# Similarity of the effects of reverberation on speech intelligibility in noise for hearing-impaired and normal-hearing listeners

Raphael Cueille, Nicolas Grimault, Mathieu Lavandier

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Raphael Cueille, Nicolas Grimault, Mathieu Lavandier. Similarity of the effects of reverberation on speech intelligibility in noise for hearing-impaired and normal-hearing listeners. Journal of the Acoustical Society of America, 2025, 158 (6), pp.4994-5007. 10.1121/10.0041883. hal-05442496

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
Similarity of the effects of reverberation on speech intelligibility in noise for
hearing-impaired and normal-hearing listeners

Raphael Cueille,¹,²,³,ᵃ Nicolas Grimault,² and Mathieu Lavandier¹

¹ENTPE, Ecole Centrale de Lyon, CNRS, LTDS, UMR5513, 69518 Vaulx-en-Velin,
France

²Cognition Auditive et Psychoacoustique UMR CNRS 5292 Centre de Recherche en Neurosciences de Lyon Centre Hospitalier Le Vinatier - Bâtiment 462 - Neurocampus 95 boulevard Pinel 69675 Bron Cedex France

³Cerema, Université Gustave Eiffel, UMRAE, 11 Rue Jean Mentelin,
Strasbourg F-67035, France

(Dated: 8 December 2025)
Hearing-impaired (HI) listeners experience difficulties to understand speech in noisy environments. The aim of this study was to determine whether they are more affected by the detrimental effects of reverberation than normal-hearing (NH) listeners. Intelligibility tests were done for NH listeners and HI listeners with various degrees of hearing loss, using headphones and real-room binaural impulse responses to simulate several spatial configurations. This allowed us to investigate different effects of reverberation on speech intelligibility in noise: the temporal smearing of the target speech impairing its intelligibility, the temporal smearing of modulated noise maskers reducing the opportunity for dip listening, the detrimental effects of reverberation on spatial release from masking. The results indicate that the HI and NH listeners were similarly affected by reverberation. The tested conditions did not reveal any effect of hearing loss asymmetry on spatial release from masking, potentially because the main asymmetries were partly compensated for by the linear amplification applied to the stimuli for the HI listeners. Finally, the data could be described reasonably well using a binaural speech intelligibility model.

<footnote>a raphael.cueille@cerema.fr</footnote>
## I. INTRODUCTION

There are several perceptual mechanisms that can improve speech intelligibility in noisy environments. If the interfering noise is temporally modulated in amplitude, the listener can benefit from listening in the dips of the noise (Festen and Plomp, 1990; Miller and Licklader, 1950). In binaural conditions, the listener benefits from spatial release from masking (SRM), the benefit from a difference in position between the target and the noise sources (Bronkhorst and Plomp, 1988). SRM relies on two mechanisms: better-ear listening and binaural unmasking. Better-ear listening is the intelligibility benefit that comes from differences of interaural level differences between the target and masker signals. This creates differences of signal-to-noise ratios (SNR) at the two ears, and the listener can benefit from whichever ear offers the best SNR at a given time in a given frequency band. Binaural unmasking relies on the differences of interaural time differences between the target and masker signals. Following the equalization-cancellation theory (Durlach, 1963), the listener should be able to equalize the masker at the two ears, to partially cancel it and improve intelligibility.

These mechanisms can be impaired by reverberation. Reverberation temporally smears the interfering signal. This can be detrimental to the dip listening benefit for modulated maskers, as it tends to reduce the masker modulations (Collin and Lavandier, 2013). Reverberation can also reduce SRM. It can decrease better-ear listening by reducing the amount of acoustic shadowing provided by the head as sound reflections travel around it (Plomp, 1976). The sound reflections also decorrelate the interfering sound at the two ears (Hart-
mann et al., 2005), which can impair binaural unmasking (Lavandier and Culling, 2008). Of course, an additional detrimental effect of reverberation is that it temporally smears the target speech, and can reduce its intrinsic intelligibility even in the absence of noise (Houtgast and Steeneken, 1985).

Hearing-impaired (HI) listeners have a harder time to understand speech in noise compared to normal-hearing (NH) listeners. They appear to have a reduced SRM (Glyde et al., 2011). This is partly due to their elevated hearing thresholds, which limit the benefit of better-ear listening. They also have a reduced sensitivity to the temporal fine structure of sounds (Füllgrabe and Moore, 2017), which might slightly limit their ability for binaural unmasking (Vicente et al., 2021). Bronkhorst and Plomp (1989) found that SRM also appears to depend on the asymmetry of the hearing loss. Asymmetric HI listeners seem to benefit less from binaural unmasking than symmetric HI listeners. HI listeners also usually display a worse dip listening benefit than NH listeners (Festen and Plomp, 1990). However this might be partially due to the differences in the SNRs at which the listeners are tested (Jensen and Bernstein, 2019). HI listeners are usually tested at higher SNRs than NH listeners, while the dip listening benefit decreases as the SNR increases (Oxenham and Simonson, 2009).

It is still unclear whether HI listeners are more affected by reverberation than NH listeners. A recent study by Cueille et al. (2022) tested NH and HI listeners in monaural conditions with varying levels of reverberation applied to the target speech and an interfering noise. They found that the monaural effects of reverberation were statistically the same between the two listener groups, that is to say the temporal smearing of the target speech and interfering noise had a similar effect for HI and NH listeners. In binaural conditions,
Helfer and Wilber (1990) tested HI and NH listeners with the target speech in front and symmetrical interfering noise sources on each side of the target. They found a significant detrimental effect of reverberation on speech intelligibility, but did not find statistical evidence for a difference of this effect between groups. Best et al. (2015) tested NH listeners and HI listeners with and without hearing aids in an anechoic chamber as well as in a simulated cafeteria environment with multiple interfering sources. They found that the decrease of intelligibility between the anechoic and reverberant environments was more important for the HI listeners than for the NH listeners. Xia et al. (2018) tested NH and aided HI listeners considering four rooms with different reverberation times. There was a significant difference of the effect of reverberation between HI and NH listeners. However, this interaction was at least partly due to ceiling effects, and the authors were unsure whether there truly was a different effect of reverberation between NH and HI listeners.

To better understand which mechanisms affect speech intelligibility, it is important to develop speech intelligibility models. We previously developed a binaural model to predict the speech reception thresholds (SRT, the SNR for 50% correct) of NH and HI listeners in noise and reverberation (Cueille and Lavandier, 2025). This model takes the audiogram, the binaural room impulse responses (BRIRs) and the test signals as inputs to account for the temporal smearing of the speech, the masker modulations and the hearing loss. It is a follow-up version of the models of Lavandier and Culling (2010) and Jelfs et al. (2011), which predict the effects of better-ear listening and binaural unmasking on SRTs.

