was 4.35 m (W) 6.00 m (D) 2.95 m (H). The loud-
speaker and listener’s chair were set 3.0 m apart from each other on the room’s diagonal axis. Listeners sat on the chair with a headrest and faced the speaker directly. The listener’s head movement was monitored with two sensors attached to the headrest so that movement during the measurement was restricted to within about 1 cm. Sound level deviations from the reference point, the midpoint of the listener’s two ears, generally met the requirements of the preferred test conditions; deviations of more than 1 dB were observed at 1 kHz and those of more than 2 dB at 10 kHz only. The bracketing method [17] was employed to estimate the threshold level. A test tone was presented repeatedly to the listener, varying the sound pressure level by 1 dB. The interval between tones was changed randomly from 800 ms to 1,200 ms at every presentation. Listeners were instructed to press a key when they detected a target tone. Five successive runs were conducted twice at each frequency. The first run was always an ascending series and was excluded from the threshold calculation. Consequently, eight measurement values were obtained at each frequency from every listener. Study participants were 46 university students (25 men and 21 women) of 18–24 years old. Otoscopic examination, monaural audiometry with an audiometer, tympanometry, and inquiry about difficulties in hearing were conducted to screen participants for otological abnormality. Consequently, 38 students (18 men and 20 women) served as listeners for threshold measurement. 2.1.2. Results of measurement Table 1 shows threshold values and their variation among listeners. Some listeners’ thresholds exceeded the maximum output level of the reproduction system at frequencies of 18 and 20 kHz. Therefore, arithmetical means and SDs were not calculated for those frequencies; some indices of distribution are missing. The table also contains reference threshold values of ISO standard [14] in the rightmost column. The median thresholds show good agreement with the reference values of ISO standard at all frequencies, except at 18 kHz; deviations of a few decibels are relatively small compared to the variability of about 5–10 dB among measurements adopted in the standard. For that reason, the present measurement thresholds can be regarded as representative samples of the target population. The discrepancy at 18 kHz may not be a measurement error, but might instead be caused by data scarcity. The ISO threshold value at 18 kHz is based on the measurement result of only one laboratory [11], whereas those at other frequencies are based on several reports from different laboratories. A normative 18-kHz threshold is not well established yet and may be re-evaluated with additional data, as described in Section 4.2.
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Acoust. Sci. & Tech. 26, 5 (2005) Table 1 Hearing threshold values in dB SPL and their statistical indices of individual differences. Frequency (kHz)
mean
SD (dB)
min
P5
P25
1 2 4 5 6.3 8 10 12.5 16 18 20
1.1 0.1 5:7 3:7 4.4 8.7 11.6 14.2 40.8 — —
3.3 3.9 4.1 4.2 5.4 6.0 5.2 9.4 17.1 — —
6:5 5:9 18:4 13:3 9:8 1:7 3.0 0.0 13.4 30.5 53.4
3:6 5:9 10:6 11:0 3:8 0.1 3.5 1.7 20.2 39.9 72.6
1:4 2:8 7:9 6:3 1.8 2.9 8.0 7.0 28.8 52.9 >83:4
median 1.5 0.1 6:4 4:1 4.7 9.3 10.8 11.5 36.4 63.5 —
P75
P95
max
n=N
3.0 2.5 3:2 0:8 7.7 12.8 15.1 20.9 51.0 73.4 —
6.2 4.9 1.4 3.8 10.9 19.4 19.3 28.1 74.0 >79:0 —
10.0 13.1 3.1 4.2 19.2 22.3 26.0 40.0 80.4 — —
38/38 38/38 38/38 38/38 38/38 38/38 38/38 38/38 38/38 32/38 10/38
ISO threshold [14] 2.4 1:3 5:4 1:5 6.0 12.6 13.9 12.3 40.2 73.2 —
Px : xth percentile >L: higher than the maximum output level, L, at the frequency n: number of listeners whose threshold values were obtained N: number of listeners who participated in the measurement
