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J Am Acad Audiol 10 : 248-260 (1999)
Loudness Scaling Revisited
Claus Elberling*
Abstract
The present work was undertaken in an attempt to evaluate whether it is reasonable to expect
that categorical loudness scaling can provide useful information for nonlinear hearing aid fitting . Normative data from seven scaling procedures show that the individual procedures
relate the perceptual categories differently to sound level and with a substantial betweensubject variance . Hearing-impaired data from four studies demonstrate that the inverse slope
of the loudness function varies linearly with hearing loss and with a constant variance . In
relation to hearing aid fitting, the slope can, in most cases, be predicted from the hearing
loss with an accuracy within the range of a normal finetuning . For the fitting of nonlinear hearing aids, the statistical properties of both normal and impaired loudness functions are equally
important. The present analysis strongly suggests that categorical loudness scaling cannot,
in general, provide significant information for the fitting process.
Key Words: Categorical loudness scaling, hearing aid fitting, loudness restoration, loudness
scaling procedures, normative reference, slope of loudness function
Abbreviations : a = slope of fitted straight line, CB = critical band, COVXY = covariance
between variables x and y, CR = compression ratio, GL = hearing aid insertion gain at input
level L, HTL = hearing threshold level, I/O = input/output, LGOB = loudness growth in 1/2-octave
bands, RETSPL = reference threshold sound pressure level, S = slope of loudness growth
function, VARX = variance of variable x, WDRC = wide dynamic range compression.
everal dimensions of a sensorineural
hearing loss are important for hearing aid
fitting (e .g ., sensitivity, dynamic range
[recruitment], and frequency resolution) . The
recent focus on dynamic range has resulted in
a seemingly "logical" signal processing strategy
called amplitude compression. Various compression schemes have been proposed for the
restoration of loudness, and it has been suggested that a (preferably multichannel) hearing
aid with flexible compressors adjusted according to the measured impaired loudness can alleviate major problems associated with hearing
impairment . However, for a variety of reasons
(e .g., loudness summation and the actual performance of the hearing aid), most straightforward "recruitment compensation methods" do
not restore normal loudness in realistic sound
environments . Further, the hearing-impaired
person may not necessarily prefer such an ampli-
S
*OTICON Research Centre, Eriksholm, Snekkersten,
Denmark
Reprint requests : Claus Elberling, OTICON Research
Centre, Eriksholm, 243 Kongevejen, DK 3070 Snekkersten,
Denmark
248
fication strategy over another, because, in sensorineural hearing loss, auditory dimensions
other than loudness are affected . This paper
will not discuss whether a hearing aid fitted to
perform loudness restoration performs as
intended with speech signals or in real acoustic
environments, nor will it discuss whether loudness restoration in itself is a useful way to alleviate hearing impairment . These issues are
important and should be properly addressed
through adequate experiments, including field
testing. Instead, the present work will focus on
fundamental issues in loudness scaling and
some of the underlying assumptions that are
made in relation to hearing aid fitting in general.
Over the years, much effort has been made
to develop adequate methods to measure loudness, and a series of different loudness scaling
procedures have been proposed especially for
hearing aid fitting, rather than for diagnostic
purposes . There is no doubt that the loudness
dimension is important for the design of hearing aids and their signal processing algorithms,
as well as for the individual fitting. At the very
least, loudness addresses issues such as audibility at low sound levels and uncomfortable
exposure to high sound levels .
Loudness Scaling Revisited/Elberling
Fitting procedures that are based on individual loudness scaling measurements have
been recommended, especially for the manage-
ment of nonlinear hearing aids (e .g., Independent Hearing Aid Fitting Forum [IHAFF ; Valente
and Van Vliet, 1997], ScalAdapt [Kiessling et al,
1995], and Real Ear Loudness Mapping [RELM ;
Humes et al, 1994] ) . There may be at least three
advantages of applying loudness scaling in the
fitting process : (1) it will focus on audibility and
listening comfort, both at low and at high sound
levels (re : the above) ; (2) it will make the hearing-impaired person feel more personally
involved ; and (3) it may lead to a more accurate
initial setting of the hearing aid . Most of the
claims that have been made about loudness
scaling and hearing aid fitting have more or
less ignored the first two arguments . However,
if the use of individual loudness scaling turns out
to be advantageous for the fitting of hearing
aids, we must be aware that there might be several reasons for such a positive effect .
The present work is an attempt to address
the latter argument, namely, the initial setting
of the hearing aid . This is done not as an experimental clinical evaluation but as an analysis of
the underlying structure of loudness scaling
data . Analyses addressing the accuracy of such
data have recently been presented by Beattie et
al (1997), Palmer and Lindley (1998), and Rasmussen et al (1998) . Published loudness scaling
data from subjects with normal hearing and
with hearing impairment indicate both differences and similarities among data obtained with
the different scaling procedures . Therefore, this
paper will analyze loudness scaling data published in the literature and ask the question
whether such data are adequate for getting a
more accurate or acceptable initial hearing aid
setting . The analysis presented herein is not
based on separate experiments designed for the
present purpose but uses loudness scaling data
published within the last decade by different
groups of researchers . The analysis is in three
parts : (1) normative data, (2) hearing-impaired
data, and (3) synthesis .