The aims of the present study were (1) to understand whether HI and NH listeners are differently affected by reverberation in binaural conditions, (2) to determine whether speech
intelligibility varies between asymmetric and symmetric HI listeners in reverberant environments, (3) to test whether the collected data could be described by the model of Cueille and Lavandier (2025), which was never tested on asymmetric hearing loss. To achieve this, an intelligibility test was done for NH and HI listeners. Real-room impulse responses were used to simulate several rooms and spatial configurations. This allowed us to evaluate the effects of reverberation on speech intelligibility as well as the interaction between reverberation and SRM, for NH and HI listeners. Some of the HI listeners had asymmetric hearing loss, which made it possible to study the interaction between SRM and hearing loss asymmetry.

## II. METHODS

### A. Listeners

Thirty-six listeners were tested in the experiment. They were 10 NH listeners, 10 HI listeners with symmetric hearing loss, and 16 HI listeners with asymmetric hearing loss. The asymmetric HI listeners consisted of 9 listeners with a worse left ear and 7 listeners with a worse right ear. The NH listeners had hearing thresholds lower than 20 dB HL from 125 to 4000 Hz and no larger than 25 dB HL from 6000 to 8000 Hz. The HI listeners had mild-to-moderate hearing loss. They were considered asymmetric when they had more than 10 dB of interaural difference in four-frequency (0.5, 1, 2, 4 kHz) pure tone average (PTA4). The PTA4 (averaged across ears) was $14.6 \pm 3.2$ dB HL for the NH listeners and $51.4 \pm 11.0$ dB HL for the symmetric HI listeners. The HI listeners with a worse left ear ("HI-worse left ear") had a PTA4 of $37.6 \pm 10.8$ dB HL, while it was $44.0 \pm 14.5$ dB HL for the HI listeners
with a worse right ear ("HI-worse right ear"). Two asymmetric listeners had an averaged PTA4 lower than 20 dB HL, with a PTA4 of 22-23 dB HL at the worst ear. To avoid this limitation, the scores of the asymmetric listener groups were not compared with those of the NH and symmetric HI groups (see the Statistical analysis subsection). To illustrate the hearing loss across ears and participants, the individual audiograms as well as the mean audiograms across listeners in each group are shown in Figure 1. The PTA4 of the listeners as well as their PTA4 interaural difference can be seen in Figure 2, illustrating the hearing loss asymmetry of the listeners.

The NH listeners were aged between 55 and 72 years old (mean 63 years, standard deviation 5 years). The symmetric HI listeners were aged between 71 and 78 years old, (mean 71 years, standard deviation 6 years). The HI-worse left ear listeners were aged between 29 and 73 years old (mean 63 years, standard deviation 14 years). The HI-worse right ear listeners were aged between 57 and 79 years old, (mean 70 years, standard deviation 8 years).

The study received approval from a French national ethic committee (CPP Ile de France X, protocol no. 05-2019). The listeners signed an informed-consent form and were paid an hourly wage for their participation.

## B. Stimuli

Sentences taken from the French Matrix test (Frmatrix, Jansen et al. (2012)) were used as target speech. It is a closed matrix test with five groups of 10 names, 10 verbs, 10 numerals, 10 objects and 10 colours. They can be arranged to form various sentences of five
<figure><img src="image_2.png" /><figcaption>FIG. 1. Audiograms (averaged across ears) of the listeners. Each listener is represented by a grey dotted line. The black solid lines represent the average audiogram across listeners in each group.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>FIG. 2. PTA4 (averaged across ears) of the listeners as a function of their PTA4 interaural difference</figcaption></figure>
words, for example: “Agnès achète cinq crayons verts” (Agnès buys five green pencils). The
words were chosen so that they best represent French phonetic distribution. The recording
of these sentences was done preserving the coarticulation between words. The sound level
of the words was calibrated so that the intelligibility was equal across words, sentences and
test lists. To preserve this equalization in the present study, only the mean level across all
sentences from all tested lists was varied, by applying the same gain to all sentences.

To ease the comparison across studies, the sentences and interfering noise used here were
those used by Cueille et al. (2022) to test NH and HI listeners in monaural conditions. The
target sentence was always presented within interfering noise that was two one-voice noise-
vocoded speech excerpts. As the vocoded speech was not intelligible, these excerpts are
just a type of modulated noise. To construct these noises, 288 semantically unpredictable
sentences from another speech material (Raake and Katz, 2006) were concatenated and
passed through a three-band vocoder, with an envelope low-pass filter-cut off frequency of
60 Hz. A finite impulse response (FIR) filter was used to match the excitation pattern of
the modulated noise with the average excitation pattern across all target sentences, so that
they had the same long-term spectrum. For each target sentence, two different excerpts of
modulated noise were randomly selected and gated with 10-ms cosine ramps. They were
one second longer than their affiliated target sentence. During the experiment, the target
sentence always started between 300 ms and 700 ms after the onset of the two noises, the
exact delay being randomly selected on each trial.

The BRIRs from four real rooms were convolved with the stimuli in order to simulate
reverberation while listening to the stimuli using headphones. One anechoic room from
the Massachusetts Institute of Technology (MIT) was used (Gardner and Martin, 1994), as well as two offices and an amphitheater measured by Lavandier et al. (2012). The source (target or masker) distance to the receiver/listener was constant within each room, but varied across rooms. Room characteristics can be found in Table I. The anechoic room has a null reverberation time (RT) and infinite direct-to-reverberant ratio (DRR), because it has no reverberation. The offices have similarly low RTs, but vary in DRR. The amphitheater has high DRR and RT, indicating a high reverberation level.

In each room, three spatial configurations were tested. First, a co-located configuration was considered, with the speech and two noise sources simulated at the same position in front of the listener. This configuration was a reference condition, with no SRM. Second, a symmetric configuration, with the speech in front of the listener and one noise source at 25° azimuth on each side of the listener. This should provide for binaural unmasking but limited better-ear listening with one noise on each side of the target speech. Third, an asymmetric configuration with the target in front of the listener and both noise sources at the same position on the right side of the listener, with a 25° azimuth separation between the target and noise sources. This condition should allow for both binaural unmasking and better-ear listening, thus the largest SRM among the three spatial configurations.

A binaural intelligibility model developed by Jelfs et al. (2011) was used to characterize the predicted SRM in the rooms (Table I). This model takes the target and masker BRIRs as input to calculate the effects of better-ear listening and binaural unmasking. It allows to predict differences of SRTs between conditions, for NH listeners and stationary noise maskers. Here it was used to roughly evaluate the maximum SRM that could be
expected for the rooms and configurations tested. The SRM was calculated as the SRT difference between the co-located and each separated configurations. The predicted SRM for the asymmetric configuration goes from 5.44 dB in the anechoic room to 3.01 dB in the amphitheater. This shows an anticipated strong interaction between reverberation and SRM. The predicted SRM in the symmetric configuration is much lower, and appears to increase with reverberation, going from 0.27 dB in the anechoic room to 2.07 dB in the second office. This SRM increase appears to be due to the better-ear component of the model: while the predicted binaural unmasking benefit goes from 0.17 dB in the anechoic room to 0.27 dB in the second office, the predicted better-ear advantage goes from 0.1 dB to 1.8 dB. This could be due to room coloration, changes in the spectral shape of the interferer due to reverberation and its difference of positions within the rooms. Reverberation can improve intelligibility when frequencies important to speech intelligibility are attenuated in the spectrum of the masker (Collin and Lavandier, 2013; Lavandier and Culling, 2010).