2.1.3. Test for fitting a normal distribution to the measurement data The hypothesis that threshold variation has a form of normal distribution was examined using the experimental data given above. For comparison, those reported by the present authors [13] were also submitted to the examination. Thresholds were unobtainable from some listeners at higher frequencies. Therefore, the data at 1–16 kHz in the former set and those at 1–15 kHz in the latter set were used. Results of the Jarque-Bera test for goodness-of-fit to a normal distribution (The MathWorks, MATLAB R14) showed that threshold values did not deviate significantly from a normal distribution at every frequency of both data sets (p > 0:05). For the 1-kHz threshold of the latter data set, the normal-distribution hypothesis was actually rejected. However, subsequent analysis revealed that 1 listener out of 51 listeners, who showed an extraordinarily high threshold at this frequency, had influenced the test result. A re-test using the remaining 50 listeners’ data after removing that listener’s data supported the hypothesis. Therefore, it can be said that variation of threshold values follows a normal distribution at every frequency from 1 to 16 kHz. 2.2. Examination of Statistical Indices in Literature In the literature, absolute thresholds have been typically expressed as representative values of listeners’ groups with some statistical indices of distribution: medians with quartiles, arithmetic means with SDs, or a combination. The normal-distribution hypothesis cannot be tested for those summarized data as in the previous section. Therefore, another method using statistical indices was introduced to examine their normality. The reported statistical values should satisfy the properties of normal distribution on skewness and kurtosis if thresholds distribute normally. First, the distance from
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the 75th percentile, P75 , to the median, Med, is equal to that from the median to the 25th percentile, P25 : ðP75 MedÞ=ðMed P25 Þ ¼ 1:
ð1Þ
Values that are larger and smaller than unity respectively indicate that the distribution is positively and negatively skewed. Second, the distances from P75 to Med and from Med to P25 are approximately 0.6745 times as large as the SD of the distribution, s: P75 Med ¼ Med P25 0:6745s:
ð2Þ
This relation can be written as ðP75 P25 Þ=1:349s 1:
ð3Þ
Values larger and smaller than unity respectively indicate that the peak of distribution is flatter and more pointed than a normal curve. When an unbiased estimate of SD of population, , is given, s is substituted for , as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ¼ ðn 1Þ=n; ð4Þ where n is the number of samples. Figures 1 and 2 show these two relations as a function of frequency calculated with literature data [8,10,13]. For comparison, measurement data in Section 2.1 were processed similarly and presented in the figures. As expected, these figures illustrate that the published data generally meet these requirements of normal distribution. Minor deviations can be observed at some frequencies, but they differ from measurement to measurement, suggesting that no systematic deviation exists along the frequency axis. Therefore, summarizing examinations in Section 2.1 and 2.2, we may conclude that the variability of absolute thresholds among individuals can be expressed in the form of a normal distribution for the frequency range of 25 Hz to 16 kHz; its mean and SD vary as a function of frequency.
K. KURAKATA et al.: STATISTICAL DISTRIBUTION OF NORMAL HEARING THRESHOLDS
ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , u m m uX X t ¼ t n i i 2 ni ; i¼1
Fig. 1 Evaluation of the normality of threshold distributions in terms of skewness as calculated using Eq. (1).
Fig. 2 Evaluation of the normality of threshold distributions in terms of kurtosis as calculated using Eq. (3).