ANALYSIS
Normative Data
Variance across Different
Scaling Procedures
For each loudness scaling procedure, a set
of data obtained from a well-defined group of subjects with normal hearing is called the norma-
tive reference . Most published scaling procedures show in graphic format the corresponding
normative reference that subsequently is used
when evaluating individual data obtained with
that procedure. Due to inherent differences
between the procedures, the normative references cannot easily be compared . The differences may be related to one or more of the
following: stimulus parameters, randomization
of stimulus levels and frequencies, anchoring and
ceiling effects, application of loudness categories,
instructions to the test subjects, and more . However, newcomers would intuitively expect that
for comparable parameters, the procedures
would result in about the same loudness rating .
In order to investigate whether this holds true,
the normative references from seven different
procedures are compared in the following section.
All of the procedures make use of narrowband stimuli and have some commonality regarding use of loudness categories (i .e ., they make use
of all or a superset of the categories : too soft, soft,
comfortable [intermediate or okay], loud, very
loud, and too loud). Some of the procedures give
stimulus level directly in dB HL and others in
dB SPL measured for a specific transducer in a
specific coupler. For the present comparison, all
data sets are referenced to the dB HL scale.
The transformation from dB SPL to dB HL of the
individual data set is based on the information
available for each procedure. Below, the seven
procedures are briefly summarized and the relevant specifications given:
1 . Allen et al (1990) used the loudness growth
in 1/2-octave bands (LGOB) procedure to rate
the loudness in seven categories (not heard,
very soft, soft, okay [comfortable], loud, very
loud, and too loud) from 11 subjects with normal hearing with a random level and frequency presentation of 250, 500, 1000, 2000,
and 4000 Hz, 1/-octave wide noise stimuli.
Stimulus levels were given in dB SPL measured in the Bruel & Kjaer 4157 coupler
(IEC 711) . First, the group average data
were read from Figure 4 in Allen et al (1990)
and since the "not heard" and "too loud"
data were not plotted in the figure, they
were estimated from the shapes of the given
input/output (I/0)-functions in their Figure
3 and the transition response levels in their
Figure 4. Second, because 1/2-octave is different from the width of the critical band
(CB), bandwidth corrections (i .e ., 10*Log[1/2octave/CB]) were calculated for each frequency. Third, to transform the dB SPL
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Journal of the American Academy of Audiology/Volume 10, Number 5, May 1999
values to dB HL, the reference threshold levels (RETSPLs) (ISO, 1994) for insert earphones in the IEC 711 coupler were applied.
Finally, since the values at 250 Hz referenced
to dB HL deviate significantly from those at
the other frequencies, the 250-Hz data were
excluded in the final analysis . The data at
500, 1000, 2000, and 4000 Hz were averaged
over frequency yielding the final normative
reference for the LGOB procedure.
2 . Elberling and Nielsen (1993) used the CAR
procedure to rate the loudness in seven categories (not heard, very soft, soft, okay [comfortable], loud, very loud, and too loud) from
10 subjects with normal hearing with a random level presentation of 500- and 2000-Hz
pure-tone stimuli. On a dB HL scale, there
were no significant differences between the
results from the two frequencies; therefore,
the data were pooled to give the normative
reference for the CAR procedure.
3. Kiessling et al (1993) used the direct loudness scaling procedure to rate the loudness
in 13 categories (seven labeled: not heard,
very soft, soft, middle loud [comfortable],
loud, very loud, and uncomfortably loud and
six nonlabeled, interleaved) on a 50-point
scale from 10 subjects with normal hearing
with a quasi-random level presentation of
1/3-octave filtered noise stimuli at the center
frequencies 500, 1000, 2000, and 4000 Hz .
Stimulus level was given in dB HL and no
significant difference over frequency was
observed . The average data (pooled over
frequency) were read from Figure 9a in
Kiessling et al (1993) and used to represent
the normative reference for this procedure.
4. Hohmann and Kollmeier (1995) used the
Horfeldskalierung procedure to rate the
loudness in five categories (very soft, soft,
intermediate [comfortable], loud, and very
loud) and 10 response possibilities from 26
subjects with normal hearing with a quasirandom level presentation of 1/3-octave filtered noise stimuli at the center frequencies
250, 500, 1000, 2000, and 4000 Hz . Each
measured data set (i.e ., category vs stimulus level [in dB HL]) was fitted to a straight
line giving the slope, m, and the level corresponding to the comfortable (intermediate)
category, L25,-Table 2 in Hohmann and
Kollmeier (1995) . For the present analysis,
the average over frequency of the two parameters was calculated and subsequently
used to compute the stimulus level for each
category. This result is used to describe the
normative reference for this procedure.
5 . Launer (1995) used a categorical scaling
procedure to rate the loudness in seven categories (inaudible [not heard], very soft,
soft, intermediate [comfortable], loud, very
loud, and too loud) and 11 response possibilities from nine subjects with normal hearing with a quasi-random level presentation
of one critical band "frozen" noise stimuli
centered at 1370, 1600, 1850, 2150, 2500,
and 2925 Hz . Each measured data set (i.e .,
category vs stimulus level [in dB HL]) was
fitted to a straight line giving the slope, m,
and the level corresponding to the comfortable (intermediate) category, L25,-Table 5.2
in Launer (1995) . For the present analysis,
the average over frequency of the two parameters was calculated and subsequently
used to compute the stimulus level for each
category. This result is used to represent the
normative reference of this categorical scaling procedure .