The mean presentation level of the target speech, averaged across ears and all tested sentences, was calibrated at 50 dB sound pressure level (SPL), without spectral weighting (Z). The noise level was adapted to reach the desired SNR in each tested condition. A linear frequency-dependent gain was applied to the stimuli of the HI listeners before presentation. The gain was set individually based on the NAL-RP prescription rule (Dillon, 2012). Gains of 10 to 25 dB were applied in this study. The NAL-RP is a linear amplification which compensates for reduced audibility. However it does not provide audibility equal to that experienced by NH listeners, i.e. it does not fully “invert” the audiogram (Glyde et al., 2015). This allowed to partly compensate for hearing loss without fully restoring audibility,
<table><caption>TABLE I. Source-to-receiver distance (in m), DRR (in dB) and RT (in s) for the target speech position in each room (the noises were always tested at the same distance to the listener than the target), along with the SRM (in dB) predicted by the model of Jelfs et al. (2011) in the symmetric (sym) and asymmetric (asym) conditions.</caption><thead><tr><th rowspan="2">Room</th><th>Source-to-receiver</th><th rowspan="2">DRR (dB)</th><th rowspan="2">RT (s)</th><th>Predicted</th><th>Predicted</th></tr><tr><th>distance (m)</th><th>SRM-sym (dB)</th><th>SRM-asym (dB)</th></tr></thead><tbody><tr><td>Anechoic</td><td>1.4</td><td>non-measurable</td><td>non-measurable</td><td>0.27</td><td>5.44</td></tr><tr><td>Office 1</td><td>0.65</td><td>4.2</td><td>0.5</td><td>1.37</td><td>4.11</td></tr><tr><td>Office 2</td><td>1.25</td><td>-0.1</td><td>0.4</td><td>2.07</td><td>3.90</td></tr><tr><td>Amphitheater</td><td>10</td><td>-8.5</td><td>1.3</td><td>1.70</td><td>3.01</td></tr></tbody></table>

in order not to focus only on the supra-threshold elements of hearing loss. The gain was applied independently at the two ears, so that the listener received a different amplification at each ear, depending on the ear's audiogram. This ensured that the stimuli were audible at the worst ear and not too loud at the best ear, in particular for the asymmetric HI listeners.

## C. Procedure

The listening test was done in a sound-proof booth (sound attenuation over 70 dB from 100 Hz to 20 kHz) with headphones (Sennheiser HD 250 Linear II). The sound levels at both ears were calibrated separately with the same artificial ear associated with a flat coupler (Larson Davis AEC101 and 824).
The stimuli on each trial were five words of the target sentence and two interfering noises.

The overall SNR was defined as the sound level ratio between the target sentence and the sum
of the two interfering noises, after convolution with their corresponding BRIR. On each trial,
for each of the five words, listeners chose one answer among the 10 possibilities presented
on a computer screen in front of them. Matrix tests are often used with 20 sentences (e.g.,
Jansen et al. (2012)) that involve twice the 50 words of the speech material for one adaptive
measure of SRT. In this experiment it was decided to measure the intelligibility scores in
percent correct at five SNRs for each listener, in order to estimate his/her full psychometric
functions. For each tested SNR, participants listened to 10 sentences that contained the 50
words of the Frmatrix. In other words, for each tested condition, 50 sentences were tested to
obtain the psychometric function. The words layout and the tested conditions were selected
in random order on a sentence-by-sentence basis.

At the beginning of the experiment, an audibility test was done to make sure that all
sentences were audible in quiet, and a loudness test was done to make sure that the stimuli
were never uncomfortable. The audibility test consisted in measuring the intelligibility for
a list of 20 sentences presented in quiet, at the level used for the target sentence in the main
test, 50 dB SPL. All listeners had an intelligibility score above 90% in this quiet condition.
The loudness test used a method similar to the contour test (Cox et al., 1997). The listeners
were presented with one stimulus (one sentence and two noises at the lowest SNR, for the
co-located configuration in the anechoic room) and had to evaluate its loudness on a 7-point
scale: 1, very soft; 2, soft; 3, comfortable but slightly soft; 4, comfortable; 5, comfortable
but slightly loud; 6, loud, but okay; 7, uncomfortably loud. The sound level of the stimulus
started at 55 dB SPL and was raised by steps of 5 dB until the listener found the stimulus uncomfortably loud. If it was necessary the SNR range was adjusted in the intelligibility test so that the listener was always tested below the sound level judged uncomfortably loud.

Each listener was tested during two sessions of 1.5 hours. The first session started with the audiogram measurement and the audibility and loudness control tests. Each session included a short practice test consisting of two 20-sentence lists in order to limit the short-term training effect that comes with closed-set speech materials (Jansen et al., 2012). The main experiment then tested 60 conditions (four rooms * three spatial configurations * five SNRs) using a total of 600 sentences, for each listener.

## D. Statistical analysis

For each listener and condition, a psychometric function was fitted to the percentage correct scores with the psignifit toolbox (Schütt et al., 2015). Each psychometric function was modelled with a cumulative Gaussian sigmoid curve $\psi(SNR)$ parametrized by its threshold $m$ at the inflexion point of the function and its width $w$ (range of SNRs containing 95% of the function) and scaled by its upper and lower asymptotic values $\lambda$ and $\gamma$. The variables $m$ and $w$ were estimated with a maximum likelihood method, as described by Wichmann and Hill (2001). $\gamma$ was fixed at 1 while $\lambda$ was allowed to vary between 0 and 0.05, to take into account the listeners' lapses in performance, that is to say the stimulus-independent errors made by the listeners (Wichmann and Hill, 2001). The sigmoid function $\psi(SNR)$ is detailed in equation 1. Before doing any statistical analysis, the individual fitted psychome-
tric curves were converted from percentage to rationalized arcsine units (RAU) to normalize
the variance across the range of percentage scores (Studebaker, 1985).

$$ \psi(SNR) = \gamma + \frac{(1 - \gamma - \lambda)}{(1 + e^{-2*\log(1/0.05-1)/w*(SNR-m)+\log(1/0.5-1)})} \quad (1) $$

For the statistical analyses, the scores of the listeners were compared at a single common SNR of the individual (RAU-converted) psychometric curves. This SNR, i.e., the optimal SNR, was chosen as the one with the maximum number of intelligibility scores between 15% and 95% (i.e., 13 RAU and 102 RAU). This ensured that there was a minimum amount of floor and ceiling effects. The analyses were done with the RAU-converted scores of the listeners and with the RAU score difference between the co-located and the other spatial configurations (for SRM analyses).