3. ESTIMATION OF THE STANDARD DEVIATION OF THRESHOLD DISTRIBUTION The normality of threshold distribution was confirmed for frequencies of 16 kHz and lower. Consequently, variation of individual thresholds can be described with SD of the normal distribution as a function of frequency. This section explains the procedure to calculate normative SDs, combining the available data that have been reported in other studies. Although the normality of distribution could not be examined for frequencies above 16 kHz in the previous section, SDs at 17 and 18 kHz were estimated as well, under the assumption of normality. Assume that we have a set of m unbiased estimates of SD, i (i ¼ 1; 2; . . . ; m), of the population from which listeners’ thresholds were sampled. We can obtain an estimate of the total SD of population, t , by integrating these SDs as
ð5Þ
i¼1
where ni is the number of listeners in the ith data set for calculating i . Note that Eq. (5) does not involve the threshold values themselves. Some differences exist in average thresholds among studies because of the different measurement methods, as suggested by Poulsen and Han [10]. However, the threshold differences can be neglected if we assume that individual thresholds vary independently of their measurement method. Note also that the SDs and the number of listeners vary as a function of frequency, e.g. i ð f Þ; nevertheless, parameter f is omitted herein for simplicity. Using Eq. (5), SDs reported in the references [2–4,6,8,10–13] and those in Table 1 were combined to produce t . Table 2 summarizes their measurement conditions. These references were selected based on these criteria: listeners were young, otologically normal and statistical indices of threshold variability are presented in numerical form. Data in these references [2–4,6,8,10–12] were also cited to determine the normative thresholds in the ISO standard [14]. For some frequencies at 10 kHz and above, thresholds were unobtainable from all listeners in some studies [8,11,13] and the present study. In these cases, SDs reported there were not used, but P75 and P25 were adopted to estimate the SD of all listeners. Using Eqs. (2) and (4), these quartiles in the ith study, P75;i and P25;i , can be transformed into i as rffiffiffiffiffiffiffiffiffiffiffiffiffi P75;i P25;i ni i : ð6Þ 1:349 ni 1 Subsequently, obtained i values were combined with those of other studies to produce t using Eq. (5). At 18 kHz, P75 was not obtainable in Kurakata et al. [13], Eq. (7) was used to calculate i instead, as rffiffiffiffiffiffiffiffiffiffiffiffiffi Med P25;i ni i : ð7Þ 0:6745 ni 1 Takeshima et al. [11] did not report the median and percentiles, the following values from their same measurement data were employed for SD calculation at 18 kHz [18]: median ¼ 73:0, P25 ¼ 64:2, and P75 ¼ 80:7, in dB SPL. The number of listeners was 32. Resulting values of SD for the entire frequency range are summarized in Table 3. Those values are represented graphically in Fig. 3, together with the SDs of each study used in the calculation. These results show a general tendency: the SDs become large at very low and very high frequencies. They also reveal a sudden drop at 18 kHz.
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Acoust. Sci. & Tech. 26, 5 (2005) Table 2 Reference data used for the estimation of total SD, t . Reference
Teranishi [2]
Brinkmann [3]
Watanabe & Møller [4]
Vorla¨nder [6]
Takeshima et al. [8]
Measurement frequencies (Hz) Number of listeners Statistical indices of threshold distribution
63–10 k 11 Mean, SD, median
63–8 k 9–56
25–1 k 12
Mean, SD
Mean, SD
1–16 k 37 Mean, SD, median
31.5–20 k 10–69 Mean, SD, min, P25 , median, P75 , max
Reference
Poulsen & Han [10]
Takeshima et al. [11]
Takeshima et al. [12]
Kurakata et al. [13]
Measurement frequencies (Hz) Number of listeners Statistical indices of threshold distribution
125–16 k 30–31 Mean, SD, min, P25 , median, P75 , max
31.5–18 k 7–32
1 k–12.4 k 21
Mean, SD
Mean, SD
1 k–20 k 8–51 Mean, SD, min, P5 , P25 , median, P75 , P95 , max
: depending on frequencies
unbiased estimates for the population or those of the measured data themselves. Consequently, we may have obtained somewhat smaller SDs because the latter type of SDs might have been included in some cases. Nevertheless, the aggregated number of listeners is so large that such cases’ influence on the overall calculation would be negligible. The effect would be less than 1% of the obtained value when the number of listeners is 100, for example.
Fig. 3 Graphical representation of the unbiased estimates of total SD, t , shown in Table 3. Marks indicate the SDs of each study used for calculating t .
Careful investigation of individual thresholds in Section 2.1 suggests that this occurs because thresholds of listeners with better hearing ability elevated more than those of listeners with worse hearing ability.