6. Ricketts and Bentler (1996) used a categorical scaling procedure to rate the loudness
in nine categories (cannot hear [not heard],
very soft, soft, comfortable but slightly soft,
comfortable, comfortable but slightly loud,
loud, very loud, and too loud) from 20 subjects with normal hearing with a random
level presentation of 1/3-octave noise stimuli
centered at 500 and 3150 Hz . The average
data of the response categories from soft to
loud were presented as bar graphs in Figures la and lb in Ricketts and Bentler
(1996) . First, for each frequency, the average values in dB SPL were read from the two
graphs . Second, to approximately convert the
dB SPL values measured with insert earphones on a Zwislocki coupler to dB HL,
the RETSPLs (ISO, 1994) for insert earphones in the ear simulator (IEC, 1981)
were applied. Finally, the dB HL values for
500 and 3150 Hz were averaged into the normative reference for this categorical scaling
procedure .
7. Cox et al (1997) used the Contour Test of
Loudness Perception to rate the loudness in
seven categories (very soft, soft, comfortable but slightly soft, comfortable, comfortable but slightly loud, loud but okay, and
uncomfortably loud) from 45 subjects with
normal hearing with an ascending level presentation of warble tone stimuli at the center frequencies 250, 500, 1000, 2000, 3000,
Loudness Scaling Revisited/Elberling
and 4000 Hz . For each frequency and each
loudness category, the mean level (dB SPL)
was calculated and presented in Table 2 in
Cox et al (1997) . To transform the dB SPL
values to dB HL, the RETSPLs (ISO, 1994)
for insert earphones in the HA-1 coupler
(IEC, 1973) were applied . The values over
frequency were averaged and used as the
normative reference for the Contour Test .
The normative reference data corresponding to the common categories very soft, soft,
comfortable, loud, very loud, and too loud from
these seven procedures are presented in dB HL
in Table 1 and are plotted in Figure 1 .
From these data, we can conclude that the
stimulus level for the individual category varies
significantly over the different procedures . For
instance, the sound level corresponding to comfortable, which is supposed to be located at a
medium loudness level, varies from about 63 to
89 dB (i .e ., a range of 26 dB for the procedures
used in the present comparison).
Discussion . The exact acoustic calibration
that underlies all of the seven referred sets of data
influences the above comparison and conclusions . For three of the referred sets of data (1, 6,
and 7), it was further necessary to transform
the original sound levels from dB SPL to dB HL
based on the available information provided in
each of the original papers . It is difficult to evaluate precisely the effect of this inherent uncertainty, but it is not likely that calibration and/or
transformation errors would exceed 5 dB in the
frequency range 250 to 4000 Hz . Therefore, the
conclusion above seems warranted .
If one used loudness scaling data to set the
gain of a hearing aid at, for example, the comfortable loudness level, then the choice of scaling procedure would have a significant impact
on the sound level at which this gain is set and,
Table 1
Very loud
Too loud
VERYLOUD
LOUD
COMFORT
o Allen et al, 1990
SOFT
VERYSOFT
NOTHEARD
0
0
20
.
40
,
60
,
" Eberling and Nielsen, 1993
c Kiessting et al, 1993
0 Hohmann and Kollmeier, 1995
it Launer, 1995
V Ricketts and Gentler, 1996
+ Cox et al, 1997
R0
100
SOUND LEVEL (dB HL)
120
Figure 1 The normative reference (i .e ., categories
versus sound level [dB HLI) for seven loudness scaling
procedures .
therefore, on the electroacoustic characteristics
of the fitted aid . The large differences between
the normative references are most likely caused
by differences in the psychoacoustic methods
applied as recently reviewed by Jenstad et al
(1997), Beattie et al (1997), and Ricketts (1997) .
Jenstad et al investigated the effect of presentation mode and the influence of a preceding reference stimulus of maximal level. Beattie et al
discussed presentation mode and the short-term
reliability of the IHAFF contour test (Valente and
Van Vliet, 1997). Ricketts discussed factors such
as number and spacing of categories, type and
bandwidth of the stimulus, presentation parameters, and instruction . However, as mentioned
above, it is not the aim of this presentation to
discuss more or less obvious procedural differences but to demonstrate the resulting effects
and thereby to increase the readers' awareness
about the existing differences between published normative references and some of the
practical implications .
Elberling and
Nielsen
(1993)
Kiessling
et al
(1993)
Hohmann and
Kollmeier
(1995)
34 .4
58 .9
78 .6
90 .2
39 .4
69 .3
89 .1
103 .8
22 .5
48 .8
64 .0
75 .0
42 .9
102 .6
125 .3
92 .5
106 .3
97 .6
6
Normative References for Seven Loudness Scaling Procedures
Allen et al
(1990)
Very soft
Soft
Comfortable
Loud
TeoLo-
115.6
87 .5
57 .0
71 .1
85 .2
99 .3
Launer
(1995)
Ricketts and
Bentler
(1996)
Cox
et al
(1997)
29 .4
20 .5
20 .3
66 .4
84 .9
62 .9
81 .8
67 .0
91 .9
47 .9
103 .4
112 .7
35 .5
-
39 .3
-
101 .0
The table shows categories versus sound level in dB HL .
