Comparison of the NAL(R) and Cambridge formulae for the fitting of linear hearing aids

R W Peters, B C Moore, B R Glasberg, M A Stone
British Journal of Audiology 2000, 34 (1): 21-36
This paper describes a laboratory-based comparison of the effectiveness of two formulae for fitting linear hearing aids, the NAL(R) formula and the Cambridge formula. The formulae prescribe the desired insertion gain as a function of frequency, based on the audiometric threshold. The two formulae have a similar rationale; both are based on the goal that, for speech with a moderate level, all frequency bands should be equally loud (equal loudness per critical band) over the frequency range important for speech (400-5000 Hz), and the overall loudness should be comfortable. However, the formulae differ; generally the Cambridge formula leads to slightly more high-frequency gain (above 2 kHz) and slightly less mid-frequency gain (between 500 Hz and 2000 Hz) than the NAL(R) formula. The two formulae were implemented using an experimental digital hearing aid whose frequency-gain characteristic could be controlled very precisely. A loudness model (Moore and Glasberg, 1997) was used to adjust the overall gains for each subject and each formula so that a speech-shaped noise with an overall level of 65 dB SPL would give the same loudness as for a normally hearing person (according to the model). The adjustments were, on average, smaller for the Cambridge than for the NAL(R) formula. A condition was also used with all insertion gains set to zero, simulating unaided listening. Evaluation was based on: (1) subjective ratings of the loudness, intelligibility and quality of continuous discourse presented in quiet at levels of 45, 55, 65 and 75 dB SPL and in babble at an 0-dB speech-to-babble ratio, using speech levels of 55, 65 and 75 dB SPL; (2) measures of the speech reception threshold (SRT) in background noise for two noise levels (65 and 75 dB SPL) and four types of background noise. Neither the subjective ratings nor the measures of the SRTs revealed any consistent difference between the results obtained using the two formulae, although both formulae led to lower (better) SRTs than for simulated unaided listening. It is concluded that the differences between the NAL(R) formula and the Cambridge formula are too small to have measurable effects, at least in a laboratory setting.

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