4.
GENERAL DISCUSSION
4.1. Evaluation of Calculated SDs This study calculated the SDs of thresholds at frequencies of 25 Hz to 18 kHz by combining available threshold data that had been measured in different studies. In this calculation, the SDs reported in the literature were assumed to be unbiased estimates of SD of the populations from which their data had been sampled. The respective authors did not clearly state whether the reported SDs were such
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4.2. Threshold at 18 kHz The experiment in Section 2.1 showed a marked deviation of the obtained threshold at 18 kHz from the normative value in the ISO standard [14]. The present experiment employed a fundamentally similar procedure to that of Takeshima et al. [11], on which the ISO value is based. The Appendix of the present paper shows that the threshold value did not change significantly in a re-test with the same listeners. Probably, the difference of these two studies is attributable to the variability in the sampling of listeners; such a large difference in thresholds would inevitably be observed at this scale of measurement. Therefore, we may say that the threshold value of 18 kHz in the ISO standard should be reconsidered in future revisions by accumulating more measurement data. For example, when medians of the two studies [11,13] and that presented in Section 2.1 are averaged, the resulting value is 69.1 dB; if weighted by the number of listeners, the average value becomes 69.2 dB.
5.
CONCLUSIONS
Unbiased estimates of SD of normal hearing thresholds were calculated for the range of 25 Hz to 18 kHz, integrating available threshold data in different studies. Examinations of threshold data revealed that threshold variability among individuals has a form of normal distribution for frequencies from 25 Hz to 16 kHz. Therefore, referring to the calculated SDs shown in Table 3 and Fig. 3 together with the normative threshold values in ISO
K. KURAKATA et al.: STATISTICAL DISTRIBUTION OF NORMAL HEARING THRESHOLDS Table 3 Unbiased estimates of total SD, t , of threshold distributions calculated by combining available measurement data. Frequency (Hz)
t (dB)
nt
25 31.5 40 50 63 80 100 125 160 200 250 315 400 500 630 750 800 1k 1.25 k 1.5 k 1.6 k 2k 2.5 k 3k 3.15 k 4k 5k 6k 6.3 k 8k 9k 10 k 11 k 11.2 k 12 k 12.5 k 13 k 14 k 15 k 16 k 17 k 18 k
(5.7) 7.4 6.5 6.2 5.3 4.4 4.2 4.2 3.2 3.9 4.1 3.6 3.3 4.0 3.7 (4.2) 4.0 4.0 4.1 (4.7) 5.9 4.7 4.9 5.4 5.2 4.1 4.8 5.4 5.7 5.8 6.1 6.2 (7.5) 6.8 (7.7) 7.9 (8.6) 10.2 15.3 16.8 (17.2) 11.9
12 47 38 39 118 37 37 179 25 26 174 41 41 172 41 31 41 345 106 31 106 251 106 51 96 332 128 51 118 330 105 241 51 85 51 189 51 161 100 196 47 102
Values in parentheses are from one laboratory only. nt : total number of listeners whose data were used in the calculation
standard [14], the entire profile of absolute thresholds is better clarified because the individual differences are considered. Results of this study also suggest that the threshold value at 18 kHz in the standard may require future revision.
ACKNOWLEDGEMENTS The authors wish to thank our colleague, Yukio Inukai, and two anonymous reviewers for helpful suggestions and a critical reading of the manuscript.