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Journal of the American Academy of Audiology/Volume 10, Number 5, May 1999
Variance across Normal-hearing Subjects
In relation to hearing aid fitting, the loudness scaling data obtained from a hearingimpaired person (with sensorineural hearing
loss) are almost always evaluated relative to
the normative reference, either directly by comparing unaided and aided loudness data to the
normative reference or indirectly by setting up
a fitting target based on normative relations, as,
for instance, loudness growth and speech levels .
Thus, in its clinical use, loudness scaling does
not differ from other audiologic measures, as, for
instance, the pure-tone threshold. Here, 0 dB HL
constitutes the normative reference (standardized in the ANSI S3 .6 [19891 and ISO 389 [19911
standards) . However, whereas many other normative references are based on data that demonstrate a limited variance over the group of
normal-hearing subjects, the clinical loudness
scaling methods described in the literature all
show a considerable variance . To illustrate this,
data from three different category rating methods are compared . The intersubject variance
can be evaluated in many ways as it affects different parameters of the resulting loudness
growth function . However, to restrict the analysis and focus attention on what may be clinically
most important, the variance at a medium loudness level (i .e ., comfortable) will be presented:
1. Elberling and Nielsen (1993) measured the
loudness functions for two frequencies on 10
subjects with normal hearing with the CAR
procedure. All data are shown in Figure 2.
TOOLOUD
VERYLOUD
LOUD
100
1~
I
80-
VERYSOFT
NOTNEARD
60-
Table 2 Between-subject Variance of the
Sound Level in dB HL Corresponding to
40
"Comfortable" in Subjects with Normal Hearing
for Three Loudness Scaling Procedures
3'0' 1
20
100
Figure 2
20
~T~T~T
40
60
80
100
SOUND LEVEL (dB HL)
All data points obtained from loudness scal-
Elberling
and
Hohmann
and
Kollmeier
(1995)
et al
(1997)
9.0
36
8.0
32
10 .5
42
Nielsen
(1993)
120
ing at two frequencies in 10 subjects with normal hearing (Elberling and Nielsen, 1993). The fitted exponential
functions for the data points for one frequency in two subjects are indicated by (MT) and (HTW).
252
For the three procedures, the calculated
standard deviations are given in Table 2,
together with the normative 95 percent intervals . (Under the assumption of a Gaussian distribution of the data, the 95 percent interval
corresponds to ±2 SD .) For the three procedures, this interval is considerable and varies
from 32 to 42 dB .
70-
COMF
SOFT
The rated categories versus stimulus level
were fitted to an exponential function by the
method of least squares and subsequently
the stimulus levels were calculated corresponding to "okay" (comfortable) on each
individual curve. Over the 20 observations
(10 subjects and two frequencies), a mean of
87 .4 dB HL and a standard deviation of
9.0 dB was found.
2. Hohmann and Kollmeier (1995) rated the
loudness from 26 subjects with normal hearing with the Horfeldskalierung procedure.
Each measured data set (i .e ., category vs
stimulus level for each test frequency) was
fitted to a straight line giving the slope and
the level corresponding to the intermediate (comfortable) category, L25 (Hohmann
and Kollmeier, 1995, Table 2) . Over the five
frequencies (130 observations), we calculated a mean of 71 .1 dB HL and a standard
deviation of 8.0 dB .
3. Cox et al (1997) rated the loudness at six frequencies on 45 subjects with normal hearing with the Contour Test . For each
frequency and each loudness category, the
mean level and standard deviation were
calculated . Over the six frequencies (270
observations) and at comfortable loudness
level, we calculated (in dB HL) a mean of
67 .0 dB HL and a standard deviation of
10 .5 dB .
SD (dB)
95% interval (dB)
Cox
The table shows both the standard deviations and the 95
intervals (±2 SD).
Loudness Scaling Revisited/Elberling
Discussion.
The loudness scaling procedures
used in this analysis are believed to constitute a
representative sample of the clinical methods presented within the last decade or so . It is concluded
that the normative reference is not just a fixed
number (at any specific loudness level) but covers
a substantial interindividual range . A significant
uncertainty exists, which at the comfortable level
corresponds to a range of about 35 dB .
As described later, the normative reference
is the basis for calculating target gain and/or
compression ratio (CR) when individual loudness
scaling data are used for fitting hearing aids .
Therefore, precision of the target gain is influenced not only by uncertainty of the loudness
scaling data acquired from the individual hearing-impaired subject but also, and to the same
extent, by uncertainty in the normative reference. It is for this reason that the evaluation presented herein is important for the application of
individual loudness scaling data in hearing aid
fitting .
Figure 3 Normalized slope versus hearing loss obtained
from 10 subjects with normal hearing and 29 subjects with
impaired hearing tested at two frequencies (from Elberling and Nielsen, 1993). The thick line is the exponential
fit to the data and the thin lines indicate the spread of
the data .
Hearing-impaired Data
Variance across Different
Scaling Procedures
Several researchers have stated that the
loudness function that corresponds to a sensorineural hearing loss cannot be estimated
from the hearing threshold but has to be measured (e .g ., Launer et al [19961) . This statement
is based on the observation that the loudness
scaling parameters (e .g ., the slope [S] of measured loudness growth functions) display an
increased variance with increasing hearing loss
and may be only weakly correlated with the
hearing threshold (e .g., Hohmann and Kollmeier
[1995]) . An example of the increasing variance
with hearing loss is given in Figure 3 . In the figure, normalized slope (i .e ., the slope of the individual loudness growth function) relative to the
normative reference is expressed .