The results of the NH and symmetric HI listeners were tested separately from those of the asymmetric HI listeners. This was done to test for a possible effect of hearing loss asymmetry on SRM independently from the effect of mean hearing loss across ears, as some asymmetric HI listeners had a low hearing loss.

All statistical analyses were conducted with Bayesian tests. A Cauchy prior distribution was used as a default prior with a scale value of 1/2, as there was not enough information to use informative priors (Rouder et al., 2012). A Bayes factor superior to 10 or inferior to 1/10 was seen as a strong proof for the presence or absence of an effect. A Bayes factor superior to 3 or inferior to 1/3 was seen as a moderate proof, while a Bayes factor between 1/3 and 3 did not allow for any conclusion (Jeffreys, 1998). Post hoc tests were corrected for multiplicity by fixing to 0.5 the probability that the null hypothesis holds across all comparisons (Westfall
et al., 1997). To further control for multiplicity, four separate Bayesian false discovery rates (FDR) were computed for the post hoc tests associated with each Bayesian ANOVA. The FDR estimates the number of discoveries (rejected null hypotheses) which are false. Following the approach proposed by Muller et al. (2006), the Bayesian FDR was estimated as the mean posterior probability of the null hypothesis, $P(H0|data) = 1/(1 + BF)$, across all positive tests where the Bayes factor is superior to 3.

E. Modelling of the measured data

A model was also used to describe the data (Cueille and Lavandier, 2025). Compared to the Jelfs model used for the SRM computations of Table I, it can also predict the effects of hearing loss, modulations in the masker, and temporal smearing of the target speech by reverberation, incorporating features from two other models based on the one of Lavandier and Culling (2010): the models of Vicente et al. (2020) and Leclère et al. (2015). It takes as input the target and interferer BRIRs, the original speech and interferer materials, the listener's audiogram, as well as the external sound level used in the experiment. Cueille and Lavandier (2025) present a detailed description of this model and its validation on various datasets from the literature.

The better-ear listening component evaluates the best SNR between ears by frequency bands and time frames. The binaural unmasking advantage is computed in each frequency band and time frame following a formula proposed by Culling et al. (2005). The binaural unmasking advantage and better-ear SNR are integrated across bands using the speech intelligibility index (SII) weightings (ANSI S3.5, 1997), averaged across time frames, and
summed in order to obtain a single broadband binaural ratio. The binaural ratio is a
value in dB which reflects speech intelligibility. A higher binaural ratio represents a better
speech intelligibility. Differences in binaural ratios between conditions can be compared to
differences between SRTs.

The model also implements an internal noise spectrum at each ear to account for hearing
loss, with spectrum levels depending on the listener's audiogram and the external sound level
(Vicente et al., 2020). In the better-ear calculation, the SNR at each ear is computed using
the highest level between the internal noise and the external noise. Cueille and Lavandier
(2025) tested two methods to create the internal noise spectra. In the first method, the inter-
nal noise level is based on the listener's audiogram and the external sound (target+maskers)
broadband level. This method was developed and calibrated by Vicente et al. (2020). In
the second method, the internal noise level is based on the listener's audiogram and the
external sound spectrum level. The advantage of the broadband level approach is that it
produces an internal noise that has the same spectral shape as the audiogram (Vicente et al.,
2020). The spectrum level approach offers the advantage of better approximating the real
sound level in the different frequency bands (which can be quite different from the broad-
band level). As the two internal noise methods gave similarly accurate predictions with the
datasets tested by Cueille and Lavandier (2025), they were both tested here. In the present
study the version using the external sound broadband level is called cueille-broadband and
the version with the external sound spectrum is called cueille-spectrum. The internal noise
method influences the predictions only for HI listeners, unless very low presentation levels
are considered for the stimuli (in which case NH predictions are influenced too).
To account for the effect of the temporal smearing of the target speech, the target BRIR is separated into an early and a late part using linear windows (Leclère et al., 2015). The raw speech material is averaged across sentences and this average target signal is convolved with the early and late target BRIRs. The early target signal is considered as useful for speech intelligibility, while the late target signal is considered as detrimental and is summed with the interferer signal (obtained through convolution with its corresponding BRIR). The early linear window starts with a constant amplitude of one, followed by a linear decrease to zero. The late window starts at zero and increases linearly to one. These windows are defined by two parameters. The early-late limit (ELL) defines the duration of the constant portion of the window, while the decay duration defines the duration of the linear decrease/increase. Cueille and Lavandier (2025) tested several methods to make the ELL room-dependent. Here, their room-independent ELL value was used, as it gave predictions as accurate as the other tested methods and is simpler to implement. The ELL was fixed at 30 ms and the decay duration at 25 ms (Leclère et al., 2015).

In the present study the raw target signal was created by averaging 280 sentence wave-
forms. The presentation level of the convolved target signals was fixed at 50 dB SPL, as in
the experiment. As the model predicts SRTs differences, the individual SRTs of the listen-
ers were estimated based on their individual fitted psychometric curves. The average SRTs
across listeners were then estimated for each of the four listener groups (NH, HI-symmetric,
HI-worse left ear and HI-worse right ear). The binaural ratios predicted by the model were
inverted to predict the SRT (the higher the binaural ratio, the lower the predicted SRT).
Differences in inverted binaural ratio can be directly compared to differences in measured
SRT. To compare absolute SRTs and binaural ratios, a reference needs to be chosen. This
reference is an arbitrary choice that does not influence the relative differences across pre-
dictions. The average SRT within a data set is often chosen as the reference (Collin and
Lavandier, 2013; Lavandier and Culling, 2010; Leclère et al., 2015; Vicente et al., 2020).
Before comparison to the data, inverted binaural ratios are then offset by subtracting their
mean and adding the corresponding average SRT (the reference), or in other words, the
average binaural ratio is aligned with the average SRT.

To evaluate the model performances, the Pearson correlation coefficient between mea-
sured and predicted SRTs averaged across listeners was calculated, along with the mean
absolute error and the largest absolute error between data and predictions. These perfor-
mance statistics were also calculated for the individual predictions. To evaluate how well
SRM was predicted by the model, the differences between the average estimated SRTs in
the co-located and the two other spatial configurations were calculated in each room. These
measured SRT differences were then compared to the differences in average predicted SRTs
using the same performance statistics.

### III. RESULTS

The optimal SNR range was between -8.9 dB and -8.7 dB, where 98% of the listeners'
scores were between 15% and 90%. The analyses were done at the SNR of -8.8 dB. The RAU
scores of the listeners at this optimal SNR can be found in Figure 3, while the corresponding
SRM can be found in Figure 4. The mean psychometric curves of each listener group are
shown in the supplementary materials, along with these psychometric function parameters
<figure><img src="image_4.png" /></figure>

FIG. 3. Mean RAU scores with standard errors across listeners at the optimal SNR (-8.8 dB), for the NH and symmetric HI listeners (top panels), and the asymmetric HI listeners (bottom panels). Each panel corresponds to a room. The spatial configuration (co-located “coloc”; symmetric maskers “sym”; asymmetric maskers “asym”) appears on the x axis.

