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Year : 2005  |  Volume : 7  |  Issue : 28  |  Page : 51--60

Hearing protector performance and standard deviation

W Williams, H Dillon 
 National Acoustic Laboratories, Chatswood, New South Wales, Australia

Correspondence Address:
W Williams
National Acoustic Laboratories, 126 Greville Street, Chatswood, New South Wales, 2067


The attenuation performance of a hearing protector is used to estimate the protected exposure level of the user. The aim is to reduce the exposed level to an acceptable value. Users should expect the attenuation to fall within a reasonable range of values around a norm. However, an analysis of extensive test data indicates that there is a negative relationship between attenuation performance and the standard deviation. This result is deduced using a variation in the method of calculating a single number rating of attenuation that is more amenable to drawing statistical inferences. As performance is typically specified as a function of the mean attenuation minus one or two standard deviations from the mean to ensure that greater than 50% of the wearer population are well protected, the implication of increasing standard deviation with decreasing attenuation found in this study means that a significant number of users are, in fact, experiencing over-protection. These users may be disinclined to use their hearing protectors because of an increased feeling of acoustic isolation. This problem is exacerbated in areas with lower noise levels.

How to cite this article:
Williams W, Dillon H. Hearing protector performance and standard deviation.Noise Health 2005;7:51-60

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Williams W, Dillon H. Hearing protector performance and standard deviation. Noise Health [serial online] 2005 [cited 2020 Oct 24 ];7:51-60
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Single number rating systems for hearing protector performance are by no means perfect. However, they do represent a simple and straight forward method of specifying hearing protectors for the workplace. The utilisation of a single number to indicate performance offers the end user a simple solution and, in keeping with OHS principles, simple solutions are more likely to be utilised in practice.

Single number ratings currently in use around the world include the SNR, NRR and the SLC 80 . The SLC 80 is the basis of the Classification method (Williams, 1999) of hearing protector selection in Australia and New Zealand and is used in the current analysis as an example. The analysis is equally applicable to other similar, single number ratings.

The general procedure for the calculation of the attenuation of a particular hearing protector is as follows.

i) Experimentally determine the octave band attenuations of the device (plug/muff);

ii) Subtract the octave band attenuations from the octave band spectral values of the chosen representative spectrum;

iii) Subtract the overall dB SPL value of the attenuated spectrum from the overall dB SPL value of the reference spectrum to give the overall dB attenuation provided by the device.

The representative spectrum is a spectrum chosen to best represent the spectrum of sound to which it is felt that typical users may be exposed (as in the case of SLC 80 ) or it may simply be a convenient spectrum for the purposes of calculation (e.g. as in the case of NRR). This general calculation gives the attenuation that would be exceeded by 50% of the users, assuming a non-skewed distribution of attenuation values across users. However, to provide adequate noise reduction for a larger proportion of the population, the attenuation at each octave band may be decreased by a function of the standard deviation. For example, in the case of the NRR the mean attenuation at each octave band is decreased by two standard deviations so that the resulting performance figure will cover approximately 98% of the population. For SLC 80 the mean attenuation is decreased by one standard deviation and the population covered is in the order of 80%.

The SLC 80 is a derivative of the SLC (Sound Level Conversion) process developed from work by Waugh (1973) and Botsford (1973). The SLC work showed that under a set of hearing protectors the difference between the C - weighted SPL on the source side and the A - weighted SPL under the hearing protector is relatively constant. While this value is not a strict constant, the variations in the average of many responses using 'common' workplace noise spectra differed 'from the individual values by at most 3 decibels which is trivial" (Botsford: 1973, p 33) and was thus considered constant across most acoustic environments for all practical purposes.

This work was extended further by Waugh (1976) and Sutton and Robinson (1981) and is well accepted as a method of predicting hearing protector performance. It is currently the basis of the development of newer performance measures (Gauger and Berger, 2004).

The aims of this paper are to document the reliability of the attenuation provided by hearing protectors, to show how this reliability varies in an adverse manner with the mean attenuation and standard deviation, and to consider the implications of this for the use (and non-use) of hearing protectors in the workplace. To achieve these calculations, we introduce a new method for calculating a single-figure index of protection, and show how results for this new method relate to results for the traditional method.