The advent of nonlinear hearing aids with
wide dynamic range compression (WDRC) has
really spurred a "bandwagon" interest in the
use of loudness scaling for hearing aid fitting.
However, it would be relevant here to mention
the pioneer work by Pascoe (1978), which early
on demonstrated the important link between
the fitting of linear hearing aids with output limiting and the residual dynamic range of the
hearing impaired .
In the present context, the difference
between a linear and a nonlinear hearing aid is
the 1/O function, which, for loudness restoration
in a nonlinear hearing aid, should mirror the normalized slope, S1 . In such a nonlinear hearing aid,
the interesting part of the I/O function, which
performs linear compression, is often charac-
120
100
80
60
40
20
0
Figure 4 A loudness model for normal and impaired
hearing. The diagonal line indicates normal hearing,
whereas the three other lines indicate loudness growth
functions with different slopes (S) but all corresponding
to a 70 dB HL hearing loss (HTL .) . For loudness restoration, the target gain is proportional to 1/S, indicated at
a 60 dB HL sound level.
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Journal of the American Academy of Audiology/Volume 10, Number 5, May 1999
0.0 1
0
20
40
60
Hearing Loss (dB HL)
80
0.0 ;
100
0
D
1.6
20
40
r
60
Hearing Loss (dB HL)
80
100
1.4
1.2
0.4
0.2
0.04
0
20
0.0
40
60
Hearing Loss (dB HL)
Hearing Loss (dB HL)
Figure 5A-D Normalized inverse slope as a function of hearing loss from four different procedures . A straight line
is fitted to each data set and also ±1 SD lines are shown . A, Elberling and Nielsen (1993) ; B, Kiessling (1995) ; C, Launer
et al (1996) ; and D, Ricketts and Bentler (1996) .
terized by the CR equal to the normalized slope,
S;,-thus, CR = S;. Another way is to characterize the I/O function by a set of gain values at two
input levels, for example, a low and a high level.
Thus, if the gain at a low input level (50 dB
SPL) is G50 and the gain at a high input level
(80 dB SPL) is Ggo, then the relationship between
G5o, G8o, and the CR (and S.) is :
1/CR = 1/ S; = 1 + (G80 - G5o)/30
(1)
This formula demonstrates that gain is
inversely proportional to both CR and S;. Another
way to demonstrate this relationship is shown
graphically in Figure 4. Here, normal loudness
is indicated by the diagonal line-the reference-and the impaired loudness by the sloping
line starting at the x-axis at 70 dB HL (hearing
254
threshold level, HTL;) . A target gain is indicated
at 60 dB HL, close to the average medium loudness level for normal-hearing subjects . Now, the
steeper the impaired loudness growth function
the lower the target gain, and the shallower the
loudness growth function the higher the gain
(i .e ., an inverse relationship between slope and
gain).
The variance in slope of the loudness functions and the practical consequences for hearing aid fitting is probably more easily understood
in relation to gain than to CR by most hearing
aid researchers. Further, the output level of the
hearing aid is dependent on the input level and
the applied hearing aid gain. It is for these reasons that the hearing aid gain is more relevant
than CR and therefore is used in the following
explanation:
Loudness Scaling Revisited/Elberling
For a fixed hearing loss, the observed variance of 1/S will be translated directly to variance
in gain . The data from Figure 3 are, therefore,
first normalized relative to normal hearing
(Sno mal hearing = 1) and thereafter plotted with the
inverse slope, 1/S,, as a function of hearing loss
in Figure 5A .
A straight line is fitted to the data by the
method of least squares . The line intersects the
y-axis at y = 1, the normalized, average value of
inverse slope, 1/Sn, for subjects with normal
hearing . As a first order of approximation, it
appears that the data can be described with a
linear relationship between 1/S and HTL and
with a constant variance of 1/S across hearing
loss . It should be noted that the variance of 1/S
now appears to be about the same for both subjects with normal and impaired hearing!
col-a fact that was considered by the authors
not to be of importance .
Variance of Inverse Slope across
Hearing-impaired Subjects
The correlation coefficients in Table 3 indicate that only about 55 percent of the variance
of 1/S in the data (mean of r2) can be explained
by the straight line approximating the relationship between 1/S. and HTL. Therefore, it is
obvious that a significant contribution to this
variance comes from other sources than the
pure-tone hearing loss . If we accept the linear
model as a reasonable descriptor of the acquired
data, we have achieved a common framework for
the evaluation of the practical consequences of
the observed variance .
Therefore, the four different data sets are
submitted to the following comparison, where the
HTL variable is grouped into the categories 10,
30, 50, 70, and 90 dB HL . In Figure 6, the data
sets are plotted with this grouping . The graph
demonstrates remarkable similarities across
the different data sets, although differences also
are noted, especially related to the difference in
a (see Table 3) .
However, in order to make a unified presentation, a weighted average of the different
data sets is calculated (by Bayesian inference ;
Box and Tiao, 1973), and the (weighted) mean
and ± 1 standard deviation are plotted in Figure
7. This figure is based on more than 1000 individual observations and demonstrates that the
variance of 1/S is approximately constant, independent of hearing loss . It also demonstrates that
the linear description is not valid for severe to
profound hearing losses . This latter observation indicates a change in rate of reduction in
dynamic range when the hearing loss exceeds
about 70 dB HL .
