Cross-frequency weights in normal and impaired hearing: Stimulus factors, stimulus dimensions, and associations with speech recognition

Abstract

Previous studies of level discrimination reported that listeners with high-frequency sensorineural hearing loss (SNHL) place greater weight on high frequencies than normal-hearing (NH) listeners. It is not clear whether these results are influenced by stimulus factors (e.g., group differences in presentation levels, cross-frequency discriminability of level differences used to measure weights) and whether such weights generalize to other tasks. Here, NH and SNHL weights were measured for level, duration, and frequency discrimination of two-tone complexes after measuring discriminability just-noticeable differences for each frequency and stimulus dimension. Stimuli were presented at equal sensation level (SL) or equal sound pressure level (SPL). Results showed that weights could change depending on which frequency contained the more discriminable level difference with uncontrolled cross-frequency discriminability. When cross-frequency discriminability was controlled, weights were consistent for level and duration discrimination, but not for frequency discrimination. Comparing equal SL and equal SPL weights indicated greater weight on the higher-level tone for level and duration discrimination. Weights were unrelated to improvements in recognition of low-pass-filtered speech with increasing cutoff frequency. These results suggest that cross-frequency weights and NH and SNHL weighting differences are influenced by stimulus factors and may not generalize to the use of speech cues in specific frequency regions.

I. INTRODUCTION

The peripheral effects of sensorineural hearing loss (SNHL) include elevations in auditory thresholds as well as suprathreshold perceptual deficits even when acoustic stimuli are made sufficiently audible. These include reduced frequency selectivity (e.g., Kidd et al., 1984; Moore and Glasberg, 1986; Tyler et al., 1983), poorer frequency discrimination (e.g., Moore and Peters, 1992; Nelson and Freyman, 1986), abnormal temporal integration (e.g., Chung, 1981; Kidd et al., 1984), poorer temporal resolution (e.g., Fitzgibbons and Wightman, 1982; Nelson and Freyman, 1987), and abnormal growth of loudness (e.g., Steinberg and Gardner, 1937; Buus and Florentine, 2002) compared to normal-hearing (NH) listeners. SNHL with its characteristic loss of audibility and reduced suprathreshold discriminability of various features, often varies in degree across frequency. Most commonly, SNHL is more severe in the high frequencies than in the low frequencies (e.g., Davis, 1989), although other hearing loss configurations are possible.

The central consequences of SNHL—and in particular SNHL varying in degree across frequencies—are not well understood. There has been some suggestion that SNHL (and its consequences) that varies in degree across frequency can lead to changes in how a listener relies on/weights low- vs high-frequency information. Prior studies have suggested that listeners with high-frequency hearing loss may learn over time to rely less on high-frequency information than low-frequency information because of experience with the reduced audibility and corresponding suprathreshold effects (e.g., greater distortion of stimulus features) in the high frequencies (e.g., Moore and Vinay, 2009; Seldran et al., 2011; Varnet et al., 2019). However, other studies employing different methods have drawn the opposite conclusion—that listeners with poorer high-frequency hearing place more weight on the high frequencies where there is greater hearing loss than do NH listeners (e.g., Doherty and Lutfi, 1996, 1999). Resolving this discrepancy could have implications for choosing among strategies for remediating hearing loss. For example, providing amplification in frequency regions that receive little weight from a listener with a high-frequency hearing loss could increase the overall speech levels unnecessarily, limiting the potential benefit of a hearing aid.

The current study, consisting of two experiments, represents an in-depth examination of cross-frequency weights in listeners with NH and SNHL. First, in experiment 1, we investigated whether the differences in weights between the groups can be explained by stimulus factors rather than by central changes in weighting directly related to peripheral hearing loss. Second, in experiment 1, we examined the extent to which weighting patterns generalize across stimulus dimensions. If cross-frequency weights reflect how cross-frequency information is used in a general sense, it might be expected—with proper implementation of experimental methods—that the same general weighting patterns for each listener and the same NH and SNHL differences would be observed regardless of task or stimulus changes. Third, in experiment 2, we assessed how well weights relate to the recognition of speech that varies in high-frequency content. If weights reflect general use of cross-frequency information, it might also be predicted that these weights would manifest in the way the information in speech is used across frequency.