To calculate a performance figure, the SLC method uses an overall weighted reference spectrum of 100 dB with octave band spectral components of 71, 81, 89, 93, 95, 93 and 86 dB at frequencies of 125, 250, 500, 1000, 2000, 4000 and 8000 Hz respectively (Waugh: 1976). For a particular device under consideration, the mean attenuation at the various octave band frequencies is calculated from experimental results using paid, volunteer test subjects. A standard deviation of the respective attenuations is also calculated for each test frequency. Testing is carried out in accordance with the requirements of AS/NZS 1270: 2002. These requirements are similar to those of ANSI S12.6 - 1997, Method B: subject fit. Test subjects are required to be inexperienced hearing protector users who fit the device according to the manufacturer's/distributor's instructions with no assistance from the tester.

From the reference spectrum, the mean attenuation of the device at each octave band is subtracted in order to get the attenuated spectrum under the device. The difference between the overall value of the reference spectrum and the attenuated spectrum provides the single figure performance or SLC of the device. This is summarised in the formula:­

[INLINE:1] where

Rfj = reference octave band spectral levels;

Mf j = mean attenuation at f j Hz; and

f j = 125, 250, 500, 1k, 2k, 4k & 8k Hz.

This value is the SLC of the device experienced by the average user and exceeded by 50% of the users. This value could be thought of as the SLC 50.

The SLC calculated in this way represents the attenuation performance achieved by 50% of the users. A more conservative measure is the SLC 80 which represents the attenuation performance experienced by at least 80% 1 of users at any one time. This is calculated by substituting the mean attenuation minus one standard deviation of performance at each octave band in the equation (1) instead of the mean attenuation alone.

An alternative method is now suggested through the use of a single-index figure (iSLC) calculated from the octave band attenuation figures for each subject. The mean iSLC determined for all subjects (miSLC) minus the standard deviation now provided a new performance figure the miSLC 80 . While this new calculation method is not identical to the old, the resulting values are extremely similar, as will be demonstrated later by the results (see [Figure 2]).

This alternate method can be applied to calculate NRR (ANSI S12.6-1997), (ISO 4869-2), SLC 80 (AS/NZS 1270; 2002) or any other single-index figure. One particular advantage is that now there is only one standard deviation rather than seven in the case of SLC 80 , eight for SNR and nine for NRR. The calculations for final measurement error estimations are also simplified through this reduction of the number of standard deviations.

An example of the calculations carried out is presented in [Table 1].

There are several points to note about the calculations in [Table 1]. The SLC is calculated from equation (1) using the mean attenuation for each octave band. The SLC 80 is calculated using the (Mean - SD) values provided along the last row of the table. The iSLC is also calculated from equation (1) for each test subject using the individual subject's attenuation at the respective octave bands. A mean value (miSLC) is then calculated for all subjects along with a standard deviation. The miSLC 80 is calculated by simply subtracting the standard deviation of the iSLC values from the miSLC.

An analysis of the available hearing protector test data was carried out for 115 devices that had been tested at the National Acoustic Laboratories as per the acoustic test conditions given in AS/NZS 1270: 2002. This process involves a subject-fit procedure with "pink" test noise of one-third octave band width, supplied at seven octave band centre frequencies for occluded and unoccluded ears. The difference between the occluded and unoccluded ear threshold hearing levels at each respective octave band was used to calculate the attenuation performance for the device under test.

In total there were 102 ear muffs and 13 ear plugs tested and included in this analysis. The ear muffs included the conventional headband types along with behind-the-neck ear muffs, helmet-mounted ear muffs and ear muffs contained within helmets (for military applications). Ear plugs included cylindrical, tapered, flanged, corded and uncorded varieties. For ear muffs there were a minimum of sixteen test subjects and for ear plugs a minimum of twenty as specified in the standard. The testing was carried out during the period of January 2001 to August 2004.


The range of SLC values for the ear plugs was 19.5 to 30.6 dB (mean = 26.2 dB) and for ear muffs was 19.1 to 36.8 dB (mean = 30.1). In respect to miSLC the generalised results are similar. For ear plugs the range of miSLC values was from 18.7 to 29.7 dB (mean = 25.3 dB, SD = 6.2) while for ear muffs it was 18.0 to 36.0 dB (mean = 29.2, SD = 3.3). This information is summarized in [Table 2]. Similar information is provided for plugs and muffs.