Since the variance of 1/S is approximately
constant over hearing loss, the data from the
individual data set can be taken relative to its
regression line and, thereafter, all data can be
Similarly, the data from subjects with normal and impaired hearing in the studies by
Kiessling (1995), Launer et al (1996), and Ricketts and Bentler (1996) have been analyzed and
the results are plotted in Figure 5B-D . The key
parameters for the fitted data are presented in
Table 3 (i .e ., the number of data points, N, the
correlation coefficient, r, the slope of the fitted line,
a, and the estimated standard deviation, SD).
Discussion . The data from the four different
procedures (Fig. 5A-D) appear reasonably similar and as a first-order approximation seem to
follow the suggested linear relationship between
inverse slope and hearing loss . The data sets display roughly the same variance of 1/S about the
regression lines as a function of hearing loss, also
including normal hearing. The exception is the
data from Ricketts and Bentler (1996) in Figure
5D, where the variance of 1/S is significantly
lower for subjects both with normal hearing and
hearing impairment . The reason for a lower
variance is not clear and the specifics of the
applied test procedure do not explain this finding. However, it appears that the test subjects
had previous experience with the test proto-
Table 3
Key Parameters of the Fitted Lines in Figure 5A-D
Elberling and
Nielsen (1993)
Number, N
78
Slope of line, a
Estimated SD
-0 .0091
0 .18
Correlation, r
0.78
Kiessling
(1995)
550
0.67
-0 .0072
0 .19
Launer et al
(1996)
284
0.65
-0 .0079
0 .20
Ricketts and
Bentler (1996)
94
0.85
-0 .0084
0 .13
Journal of the American Academy of Audiology/Volume 10, Number 5, May 1999
1 .6,
1 .4-
1 .2E
e
z
1 .0Launeretal
(N = 284)
Rickett and Bentler
(N = 93)
CL 0.8-
W
0
E2 0.6
C
0.4Elberling and Nielsen
(N = 78)
0.20.0
20
0
40
60
Hearing Loss (dB HL)
80
Figure 6 Comparison ofthe four different data sets from
Figure 5A-D. In this graph, the data are grouped into five
hearing loss classes and the mean value for each data set
is plotted for each class.
collapsed over hearing loss . The observed distribution of deviations of inverse slope, 1/S;,
from expectations (the individual regression
lines) can thus be produced as shown in Figure 8.
If we go back to formula 1 and vary the
gain for high input, G80, for instance, ±5 dBas would be relevant during finetuning of a
hearing aid-this variation in 1/S; would correspond to ±0 .17 . Now, with reference to Figure
8, a range of deviations of ±0 .17 covers about 70
percent of the cases, with about 12 percent of the
0.6
h
0.2 0.0
0
20
40
60
Hearing Loss (dB HL)
80
100
Figure 7 Weighted means and ±1 SD of the data
underlying Figure 6. Two straight lines (dotted) are fitted
to the mean values : one for the values at 10, 30, 50, and
70 dB HL and another for the values at 70 and 90 dB HL .
256
-1.00
-0.80
-0.60
-r~
-0.40
-0.20
0.00
0.20
y
rm'as°' ., -
0.40
0.60
0.80
Deviations of Inverse Slope (I/S)
1 .00
1.20
Figure 8 Observed distribution o£ deviation of the
inverse slope from regression line . The deviations are collapsed over hearing loss and over the four procedures in
Figure 5.
100
0.4
0 i--n--
observed values being below this range and
about 17 percent being above it . Lower values
mean steeper loudness growth and higher values mean shallower loudness growth . About 70
percent of the observations would, therefore, be
covered by a finetuning of -} 5 dB, and, in these
cases, the target CR could be obtained without
individual loudness scaling testing.
Discussion. It is obvious that the observed distribution in Figure 8 is skewed . Some of the
asymmetry may be attributed to a ceiling effect
for lower values (toward -1 .0 in Fig. 8) . For
higher values, the effect of conductive components in the hearing loss or contribution from
presbycusis (Knight and Margolis, 1984) is
known to give shallower loudness growth function than in pure sensorineural hearing losses
(toward higher values in Fig. 8) . Thus, the
observed skewness could be a result of an inhomogeneous diagnostic classification . However,
there are also other possible causes-for
instance, a different etiology underlying the
hearing losses and a different pattern of damage in the Organ of Corti, as discussed by Launer
et al (1996) .
Two points should be stressed : First, as indicated in Figure 7, the variance of 1/S is constant across hearing loss, but only as a first-order
approximation . The Kruskal-Wallis one-way
analysis of variance test (Siegel, 1956) finds a
statistically significant difference (p < .01) in the
underlying distributions of the data at the different levels of hearing impairment . However,
the differences are small and are not believed to
invalidate the global description of the data presented here . (It should also be noted that the data
contain a complex mixture of independent and
dependent observations ; the true p value is,
Loudness Scaling Revisited/Elberling
are used for the setting of a nonlinear hearing aid,
the different procedures result in procedural
effects-or biases-that will influence both the
position and the slope of the 1/0 function .
therefore, higher than . 01) . Second, it is important to acknowledge that, in this presentation,
only the slope of the loudness function has been
used . However, depending on the complexity of
the underlying mathematical model, loudness
functions acquired by loudness scaling need at
Effect of Variance of Inverse Slope
least one more parameter for their descriptionfor instance, slope and offset . For loudness
restoration, the offset parameter controls the
gain independent of input level and would, therefore, correspond to the setting of a linear hearing aid . Therefore, other parameters than slope
have been ignored in the present evaluation .