REFERENCES [1] D. W. Robinson and R. S. Dadson, ‘‘A re-determination of the equal-loudness relations for pure tones,’’ Br. J. Appl. Phys., 7, 166–181 (1956). [2] R. Teranishi, ‘‘Study about measurement of loudness — On the problems of minimum audible sound —,’’ Res. Electrotech. Lab., No. 658 (1965). [3] K. Brinkmann, ‘‘Audiometer-Bezugswelle und FreifeldHo¨rschwelle,’’ Acustica, 28, 147–154 (1973). [4] T. Watanabe and H. Møller, ‘‘Hearing thresholds and equal loudness contours in free field at frequencies below 1 kHz,’’ J. Low Freq. Noise Vib., 9, 135–148 (1990). [5] K. Betke, ‘‘New hearing threshold measurements for pure tones under free-field listening conditions,’’ J. Acoust. Soc. Am., 89, 2400–2403 (1991). [6] M. Vorla¨nder, ‘‘Freifeld-Ho¨rschwellen von 8 kHz–16 kHz,’’ Fortschr. Akust. — DAGA ’91, pp. 533–536 (1991). [7] T. Poulsen and L. Thøgersen, ‘‘Hearing threshold and equal loudness level contours in a free sound field for pure tones from 1 kHz to 16 kHz,’’ Proc. Nord. Acoust. Meet., pp. 195– 198 (1994). [8] H. Takeshima, Y. Suzuki, M. Kumagai, T. Sone, T. Fujimori and H. Miura, ‘‘Threshold of hearing for pure tone under freefield listening conditions,’’ J. Acoust. Soc. Jpn. (E), 15, 159– 169 (1994). [9] M. Lydolf and H. Møller, ‘‘New measurements of the threshold of hearing and equal-loudness contours at low frequencies,’’ Proc. 8th Int. Meet. Low Freq. Noise Vib., pp. 76–84 (1997). [10] T. Poulsen and L. A. Han, ‘‘The binaural free field hearing threshold for pure tones from 125 Hz to 16 kHz,’’ Acustica Acta Acustica, 86, 333–337 (2000). [11] H. Takeshima, Y. Suzuki, H. Fujii, M. Kumagai, K. Ashihara, T. Fujimori and T. Sone, ‘‘Equal-loudness contours measured by the randomized maximum likelihood sequential procedure,’’ Acustica - Acta Acustica, 87, 389–399 (2001). [12] H. Takeshima, Y. Suzuki, K. Ashihara and T. Fujimori, ‘‘Equal-loudness contours between 1 kHz and 12.5 kHz for 60 and 80 phons,’’ Acoust. Sci. & Tech., 23, 106–109 (2002). [13] K. Kurakata, K. Ashihara, K. Matsushita, H. Tamai and Y. Ihara, ‘‘Threshold of hearing in free field for high-frequency tones from 1 to 20 kHz,’’ Acoust. Sci. & Tech., 24, 398–399 (2003). [14] ISO/FDIS 389-7, Acoustics — Reference zero for the calibration of audiometric equipment — Part 7: Reference threshold of hearing under free-field and diffuse-field listening conditions (ISO, Geneva, 2004). [15] K. Ashihara, K. Kurakata, T. Mizunami and K. Matsushita, ‘‘Hearing threshold for pure tones above 20 kHz,’’ Acoust. Sci. & Tech. (in press). [16] ISO/TC43/WG1/N122, Preferred test conditions for the determination of the minimum audible field and the normal equal-loudness level contours (1988). [17] ISO 8253-1, Acoustics — Audiometric test methods — Part 1: Basic pure tone air and bone conduction threshold audiometry (ISO, Geneva, 1989). [18] H. Takeshima (personal communication, Aug. 5, 2004).