On average ear muffs provide more attenuation than ear plugs and have smaller overall variance. However, it must be emphasised that this generality does not apply to individual devices. Some ear plugs show a larger SLC and smaller standard deviation than some ear muffs.

It should be noted that the SLC and the miSLC and the SLC 80 and the miSLC 80 are not mathematically equivalent, however, they are consistently very close in value. This is illustrated in [Figure 1],[Figure 2] showing graphs of SLC versus miSLC and SLC 80 versus miSLC 80 respectively. Larger differences tend to arise at the lower values where the variance in attenuation values is greater (see below).

An important generalization from the analysis is the negative relationship between miSLC and the standard deviation, illustrated in [Figure 3].

Similar results apply for ear muffs and ear plugs independently.

The negative relationship between miSLC and standard deviation for plugs and muffs is given by,


Similarly for muffs and plugs alone the two respective relationships are,



Using the relationship


and equation (2) it is easily shown that,




As discussed previously, the SLC, and miSLC and the SLC 80 and miSLC 80 are not mathematically equivalent. However, in practice as the respective values are very similar as displayed in [Figure 1],[Figure 2] the miSLC and miSLC 80 will be used in the rest of this paper for convenience and simplicity during discussions.


The relationship found between across-subjects variability and mean attenuation (shown in equations (2) to (4)) implies that mean attenuation drops by around 1.3 dB for every 1 dB increase in standard deviation. More generally, all hearing protectors are capable of providing a high degree of attenuation to some individuals. For example, consider a hearing protector with an miSLC of 18.0 dB and a standard deviation of 9.5 dB. The miSLC 80 would be 8.5 dB, and yet it is capable of providing an iSLC greater than or equal to 37.0 dB (miSLC+ 2 SD) to over two percent of users, while 16% of users will attain an miSLC 80 greater than or equal to 27.5 dB (miSLC+ SD).

Hearing protectors that provide a low mean attenuation do so largely because of their wide spread of attenuation values across the population and not through specific design. It is now important to consider the wider implications of the above results with a more practical example.

In the practice of specifying hearing protectors by their SLC 80 , miSLC 80 or any other current single number, rating we attempt to match the noise exposure of the individual and the rating of the hearing protector such that the resultant equivalent at-ear noise exposure level experienced by the hearing protector user is less than that specified by the applicable Occupational Health and Safety (OHS) regulations.

Consider as a specific example, individuals who work in a noisy area where their L Aeq.8h is 92 dB.

They are working in what would be regarded as a hazardous area with respect to noise exposure as defined by the local OHS regulations that specify a critical L Aeq.8h of 85 dB. To apply the SLC 80 method we need the L Ceq.8h . This will typically be a few dB more than the correspondingL Aeq.8h. In this case we will assume an L Ceq.8h of 95 dB. (In order to simplify matters miSLC 80 values will be substituted in place of SLC 80 values from this point.)

The formula (Waugh: 1976) that relates the C - weighted exposure level, the miSLC 80 and the equivalent A - weighted exposure level at the wearer's ear is:



L Aeq.8h ' = the A-weighted equivalent free field noise exposure at the protected ear (dB);

L Ceq.8h = the C-weighted equivalent free field noise exposure at the unprotected ear (dB); and miSLC 80 = the rating of the hearing protector (dB).

If we choose a hearing protector with an miSLC 80 of 15 dB the protected A - weighted exposure level, L Aeq.8h ', for 80% of users is calculated to be less than or equal to 80 dB (i.e. 95 -15).

From equation (5) above 50% of users would experience an miSLC of around 23 dB (i.e. mean miSLC 80+ SD, 15 + 7.9) the standard deviation being calculated to be approximately 8 dB, using equation (7). This implies that 50% of users receive a protected equivalent A -weighted free field level of around 72 dB or less under their hearing protectors.

European Standard EN 458 recommends that an "acceptable attenuation" from a hearing protector is one that provides an A - weighted equivalent at-ear level of not less than 70 dB when the specified L Aeq.8h is 85 dB. Thus close to 50% of users could be regarded as being "over-protected" or receiving too much attenuation.