As evaluated for the normative data and
for the hearing-impaired data, it appears to a
first-order approximation that the variance of
inverse slope is independent of the hearing loss,
including normal hearing . Figure 9 gives :
G50 = 50* (1/S- - 1/Sn) + HTL.
G8o = 80* (1/Si -1/Sn) + HTL.
Synthesis
(2)
(3)
which inserted into formula 1 gives the following formulation for the compression ratio:
Effect of Procedural Differences
For the normative references evaluated earlier, the scaling procedures produce different
relationships between the loudness categories and
the acoustic (physical) domain (see Fig. 1 and
Table 1) . Therefore, if an amplification strategy
is targeted at a specific loudness level in normalhearing subjects (e .g ., comfortable), this would
correspond to quite different acoustic sound levels in the hearing aid, dependent on the applied
scaling procedure . Regarding the data from the
hearing impaired, the different procedures yield
different normalized data (see Table 3), which
have yet to be related to acoustic settings of the
hearing aid . Therefore, the information about the
average relationship between inverse slope and
hearing loss for each of the four procedures has
been used to calculate the relative gain settings
in a nonlinear hearing aid with linear WDRC .
These gain settings are given in Table 4 as dif-
1/CRi = 1 + WS . - 1/Sn)
(4)
Now, for a given hearing loss, HTL., only 1/S; and
1/S n will be the unknown variables .
Until now, we have assumed that loudness
restoration means the restoring of loudness to
its average normal value as represented by the
normative reference. However, due to the significant variance in loudness data in normalhearing subjects, (see Table 2 and Fig. 7), it
could be more appropriate to define loudness
restoration as the restoration of loudness to the
value for the individual hearing impaired had
he/she been normal hearing. A consequence of
not accepting this (new) definition would be that
even subjects with normal hearing would require
loudness restoration whenever their individual
loudness function deviates from the normative
reference! As described in formula 4, the problem is that there are two unknown quantities,
which both contribute to the total variance,
VARwCR>> of the target CR .
Since it is the difference between the two
variables that enters formula 4, the total variance can be developed, informally, as follows:
ferences between the gain for high (80 dB SPL)
and for low (50 dB SPL) input levels .
The difference between the four procedures
increases with the magnitude of the hearing
loss . The maximum difference is 2.3 dB at 40 dB
HL but amounts to 4.5 dB at 80 dB HL . Consequently, when measured loudness scaling data
Table 4 Differences in Gain between a 80 dB HL and a 50 dB HL Input Sound Level for a
Nonlinear Hearing Aid Fitted Based on the Results from the Four Procedures Shown in Figure 5A-D
G,, -G,, (dB) at.:
Elberling and
Nielsen (1993)
40 dB HL
-10 .9
80 dB HL
-21 .8
60 dB HL
-16.4
Kiessling
(1995)
-8 .6
-13 .0
-17 .3
Launer et al
Ricketts and
(1996)
Gentler (1996)
-9 .5
-10 .1
-19 .0
-20 .2
-14.2
-15.1
The average loudness scaling data (see Table 3) are used for the calculations .
257
Journal of the American Academy of Audiology/Volume 10, Number 5, May 1999
Table 5 Resulting Variance of the
Estimated Target Compression Ratio
Depending on the Fitting Alternative (A or B)
and the Value of the Correlation Coefficient, r
r= O
r=0.5 r=1 .0
VAR(I)S) VAR(1/S) VAR(1/S)
(A) with loudness scaling
(B) without loudness scaling 2* VAR(1/S) VAR(1/S)
0
Sound Level (dB HL)
too , lio
Figure 9 Loudness model for normal and impaired
hearing as shown previously in Figure 4. Here, the two
sets of dotted lines indicate the variance of the slope of
the loudness function : (left) S. in subjects with normal
hearing and (right) S; in subjects with a hearing threshold = HTL. . Geo and Gso indicate the target gain necessary for restoring loudness at 80 and 50 dB HL,
respectively. For further details, see text.
VAR(VCR) _
(1isi)+VAR(vsa)- 2*COVvsO/sn)(5)
where the COV term refers to the covariance
between the observed distribution of inverse
slope for subjects with a given hearing loss,
HTL;, and the corresponding distribution for
the same subjects had they been normal hearing. Since VARaisO and VAR(1/sn) are approximately the same (= VAR(vs), as found in the
section on variation of inverse slope across hearing-impaired subjects and Fig. 7) and the covariance can be expressed by the correlation
coefficient, r, by
rais(,lisn)=COV(vs(,vsn)/
[VAR(vs1) VAR(lisn)7 (6)
we arrive at the following expression for the
total variance :
VAR(1/CR)=2 * VAR(vs)* [l-rwsOvsn)j
(7)
Now, let us consider the alternatives : (A) individual loudness is measured by loudness scaling and used together with the normative
reference for fitting of the hearing aid's CR, and
(B) individual loudness is not measured but the
estimated value of 1/S; is used together with an
individual, unknown reference for the fitting.
258
Alternative A. If we disregard any test-retest
variability and other uncertainties in the acquisition of the individual loudness data, both the
variance, VAR(1/si) and the COV term in equation
5 will be zero . The total variance VAR(1/CR) will
be constant = VAR(g) .