A. Prior weighting studies

Psychophysical reverse correlation weighting techniques [see the conditional-on-a-single-stimulus procedure (COSS) in Berg (1989, 1990); also see Dai and Micheyl (2010)] are commonly used to assess the contributions of individual frequency components to the overall perception of a stimulus in terms of its strength along a particular dimension (e.g., overall loudness). In one relevant implementation of this approach employed by Doherty and Lutfi (1996) and Jesteadt et al. (2014), among others, a multitone complex—typically with six tones—with widely spaced frequency components is presented in two intervals of an experimental trial (or using a single-interval YES-NO task; see Berg, 1989). On each presentation, the level of each frequency component in each interval is randomly and independently drawn from a Gaussian distribution of levels having a mean and variance specified by the experimenter. Typically, the components in the two intervals are drawn from distributions with different means (but equal variances), and listeners are instructed to indicate which interval had components drawn from the distribution with the higher mean level (“sample discrimination”; Doherty and Lutfi, 1996; Kortekaas et al., 2003; Leibold et al., 2009; Jesteadt et al., 2014), or listeners are instructed to indicate which interval was “louder” (Leibold et al., 2007). Jesteadt et al. (2014) demonstrated that equivalent weights are obtained if all components in each interval are drawn from the same distribution and listeners indicate which interval was “louder.” The difference in level between the two intervals at each frequency on each trial is regressed against the listener's response (selection of an interval) on each trial, yielding regression coefficients for each frequency. The regression coefficients are normalized to sum to 1, and these normalized coefficients are considered to be the relative “weights” (Berg, 1989; Lutfi, 1995; Richards and Zhu, 1994; Kortekaas et al., 2003; Dai and Micheyl, 2010).

In most weighting studies pertaining to loudness perception, the typical NH weighting pattern across frequency approximates a “bowed” shape with greater weight placed at the lowest and highest frequencies than on the mid frequencies (e.g., Leibold et al., 2007, 2009; Kortekaas et al., 2003; Jesteadt et al., 2014). Standard peripheral-based loudness models do not predict these patterns of weights (Jesteadt et al., 2014; Joshi et al., 2016), possibly because the weighting patterns reflect an “edge effect” where gain is applied to spectral edges in loudness perception at some central (rather than peripheral) stage of processing (Joshi et al., 2016).

Some studies have compared listeners with NH and listeners with SNHL in their weighting of frequencies for the overall perception of loudness. Doherty and Lutfi (1996) showed that the majority of the listeners with SNHL with greater hearing loss in the high frequencies placed greater weight on the high-frequency components relative to NH listeners. In contrast, Jesteadt et al. (2017) reported that the listeners with SNHL (most of whom also had poorer hearing in the high frequencies than low frequencies) put less weight on the high frequencies than did NH listeners. However, no corrections for audibility were made for listeners with hearing loss in that study, and thus some frequencies on some trials likely were near threshold or inaudible. Thrailkill et al. (2019), using the procedures of Jesteadt et al. (2017), confirmed that in listeners with high-frequency SNHL, weights were greater in the low frequencies than in the high frequencies relative to NH listeners without frequency-specific amplification but changed to reflect greater weight on the high frequencies and less weight on the low frequencies when amplification was provided. In another study, Doherty and Lutfi (1999) showed that the same pattern of differences in cross-frequency weights between listeners with NH and SNHL remained to some extent even when listeners were instructed to judge the level of a particular target tone in a multitone complex.