(Suppl. Fig. 1-4 and Suppl. Table I)¹. The estimated SRTs can be found in Figure 5 along with the model predictions (subsection C). The detailed results of the statistical analyses are shown in the supplementary materials (Suppl. Tables II and III).

### A. Symmetric listeners

A first Bayesian ANOVA (“ANOVA 1”) was done with the scores of the NH and symmetric HI listeners to study the potential interaction between hearing loss and reverberation. It showed that the two groups experienced SRM, were affected by reverberation, and that the symmetric HI listeners had worse performances than the NH listeners. This can be seen
<figure><img src="image_5.png" /></figure>

FIG. 4. Mean SRM (in RAU) with standard error across listeners, measured at the optimal SNR (-8.8 dB), for the NH and symmetric HI listeners (top panels), and the asymmetric HI listeners (bottom panels). It corresponds to the score difference between the co-located configuration and the other two configurations (Figure 3). Each panel corresponds to a room. The spatial configuration (symmetric maskers; asymmetric maskers) appears on the x axis.

in Figure 3, where the scores are slightly lower in the amphitheater than in the anechoic room, higher in the asymmetric configuration than in the co-located configuration, and lower for the HI listeners than for the NH listeners. HI and NH listeners highlighted the same amount of SRM and were statistically similarly affected by reverberation. The post hoc tests showed that in the co-located configuration, there were significant scores differences between the amphitheater and the other rooms as well as between the first and second offices. This corresponds to significant detrimental effects of the temporal smearing of the speech and noises by reverberation. In the symmetric configuration the scores were significantly higher
in the first office than in the anechoic room and the amphitheater. This indicates that in the symmetric configuration reverberation was detrimental to intelligibility in the amphitheater, while it was slightly helpful in the first office. In the asymmetric configuration, the scores were significantly higher in the anechoic room than in all other rooms, and significantly lower in the amphitheater than in all other rooms, highlighting the detrimental effect of reverberation on SRM.

To further study the interaction between SRM and reverberation, a second ANOVA was done with the SRM of the NH and symmetric HI listeners (“ANOVA 2”). NH and symmetric HI listeners experienced similar SRM, as highlighted in Figure 4. There was also a significant interaction between the effects of the room and spatial configuration. The post hoc tests showed that, in the symmetric configuration, SRM was significantly more important in the second office than in the anechoic room. In the asymmetric configuration, SRM was significantly more important in the anechoic room than in the first office and amphitheater. The SRM was significantly more important in the asymmetric configuration than in the symmetric configuration, in all rooms.

## B. Asymmetric listeners

The ANOVA on the scores of the asymmetric HI listeners (“ANOVA 3”) showed strong effects of the room and spatial configuration. However there was a statistical absence of effect of the asymmetry of the hearing loss. This can be seen in Figure 3, where both listener groups have similar scores in all conditions. There was a significant. The post hoc tests indicate that there were significant score differences between all spatial comparisons in
each room, the only exception being between the co-located and symmetric configurations in
the anechoic room. In the co-located configuration, the scores were significantly higher in the
anechoic room and the first office than in the amphitheater. In the symmetric configuration,
the scores were significantly higher in the two offices than in the anechoic room and the
amphitheater. In the asymmetric configuration, the scores were significantly lower in the
amphitheater than in the three other rooms.

The ANOVA done with the SRM of the asymmetric HI listeners (“ANOVA 4”) showed
significant effects of the room and spatial configuration. ANOVA was inconclusive regarding
the main effect of the listener group, leaning towards the absence of effect. Figure 4 also
shows little SRM difference between the two groups of asymmetric HI listeners. The post
hoc tests showed that in the symmetric configuration, there was a small but significant
positive effect of reverberation on SRM, with a 10% score difference between the second
office and the anechoic room. In the asymmetric configuration, SRM was significantly higher
in the anechoic room than in the first office and the amphitheater. The post hoc tests also
show a significantly higher SRM in the asymmetric configuration than in the symmetric
configuration, for all rooms.

For each Bayesian ANOVA, the false discovery rate (FDR) was calculated for the inter-
action between the effects of the room and the spatial configuration. The FDR was lower
than 10% for all Bayesian ANOVAs. Given the number of detected effects (between 7 and
22 by Bayesian ANOVA), these results indicate that the post hoc tests are moderately ro-
bust, with one or two expected false discoveries by Bayesian ANOVA. The FDR analysis is
detailed in the supplementary materials (Suppl. Table IV).
To evaluate the size of a potential SRM difference between the two groups of asymmetric HI listeners, a Monte Carlo power analysis was done in order to estimate the number of listeners that would have been necessary to detect a difference between the SRM of these two groups. More specifically, a sequential Bayes factor analysis was done (Schönbrodt and Wagenmakers, 2018). The ANOVA 4 was applied with 14 simulated listeners (7 listeners in each group), whose results in each condition were artificially generated based on the mean and standard deviation of the results obtained by the real asymmetric HI listeners in the experiment. The number of listeners was then raised progressively (two-by-two, one supplementary listener in each group) until a Bayes factor superior to 3 or inferior to 1/3 was reached. This procedure was repeated 2000 times. With the results obtained in the experiment, it was estimated that 170 listeners would be necessary (85 in each group) to detect a significant SRM difference between the groups with a probability superior to 0.9. This implies that the potential difference of SRM between the two groups of asymmetric HI listeners tested here, if any, is small and probably negligible.

### C. Model predictions

The estimated averaged SRTs of the NH and HI listeners based on their individual fitted psychometric curves can be found in Figure 5, along with the predictions of the two versions of the model. Figure 6 presents the corresponding SRMs. The individual predictions of the HI listeners can be found in the supplementary materials (Suppl. Fig. 5). As the model only uses the audiograms as individual inputs, it gives very similar prediction for the NH listener and cannot predict their individual variability (Lavandier et al., 2021). Thus, the
<figure><img src="image_6.png" /><figcaption>FIG. 5. Mean estimated SRTs with standard errors across listeners within each group, along with the predictions of the two model versions.</figcaption></figure>

individual predictions of the NH listeners are not shown. The performance statistics of the two models can be found in Table II, and a comparison of SRT differences between groups and conditions can be found in Table III.

The *cueille-broadband* model has worse performance statistics than the *cueille-spectrum* version for the mean SRT predictions. The *cueille-broadband* version greatly overestimates the effect of hearing loss on speech intelligibility, especially for the symmetric HI listeners as highlighted in Figure 5 and in the individual predictions (Suppl. Fig. 5). The two model versions predict a similar difference between the anechoic room and the other rooms in the co-located configuration (Table III). This indicates that the effect of the temporal smearing of the speech and noise by reverberation is well predicted by both models. They also have similar performance statistics for the mean SRM predictions. They both underestimate SRM
<figure><img src="image_7.png" /></figure>

FIG. 6. Mean estimated SRMs with standard errors across listeners within each group, along with the predictions of the two model versions.

in the asymmetric configuration and overestimate SRM in the symmetric configuration, as highlighted in Figure 6.