Alternative B. The total variance, VAR(1,CR),
will depend upon the correlation coefficient,
raisijisn), in equation 7. The results corresponding to three different values of r are indicated
in Table 5.
What do we know about the correlation coefficient r(vSOisn)? Unfortunately, it is only on rare
occasions that loudness information would be
available for the individual subject both with and
without a hearing impairment. However, a positive correlation possibly exists because we
expect, intuitively, that both the perception and
the interpretation of different loudness categories are subject specific . In an attempt to
obtain more information about this correlation,
the following analyses were carried out:
1. The scaling data by Elberling and Nielsen
(1993) contain loudness data from 29 subjects at 500 Hz and 2 kHz. The inverse slope
values were corrected for the mean effect of
the hearing loss by calculating the difference
between each value and the linear trend
given by 1/S = -0 .0091*HTL + 1 .0 (see Table
3) . Between the corrected inverse slope values at 500 Hz and at 2 kHz, a correlation
coefficient of 0.38 was found (t = 2.15, df = 27,
p < .02).
2. Similarly, the scaling data by Kiessling
(1995) contain loudness data from 116 subjects measured both at 500 Hz and 4 kHz.
As above, correction was made for the mean
effect of the hearing loss by calculating the
difference between each value and the linear trend given by 1/S = -0 .0072*HTL + 1.0
(see Table 3) . Between the corrected values
at the two frequencies, a correlation coefficient of 0 .42 was found (t = 4.9, df = 114,
p < .0005) .
Loudness Scaling Revisited/Elberling
3 . In the same set of data by Messling (1995),
it was possible to isolate 70 subjects with
sloping hearing losses (HTL4kHz - HTL50OHz
> 15 dB HL) . The average hearing loss was
26 dB HL at 500 Hz and 65 dB HL at 4 kHz,
which means close to normal hearing at low
frequencies and a substantial hearing loss
at high frequencies . As above, the inverse
slope values were corrected for the mean
effect of the hearing loss and a correlation
coefficient of 0 .41 was found (t = 3 .7, df = 68,
p < .001) . This analysis expresses the relationship between the loudness in frequency
areas corresponding to normal and to
impaired hearing when the effect of the
hearing loss has been removed .
The above analyses demonstrate that the
loudness scaling values obtained at different
frequencies in the individual are positively correlated-also when comparing frequency areas
with approximately normal and impaired hearing . The results support the underlying assumption for the alternate monaural loudness balance
test (Reger, 1936), which has been used extensively for the diagnostic evaluation of recruitment in bilateral hearing losses . Since most
loudness scaling studies both in subjects with
normal hearing and hearing impairment have
indicated a significant effect of hearing loss but
only a limited (if any) effect of frequency, the
results also indicate the expected positive correlation between the loudness scaling values
obtained in the individual hearing impaired
with and (hypothetically) without a hearing
loss .
If in equation 7 we substitute the unknown
correlation coefficient with the value =0 .4, the
total variance of the calculated compression
ratio becomes =1 .2*VARn/s) - VAR,l/s) . For all
practical purposes, this surprising result means
that the variance of the target CR would be
independent of whether loudness scaling is performed or not!
SUMMARY AND CONCLUSIONS
1 . In normal-hearing subjects, the different
scaling procedures relate the perceptual
categories differently to the physical domain
(viz . sound level) .
2. Normal-hearing subjects display a large
variance in the sound level associated with
a specific loudness category (approximately
35 dB at the comfortable level) .
3 . In about 70 percent of the hearing impaired,
the slope of the measured loudness function
can be predicted from the hearing loss with
an accuracy corresponding to a ±5-dB finetuning of gain .
4. The remaining 30 percent of hearingimpaired persons could be referred to as
outliers . These outliers consist of the "sound
sensitive" (12%) and the "sound addicts"
(17%). The latter could also reflect an inhomogeneous diagnostic classification .
5 . When individual loudness data are used to
fit a nonlinear hearing aid, the scaling procedures will produce different I/O characteristics of the hearing aid .
6 . If a broader view is made on the use of loudness scaling for fitting nonlinear hearing
aids, it becomes apparent that the statistical properties of the normative reference
are as important as the variance of the loudness functions in the hearing-impaired subjects . Therefore, the variance of the setting
of the CR in a nonlinear hearing aid seems
to be independent of whether the loudness
function is measured or estimated .
It should be stressed that, for the reasons
given in the introduction, the loudness dimension is important both for the design and the fitting of modern hearing aid algorithms . However,
the multiple effects described above make it difficult to promote the general use of loudness
scaling procedures for the fitting of nonlinear
hearing aids .
Acknowledgment. I would like to thank the authors of
the following publications : Kiessling (1995), Launer et
al (1996), and Ricketts and Bentler (1996) for providing
their original data from their hearing-impaired subjects .
Without access to these data, the analysis presented
herein would not have been possible . This paper was presented in part at the British Society of Audiology, Cardiff,
1997 ; Vorkollogium Horgerate, DAGA, Zurich, 1998 ; the
American Academy of Audiology, Los Angeles, 1998 ;
"Issues in Advanced Hearing aid Research," Lake
Arrowhead, 1998 ; and the XXIV International Congress
of Audiology, Buenos Aires, 1998 .
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