Standards (EN 458: 1993; AS/NZS 1269.3: 1998), codes of practice (eg NOHSC: 2000; WorkSafe WA 2002; OSH: 2003) and recently Gauger and Berger (2004) recommend that over­protection be avoided as this is one of the conditions that can cause individuals not to use hearing protectors. Over-protection tends to make wearers feel isolated from their environment and their work colleagues, and impedes communication. In the example, almost 50% of users are over-protected and in the long term are more unlikely to continue to wear hearing protectors.

If another example was selected where the noise level was lower and a correspondingly lower value of miSLC 80 was appropriate, due to the steady increase in size of the standard deviation as the miSLC decreases, a greater number of individuals would be over-protected and are hence less likely to use their hearing protectors. For example, if the selected miSLC 80 was 10 dB then the standard deviation would be in the order of 10 dB and subsequently around 50% of users would receive 20 dB of attenuation. This is much too high a value compared to what is required.

The steady increase in the standard deviation with decreasing miSLC compounds the overall problem of hearing protector selection and use leading to the phenomenon that in lower noise areas, fewer individuals are likely to use their hearing protectors because they receive too much attenuation.

Conversely if we choose a work area where the noise exposure level was higher, standard deviations for the attenuation of an appropriate hearing would be less and all users would be receiving a very similar level of noise reduction. For example, if an miSLC 80 of 25 dB is selected the standard deviation is reduced to approximately 3.6 dB.

Individuals who work in a high-noise environment have been shown to be more likely to utilise hearing protectors compared to when working in a low-noise environment even though the low-noise equipment may represent a greater noise hazard as it is in use for a much longer time (Williams, et al, 2002). Part of this non-use may be explained by the fact that the perception of the hazard is less but part may also be due to the increased isolation experienced by many users when over-protected. This would not occur if the performance of the devices were not so widespread at lower attenuations.

"Noise-induced hearing loss is a significant problem that has not been solved by mandatory hearing conservation programs, in part because workers' perceptions have not been addressed" (Lusk et al, 1995, p 639) and over protection with subsequent feelings of isolation from the workplace is one of these perceptions. Industries that reasonably expect to have a low overall risk of noise injury and incidence of hearing loss, still experience difficulties because of over­protection and hence non compliance with hearing protector programmes. Thus even in apparently low-noise industries the reliance on the use of hearing protectors to solve the noise exposure problem can be unsuccessful. Industry either needs hearing protectors that can give a more predictable degree of attenuation or, better still, strategies that eliminate the noise hazard.

Workplace noise exposure is a large problem all over the world. In the UK it is estimated that "at least 1.3 million employees are exposed to noise levels above 85 dB(A)" during the regular course of their work (RNID: 1999, p 4). "Hearing loss is one of the most pervasive occupational health problems in America today" (NIOSH: 1996. p v) with the American Academy of Audiologists (2003) and the NIDCD (2004) both estimating that there up to 30 million workers occupationally exposed to high noise levels on a daily basis. In Australia it was estimated that there were around 500,000 workers potentially exposed to hazardous levels of noise (Waugh: 1991) while New Zealand estimates that "25 percent of New Zealand's workers are exposed to noise levels which are harmful to their hearing" (OSH: 2002).

An examination of the 'typical' industrial noise levels and spectra 2 experienced in workplaces - the "SA 300" used by Waugh (1984), originating from a survey by the Department of Public Health in South Australia (1969) and the NIOSH 100, derived from Kroes et al (1975) which were in turn selected from 579 noise spectra measured by Karplug and Bonvallet (1953) and from 291 common agricultural noise sources (Depczynski et al: 2004) - shows that most workplace noise exposure levels, L Aeq , for common tasks are below 100 dB. This is important because of the implication that for the most part individuals who work with noise do not work with extremely loud noises, but rather work with A - weighted levels below 100 dB. This means that they would normally be selecting hearing protectors with miSLC 80 values of 20 dB or less.

With an miSLC 80 of 20 dB the standard deviation is already 5.8 dB and this spread of attenuation means that many users start to experience overprotection. The lower the noise, the lower the miSLC 80 , the more overprotection and the more likely it is that individuals are not going to use their hearing protectors.


Hearing protectors should be designed such that all users experience similar levels of attenuation from the same device. Some variation in performance is to be expected, however, this variation should not be a function of the attenuation of the device. Analysis of routine NAL test data using a simplified method shows that this is not currently the case.


Thanks are gratefully acknowledged to Geoff Colin-Thome for the results of his hearing protector testing program[27].


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