## IV. DISCUSSION

The statistical analysis of the results evidences an absence of difference of the overall effect of reverberation between listener groups, as can be seen with ANOVA 1 and 3. This is in accordance with the results of Cueille et al. (2022), who tested NH and HI listeners in monaural conditions, and found a statistical absence of interaction between reverberation and hearing loss. The present study extends their results to binaural conditions and real-room reverberation. Xia et al. (2018) compared NH and aided HI listeners in binaural conditions at several reverberation levels and found a weak, yet significant difference in the
<table><caption>TABLE II. Pearson correlation coefficient, mean and largest absolute errors between data and predictions obtained with the *cueille-spectrum* and *cueille-broadband* models. Data and predictions are averaged across listeners within each group (mean SRT, mean SRM) or individual data/predictions are considered for the three HI groups.</caption><thead><tr><th>Dataset</th><th>cueille-spectrum</th><th>cueille-broadband</th></tr></thead><tbody><tr><td>Mean SRT</td><td>0.81, 1.2 dB, 3.5 dB</td><td>0.76, 2.2 dB, 6.1 dB</td></tr><tr><td>Mean SRM</td><td>0.46, 1.7 dB, 4.6 dB</td><td>0.53, 1.7 dB, 4.6 dB</td></tr><tr><td>Individual SRT (symmetric HI)</td><td>0.55, 2.3 dB, 7.3 dB</td><td>0.28, 4.8 dB, 18.1 dB</td></tr><tr><td>Individual SRT (HI-worse left ear)</td><td>0.63, 2.2 dB, 6.7 dB</td><td>0.7, 2.3 dB, 7.6 dB</td></tr><tr><td>Individual SRT (HI-worse right ear)</td><td>0.68, 2.8 dB, 8.5 dB</td><td>0.79, 2.6 dB, 10.1 dB</td></tr></tbody></table>

446 effect of reverberation between the two groups. They were unsure whether this was due to 447 a real difference of effect of reverberation between groups, or to ceiling effects. The present 448 study goes further by proving the absence of such interaction using Bayesian statistics. This 449 implies that there would be no additional adverse effects of reverberation for HI listeners 450 compared to NH listeners.

451 All listener groups experienced a significant effect of reverberation in this study, as can 452 be seen in (Figure 3). In the co-located configuration, in which there is no binaural effects 453 involved and reverberation can impair intelligibility only through the temporal smearing of 454 the target speech and the decrease of the dip listening benefit, the listeners had significantly 455 worse scores in the amphitheater than in all other rooms. There was no significant differences
<table><thead><tr><th>SRT difference</th><th>Data</th><th>cueille-spectrum</th><th>cueille-broadband</th></tr></thead><tbody><tr><td>NH-HI (symmetric) (dB)</td><td>-3.6</td><td>-4.1</td><td>-9.8</td></tr><tr><td>NH-HI (worse left ear) (dB)</td><td>-0.3</td><td>-0.6</td><td>-2.1</td></tr><tr><td>NH-HI (worse right ear) (dB)</td><td>-3.3</td><td>-2.6</td><td>-5.9</td></tr><tr><td>anechoic room-reverberant rooms (coloc) (dB)</td><td>0.5, -0.7, -1.5</td><td>-1.1, -0.5, -2.6</td><td>-0.5, -0.12, -2.3</td></tr><tr><td>sym-coloc (anechoic room) (dB)</td><td>-0.4</td><td>-2.1</td><td>-1.5</td></tr><tr><td>asym-coloc(anechoic room) (dB)</td><td>-5.4</td><td>-3.8</td><td>-3</td></tr></tbody></table>

TABLE III. Comparisons of mean SRT differences in the experiment and in the predictions of the *cueille-spectrum* and *cueille-broadband* models. The differences between groups show the prediction of hearing loss. The differences between the anechoic and other rooms (office 1, office 2, amphitheater) show the prediction of the effect of reverberation. The differences between spatial configurations illustrate the prediction of SRM.

between the anechoic room and the two offices. This is not surprising as the two offices have low reverberation levels in comparison to the amphitheater (Table I). There was a significant difference between the first and the second offices for the symmetric listeners. This is due to the scores in the first office being slightly (but not significantly) better than those in the anechoic room.

Even in the amphitheater, the detrimental effect of reverberation impairs intelligibility by only up to 10% word correct, which is lower than observed in other studies. For example, Cueille et al. (2022) tested NH and HI listeners in simulated rooms with RTs ranging from
0.5 s to 1.5 s, and found a score decrease of 20% to 30% due to these monaural effects of reverberation. Xia et al. (2018) tested NH and aided HI listeners in rooms with RTs going from 0.6 s to 1.88 s, and obtained score decreases of 10% to 25% due to reverberation. There is some evidence that matrix speech materials are more resistant to reverberation (Rennies et al., 2014). However, Cueille et al. (2022) used the FRmatrix test and Xia et al. (2018) used the Speech Pattern Contrast test, which is also a closed-set speech material, so this would not explain the differences reported here. There is also no strong evidence that these differences could be explained by the masking noise. Cueille et al. (2022) used the same vocoded speech as the one tested here. Xia et al. (2018) used a babble noise, a competing talker, or no masker. They observed a significant interaction between reverberation and masker type, but they were not able to draw more precise conclusions regarding this interaction. Regardless of the masker type, the effect of reverberation measured by Xia et al. (2018) decreased the intelligibility scores by 10 to 25%, which is higher than what was observed in the present study. Another explanation could be that reverberation times no higher than 1.3 s, while Xia et al. (2018) and Cueille et al. (2022) used virtual rooms with reverberation times up to 1.88 s and 1.5 s, respectively. This would be in accordance with Lavandier and Culling (2008), who tested NH listeners in simulated rooms with DRR from 0.6 to -10 dB and obtained a significant effect of reverberation on the target speech only for the DRR of -10 dB (which is in the range of the -8.5-dB DRR of the amphitheater tested here), showing that the temporal smearing of the target speech impairs intelligibility only at high levels of reverberation. It is also important to mention that Xia et al. (2018) tested HI listeners
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wearing hearing aids. Amplification and other signal processing like noise reduction could
also have altered the detrimental effect of reverberation in their study.