APPENDIX: HIGH-FREQUENCY THRESHOLD MEASUREMENT WITH LOW-FREQUENCY NOISE For measurement of thresholds at frequencies of 16 kHz and above, a target tone is frequently presented at a sound
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Acoust. Sci. & Tech. 26, 5 (2005) Table A.1 Threshold values of hearing in dB SPL and their statistical indices of individual differences measured with lowfrequency masking noise. In parentheses are the increment of threshold in dB or that of the number of listeners from the corresponding values without the masking noise. Frequency (kHz) 16 18 20 22.4
min 16.4 28.5 49.4 74.0
(1:5) (11.5) (3:0) (8.5)
P5 19.0 34.8 52.4 84.7
(1:3) (5.9) (12:0) (9.7)
P25
median
P75
P95
max
27.9 (3.0) 54 (1:5) >83:4 () >86:5 ()
36.9 (1.5) 62.5 (1.0) — —
43.9 (3.0) 75.5 (2.0) — —
69.1 (3.1) >79:0 () — —
80.4 (4:5) — — —
n=N 29 25 7 3
(0)/29 (0)/29 (0)/29 (1)/29
Px : xth percentile >L: higher than the maximum output level, L, at the frequency n: number of listeners whose threshold values were obtained N: number of listeners who participated in the measurement
pressure level of 80 dB or higher. Table 1 shows that not a few listeners have a threshold of 10 dB or lower at 4 and 5 kHz. Therefore, the measurement system must have a dynamic range of 100 dB or wider; otherwise listeners may detect low-level noises that accompany with tone presentation and falsely respond that they detected the target tone. A supplementary experiment was conducted to verify that the threshold measurement in Section 2.1 at 16 kHz and higher was not adversely affected by such false detections. The measurement procedure was fundamentally similar to that of Section 2.1. A major difference was that a lowfrequency noise was introduced to mask noises, if any, that listeners may falsely detect. For noise presentation, another loudspeaker (Tannoy, i8) was set just below the main speaker. The noise was a pink noise band-limited from 100 Hz to 10 kHz. The sound pressure level was 43 dB, which corresponded to 30 dB per one-third octave band. The masking noise was continuously presented to listeners during measurement. The target tone frequency was 16, 18, 20, or 22.4 kHz. The tones were generated with 24-bit resolution and 96-kHz sampling. Listeners were 29 students (13 men and 16 women) who participated in the measurement in Section 2.1, about two months before this experiment. Table A.1 summarizes the results. Minimum and P5 values indicate that the threshold changed more than 10 dB in some cases. This fact suggests that the values of these listeners showing a low threshold might have been contaminated by false detection responses. The other values from P25 to maximum values at 16 and 18 kHz, however, did not change remarkably. A sign test on the medians (The MathWorks, MATLAB R14) confirmed that the effect of masking noise was not significant for both frequencies (p > 0:05). Therefore, we may conclude that the responses of listeners for 16- and 18-kHz tones are
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generally reliable and that the P75 and P25 values are valid as indices of threshold distribution at those frequencies. Results of that experiment also demonstrate that at least seven and three listeners had measurable thresholds, even at 20 and 22.4 kHz, respectively. Although the thresholds were affected considerably by the noise, their responses during measurement were relatively stable, suggesting that they did detect the target tone. Kenji Kurakata received his B.A. degree from Waseda University in 1989 and his Ph.D. degree in psychoacoustics from Osaka University in 1994. He is currently a Senior Research Scientist at the National Institute of Advanced Industrial Science and Technology, Japan. His research interests include aging effects on auditory perception and human-machine interfaces using auditory signals. He has been engaged in standardization work with the Japanese Industrial Standards Committee, ISO, and IEC. He received the Awaya Prize from the Acoustical Society of Japan in 1996. Tazu Mizunami received her Ph.D. degree in psychoacoustics from Osaka University in 2001. She is currently a Post-Doctoral Research Scientist at the National Institute of Advanced Industrial Science and Technology, Japan. Her research interests are psychological evaluation of auditory signals and the design of sound environments. She is a member of ASJ, INCE/J, and JES. Kazuma Matsushita received his B.Eng. degree from Tohwa University in 1990, then entered the International Trade and Industry Inspection Institute, Japan. After engaging in various government affairs including international certification and research management, he has been involved in domestic and international standardization work on ergonomics since 1999. He is currently a chief of the Standardization and Technology Division, National Institute of Technology and Evaluation, Japan. Kaoru Ashihara received a Ph.D. degree from Tsukuba University in 1991. After joining the Electrotechnical Laboratory in 1992, he has been engaged in studies of hearing systems and acoustic measurement. Since 2001, he has worked as a Senior Research Scientist at the National Institute of Advanced Industrial Science and Technology.