Whether these results reflect genuine differences between listeners with NH and SNHL in cross-frequency weighting, rather than stimulus differences between groups, currently is unclear. Several studies have demonstrated the effects of increasing level [e.g., increasing the mean level from 55 to 70 dB SPL while maintaining the same standard deviation (SD) of the distributions from which levels are sampled] on the weights obtained. Even within NH listeners, increasing the mean level results in increased relative weights at higher frequencies (Leibold et al., 2009; Jesteadt et al., 2014) independent of sensation level (SL) at those frequencies (Leibold et al., 2009). Of the studies that tested listeners with NH and SNHL, Doherty and Lutfi (1996, 1999) and Thrailkill et al. (2019) presented higher mean sound pressure levels (SPLs) of the tones for the listeners with SNHL to ensure sufficient audibility but did not test the NH listeners at the same higher SPLs. As such, the finding of greater weight at the higher frequencies in the SNHL group may have been due to the overall higher SPLs rather than to the suprathreshold perceptual consequences of hearing loss per se. Jesteadt et al. (2017) presented the stimuli at the same mean SPL to both groups, but the levels were fairly low and the authors determined that audibility (low SL) was an issue for some listeners with SNHL at some frequencies. Thus, the reduced weight in the high frequencies for the listeners with SNHL may have been due to the low SL at these frequencies. To our knowledge, no studies have tested NH listeners at the same high mean SPL as listeners with SNHL.

Another potentially important issue when comparing weighting patterns for listeners with NH and SNHL is the range of stimulus levels that may be presented (i.e., the SD of the distribution from which levels are sampled), which directly impacts the size and range of level differences that may be presented between intervals. It is possible that the stimulus level ranges or, more directly, the level differences may need to be adjusted for listeners with SNHL relative to those with NH to account for factors such as loudness perception and the variability in feature discriminability [e.g., just-noticeable differences (JNDs)]. Furthermore, given that discriminability JNDs vary across listeners even within NH and SNHL groups (e.g., Schroder et al., 1994) and given the fact that severity of suprathreshold deficits in SNHL listeners can vary across frequencies, the level ranges may need to be adjusted across frequency on an individual basis. If the level selection ranges are not adjusted for each listener and frequency, then listeners may modify their weighting strategy based on relative cross-frequency discriminability of the stimulus, which could hinder our ability to determine general weighting differences between listeners with NH and SNHL. For example, if the majority of trials present level differences that are barely discriminable at some frequencies but are highly discriminable at other frequencies for certain listeners, then these listeners could place greater weight on the more discriminable tones when they may not have done so otherwise. To avoid this potential stimulus-related influence on weights that could vary across listeners, it may be more appropriate to equate not the external level ranges but rather the internal level ranges based on listener- and frequency-specific sensitivity.

Some previous studies comparing perceptual weights in listeners with NH and SNHL have acknowledged the need to adjust the stimulus level ranges to account for differences in discriminability between groups. For example, Doherty and Lutfi (1999) employed a distribution SD of 5 dB for listeners with NH but reduced the SD to 3 dB for listeners with SNHL to compensate, likely in part, for expected differences in loudness perception due to loudness recruitment. However, the same correction was applied for all listeners with SNHL without taking into account individual perceptual abilities. More typically, a single distribution range is used. In Doherty and Lutfi (1996) and Jesteadt et al. (2014), the level distribution had a SD of 5 dB. In Jesteadt et al. (2017) and Thrailkill et al. (2019), the distributions were rectangular and the levels ranged from −6 to +6 dB around the mean level in 1 dB steps. Importantly, in all of these studies, the same level range was applied across frequencies. It is not known whether these level ranges were sufficient to yield valid weights despite the variations in sensitivity to the presented level differences across listeners and frequencies. Other studies have concluded that the distribution level range—at least for listeners with NH—generally should not alter weighting estimates, except in cases where the external level variations are either very large or not discriminable with respect to internal sensitivity (see Lutfi, 1989; Jesteadt et al., 2003; Dai and Micheyl, 2010). However, in comparisons between listeners with NH and SNHL, the possible role of significant differences in stimulus resolution and salience—across frequency within a listener and across listeners according to the magnitude and configuration of hearing loss—raises questions about the interpretation of patterns of weights.