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In the present study, both the NH and HI listeners experienced SRM (Figure 4). As ex-
pected (Table I), SRM was significantly larger in the asymmetric configuration, which allows
for both better-ear listening and binaural unmasking, than in the symmetric configuration,
in which there is much less better-ear listening (with no long-term better ear available).
SRM was significantly reduced by reverberation in the asymmetric configuration, in the
first office and the amphitheater (also as expected, Table I). In the spatial configuration, a
slightly higher SRM was observed in the second office, with a SRM of 0.9 dB in the anechoic
room, and a SRM of 2 dB in the second office for the NH listeners. The model developed
by Jelfs et al. (2011) predicted a SRM of 0.3 dB in the anechoic room and a SRM of 2.1 dB
in the second office. The high SRM in the second room comes from the better-ear listening
component of the model, as in this spatial configuration the predicted binaural unmasking
is under 0.5 dB in all rooms. This could imply that room coloration increased SRM in the
second office. Such an effect of coloration on speech intelligibility has been reported before
(Collin and Lavandier, 2013). The Jelfs model also slightly underestimates SRM in the ane-
choic room, which could be due to the model not taking into account the modulations of the
masker and better-ear glimpsing. The model from Cueille and Lavandier (2025) predicts a
SRM of 2.7 dB in the anechoic room, and a SRM of 0.8 dB in the second office for the NH
listeners. The high SRM predicted in the anechoic room was already observed by Cueille
and Lavandier (2025) with a dataset involving a similar symmetric configuration in the first
office tested here (experiment four of Collin and Lavandier (2013)). This could be due to

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a “sluggishness” of the binaural system, which induces a poorer temporal resolution than
the monaural system and decreases its performance (Vicente and Lavandier, 2020). The two
model versions account for this binaural sluggishness in its binaural unmasking component,
but not in its better-ear listening component. This SRM overestimation in the anechoic room
could mask the effect of room coloration on speech intelligibility in the other rooms for this
configuration.

The SRM measured in the asymmetric configuration is larger than what other studies
with similar conditions obtained. For example, Lavandier et al. (2012) tested NH listeners
with the BRIRs of the first office, with the masker noise in front of the listener and the
target speech 25° to its right. They obtained a SRM of 2.6 dB, against 5 dB here. In their
fourth experiment, Collin and Lavandier (2013) also measured the SRTs of NH listeners
with the BRIRs of the first office. The target source was located in front of the listener and
a two-voice modulated masker source was located 25° to its right (while it was 25° to its left
in the present study). They also found a SRM of 2.5 dB. The difference between the SRM
measured by Lavandier et al. (2012) and Collin and Lavandier (2013) and the one obtained
here might be due to the speech material used. In the present experiment, predictable
sentences from the FRmatrix test were used, for which there was only 10 options for each
keyword in this closed set speech material, while unpredictable sentences from open set
speech materials were used in the other studies mentioned. There is some evidence that the
benefit derived from amplitude fluctuations in the masker is higher with predictable target
sentences (Best et al., 2019; Schoof and Rosen, 2015). The SRM measured here might have
been similarly increased by the predictability of the words of the FRmatrix test. A short
glimpse at a word might be sufficient to guess it. Even if it is only slightly unmasked, it can
be fully guessed. Such guessing is more complicated with open set materials, which would
then lead to smaller release from masking, both for SRM and dip listening.

It appears that NH and symmetric HI listeners similarly benefited from SRM in the present study. This is surprising, as among the studies from the literature which evaluated SRM for HI listeners, many found that the HI listeners experienced significantly less SRM (see Glyde et al. (2011) for a review of the effects of hearing loss and age on SRM). Dubno et al. (2002) did an intelligibility test with HI and NH listeners of various ages with a non-predictable speech target and an unintelligible noise in two spatial configurations: one where the speech and masker sources were co-located and one where there was a 90° azimuth separation between the sources. They found that the HI listeners experienced less SRM than the NH listeners. Gelfand et al. (1988) tested HI and NH listeners in similar spatial configurations with a predictable speech target and a babble noise and also found that the HI listeners benefited less from SRM. Arbogast et al. (2005) tested HI and NH listeners with predictable sentences, and unintelligible and intelligible maskers. They found that the HI listeners experienced similar SRM as the NH listeners with intelligible maskers, but significantly less SRM than NH listeners with unintelligible maskers. Glyde et al. (2013) tested NH and HI listeners with various ages and degrees of hearing loss with unpredictable sentences and an intelligible masker, and found that HI listeners experienced significantly less SRM. However, they only used intelligible maskers introducing informational masking. This complicates the comparison with the present study that only involves energetic masking. Vicente et al. (2021) compared binaural unmasking of NH and HI listeners with predictable
speech as a target, and vocoded speech and speech-shaped noise as maskers. They found
that the HI listeners experienced slightly less binaural unmasking. Overall, among these
studies, the most similar to the present study are those of Vicente et al. (2021), which used
vocoded speech as masker, and Gelfand et al. (1988), which used predictable sentences as
target speech. Both found that HI listeners experienced a significantly lower SRM than NH
listeners. The lack of SRM difference between HI and NH listeners here could be partly
explained by the linear amplification applied to the stimuli of the HI listeners, which might
have partially restored audibility and thus their better-ear listening advantage. This would
be in accordance with the results of Rana and Buchholz (2018), who found that restoring
audibility restores better-ear listening. However, a linear amplification was also applied to
the stimuli of the HI listeners in some of the mentioned studies (Dubno et al., 2002; Glyde
et al., 2013; Vicente et al., 2021).

The two groups of asymmetric HI listeners obtained overall similar results (Figures 3 and 4). ANOVA 3 showed a statistical lack of difference of the effect of spatial configuration between the two groups. ANOVA 4 was inconclusive regarding any SRM difference between groups, with a Bayes factor leaning toward the absence of difference. This is surprising, because in the asymmetric configuration the HI listeners with a worse right ear had the noise source on the side of their good ear and should have experienced less SRM than the HI listeners with a worse left ear. This could be due to an insufficient sample size, as the asymmetric listener groups are small. The asymmetric HI listeners also show important individual variations in hearing loss and hearing loss asymmetry, which could have affected their results. However, the Monte Carlo power analysis based on their results indicates
that the difference of SRM between groups would only be present with a very large number of listeners (85 in each group), indicating that the effect is small and probably negligible. This absence of effect might also be due to an insufficient degree of asymmetry for the tested listeners: in this study, the criterion was a 10 dB difference between the two ears, which is relatively low. It could also be due to the amplification applied to the stimuli. In order to make sure that the good ear did not receive too loud stimuli, the gain was applied independently at the two ears, depending on the audiogram of each ear. This method partially compensated for the hearing loss asymmetry of the listeners and might have reduced the SRM difference between groups. This would imply that the effect of asymmetry on SRM is probably negligible for aided HI listeners in realistic rooms, except for large or non-compensated degrees of asymmetry. It would be interesting to extend the present study by testing HI listeners with larger degrees of asymmetry.

The data collected here also allowed to test the model developed by Cueille and Lavandier (2025) for the effects of hearing loss, reverberation and SRM. The only other dataset with HI listeners and SRM on which the model was tested before (Vicente et al., 2021) used artificial BRIRs with no head simulated for the listener and no temporal smearing of the target speech by reverberation (only nearby targets). Cueille and Lavandier (2025) tested two methods to implement the internal noise simulating hearing loss. Here, the *cueille-broadband* version greatly overestimates the effect hearing loss for the symmetric HI listeners. This further supports the initial findings of Cueille and Lavandier (2025), who found that the *cueille-broadband* version overestimated the SRTs for HI listeners with a high degree of hearing loss. As the symmetric HI listeners tested in this study have a large hearing loss, the internal
noise level is so high that it creates a large overestimation of the SRTs, as can be seen in
the individual predictions (Suppl. Fig. 5). This is because the *cueille-broadband* version
predicts a higher internal noise level than the *cueille-spectrum* version. For example, with
the *cueille-broadband* version, the mean internal noise level (across ears and frequency) of the
symmetric HI listener with the highest hearing loss (mean PTA4 of 69 dB HL across ears) is
of 77 dB SPL in the co-located configuration in the anechoic room. With the *cueille-spectrum*
version, the corresponding level is 58 dB SPL. This leads to an overestimation of the SRT
by 11 dB with the *cueille-broadband* version, while the *cueille-spectrum* version accurately
predicts the SRT of this listener with an error below 0.1 dB. To improve the *cueille-broadband*
version, it would be necessary to introduce a floor in the better-ear component of the model,
as proposed by Lavandier et al. (2021). However, to add this modification, the model must
take as input the average SRTs across listeners in each condition, which makes it impossible
to predict SRT differences across both listeners and conditions (see Lavandier et al. (2021)
for a detailed discussion on this issue).

Cueille and Lavandier (2025) also found that the *cueille-spectrum* version of the model
tended to slightly underestimate the SRTs of HI listeners with a mild hearing loss. However,
with the present dataset, the performances of these listeners appear to be more underes-
timated with the *cueille-broadband* version, as can be seen with the individual predictions
(Suppl. Fig. 5). For example, the mean internal noise level of one of the HI listener with
a mild hearing loss (mean PTA4 of 30 dB HL across ears) in the co-located configuration
in the anechoic room is of 33 dB SPL with the *cueille-broadband* model against 29 dB SPL
with the *cueille-spectrum* model. The predicted SRT is underestimated by 3.5 dB with the
cueille-broadband model and only by 1.5 dB with the cueille-spectrum model. As the models can only predict differences between SRTs, it is necessary to fit the mean of the model predictions to the mean of the measured SRTs across listeners and conditions. With the cueille-broadband model, there are large errors for the predictions of the HI listeners with high hearing loss, which affect the mean of the model predictions. This makes it impossible to focus on the predictions of the HI listeners with low hearing loss, as they are affected by the prediction errors of the HI listeners with high hearing loss. The predictions of the cueille-spectrum model are not biased by such errors, which makes it possible to see the slight underestimation of the SRTs of the HI listeners with a low hearing loss.

The only difference between two model versions tested here is the implementation of internal noise, which only affects the prediction of the effect of hearing loss. The two model versions give identical predictions for all effects unrelated to hearing loss. The effects of the temporal smearing of the speech and noise by reverberation are well predicted by both models. However, for all listener groups, both models underestimates the SRM in the asymmetric configuration, (Figure 6). At first, this appears surprising as the model has been previously shown to accurately predict SRM. Cueille and Lavandier (2025) tested the model with three datasets involving SRM. Both the cueille-broadband and the cueille-spectrum versions gave accurate predictions and good performance statistics, with correlations between data and predictions higher than 0.91, mean prediction errors lower than 0.9 dB, and largest prediction errors lower than 1.9 dB. The SRM underestimation observed here might be partly due to the speech material used. As explained above, the SRM might have been increased by the predictability of the words used. This is something that both models tested
here cannot predict. The good performances of these models were almost always obtained for datasets involving unpredictable sentences from open set materials (Bench et al., 1979; IEEE, 1969; Raake and Katz, 2006), and nothing in the model input takes into account the predictability of the target speech. The only dataset using a matrix test on which they were tested was the one of Cueille et al. (2022), which was a monaural experiment without any SRM. The SRM predicted here is close to the SRM values obtained in experiments using open set materials in similar rooms/configurations. As explained above, Lavandier et al. (2012) and Collin and Lavandier (2013) both obtained a SRM of 2.5 dB for NH listeners and an asymmetric configuration in the first office, while our model predicts a SRM of 2.1 dB in this room in a comparable configuration. It is also interesting to note that the two models overestimate SRM in the symmetric configuration in the anechoic room and the first office. This was already observed when tested on the experiment 4 of Collin and Lavandier (2013), which included the same symmetric configuration. This could be due to binaural sluggishness not being taken into account in their better-ear listening component (Vicente et al., 2020).

Overall the *cueille-spectrum* model appears to more accurately predict the effect of hearing loss than the *cueille-broadband* model. Its only drawback is its underestimation of the SRTs for HI listeners with mild hearing loss, that is to say its underestimation of the effect of hearing loss for HI listeners who do not have much more hearing loss than NH listeners. This has much less effect on the predictions than the large overestimations of the *cueille-broadband* model for the HI listeners with high hearing loss. Compared to Cueille and Lavandier (2025), the presents study points to the better performances of the *cueille-spectrum* model. Further
661 testing is required as the variations of SRM due to the speech material still cause some issues.

662

663 V. CONCLUSION

664 An intelligibility experiment was done for NH and HI listeners with various degrees of
665 hearing loss in order to compare their performances in binaural conditions and reverberant
666 environments. HI listeners with symmetrical hearing loss were found to be as affected as
667 NH listeners by reverberation. They also similarly benefited from SRM. This last result
668 could be partly due to the linear amplification applied to the stimuli of the HI listeners,
669 which has partially restored audibility and thus SRM. HI listeners with an asymmetrical
670 hearing loss did not suffer from a reduced SRM either. This might also be explained by
671 the linear amplification that was applied independently at each ear, and thus compensated
672 at least partly for the hearing loss asymmetry. The estimated SRTs were also compared
673 to predictions from two versions of a binaural speech intelligibility model. The version
674 with an internal noise based on the broadband level of the external stimuli overestimated
675 the SRTs for the HI listeners with a high degree of hearing loss. The version defining the
676 internal noise based on the spectrum of the external stimuli gave more accurate predictions.
677 The two versions underestimated the measured SRM, which was also larger than the SRM
678 previously measured in similar conditions with open-set speech materials, as opposed to the
679 closed-set material used here.
ACKNOWLEDGMENTS, AUTHOR DECLARATIONS AND DATA AVAILABIL-
ITY STATEMENT

This work was conducted within the LabEx CeLyA (Grant No. ANR-10-LABX-0060).

It has received funding from the European Union's Horizon Europe research and innovation program under grant agreement No 101129903. The authors state that they have no conflict of interests to disclose. They acknowledge Maxime Bonneuil, audioprothesist, for his precious help in recruiting hearing-impaired participants with particular audiometric specifications. They would also like to thank the HörTech gGmbH company who allowed to use the copyright-protected audio material of the French Matrix Test. The data from the experiment will be made publicly available on Zenodo.

SUPPLEMENTARY MATERIALS

See supplementary materials at [URL will be inserted by AIP] for the mean fitted psy-
chometric functions of each listener group and their parameters, the tables containing the
results of the statistical tests, and the individual predictions of the two versions of the model.

<footnote n="1">¹See supplementary materials at [URL will be inserted by AIP]</footnote>

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