The weighting studies described earlier examined cross-frequency weights with respect to the overall loudness of a multitone complex. A few previous studies have looked at the consistency of weights across stimulus dimensions in listeners with NH (e.g., intensity discrimination and interaural time difference discrimination; Dye et al., 2005), but to our knowledge none have compared listeners with NH and SNHL in their weights across stimulus dimensions. If the weights obtained in the loudness tasks reflect the general use of cross-frequency information, we might expect consistent weights—and consistent NH vs SNHL differences in weights—regardless of the stimulus dimension of the discrimination task.

None of the weighting studies discussed earlier tested the hypothesis that alterations in weights in listeners with SNHL are due to the unevenness in hearing loss and/or the variability in suprathreshold processing resolution across frequencies. Because the listeners with SNHL tested in those studies had predominantly high-frequency hearing loss, it is not known if weights follow the regions of greater hearing loss. For example, it is not known whether listeners with greater hearing loss in the low frequencies would show greater weighting of low frequencies rather than high frequencies. Furthermore, if cross-frequency weights are not universal across stimulus dimensions, then it is uncertain whether listeners with SNHL would show greater asymmetries in weights for stimulus dimensions for which there are clear SNHL-related deficits in discriminability (i.e., frequency discrimination; Zurek and Formby, 1981).

To summarize the first two questions, it is not clear whether differences in the patterns of weights found between listeners with NH and SNHL were due to the stimulus factors noted earlier or to centrally based differences in the use of cross-frequency information. Furthermore, it is not known how the weighting patterns (and any differences between listeners with NH and SNHL) generalize to multiple stimulus dimensions such as frequency or duration discrimination. It is also not known if alterations in cross-frequency weights in listeners with SNHL are directly linked to the unevenness in the hearing loss and/or suprathreshold deficits (e.g., discriminability of features) across frequency or if there are greater alterations in weights for stimulus dimensions with known SNHL-related deficits.

B. Associations with speech recognition

The third question focuses on whether/how cross-frequency weights relate to the use of cross-frequency information in more ecologically relevant stimuli such as speech. If uneven hearing loss across frequencies induces alterations in the general use of cross-frequency information, it might also manifest in the use of speech information in different frequency regions for the task of speech recognition. Calandruccio and Doherty (2008) compared listeners with NH and SNHL in their weighting of different frequency bands for sentence recognition in noise. They employed the psychophysical reverse correlation weighting technique described earlier for pure-tone stimuli, except in this case, there were random and independent variations in the signal-to-noise ratio (SNR) in each frequency band from trial to trial. They reported relatively greater weight for the highest-frequency band (2807–11 000 Hz) in listeners with SNHL than in listeners with NH. However, Calandruccio et al. (2016) showed that presenting higher-level stimuli to the listeners with NH resulted in similarly high weights on the highest-frequency band compared to the listeners with SNHL. Generally, these sentence recognition weighting results were consistent with prior pure-tone weighting results (e.g., Doherty and Lutfi, 1996; Jesteadt et al., 2014) but were not entirely consistent with results from studies of the use of frequency information for speech recognition that used other methods.

Some other previous studies using different methods have suggested that listeners with high-frequency SNHL make less effective use of audible high-frequency speech information than listeners with NH (Ching et al., 1998; Hogan and Turner, 1998; Turner and Brus, 2001; Turner and Henry, 2002). Those studies used low-pass-filtered speech with a range of cutoff frequencies and compared speech recognition as a function of bandwidth by listeners with SNHL to predictions based on NH data over a range of bandwidths and articulation index (AI) values (ANSI, 1997). However, results of other studies indicate that lack of benefit of the high-frequency content of filtered speech for listeners with SNHL may be related to cochlear dead regions (Vickers et al., 2001; Baer et al., 2002), while still others have reported that listeners with SNHL do not differ from NH listeners in their use of high-frequency speech information as long as individualized gain is provided (Horwitz et al., 2008). On a conceptual level, the relationship between perceptual weights obtained from psychoacoustic discrimination tasks and the use of speech information in different frequency regions using filtered speech has not been established; nor have the two been linked empirically in studies comparing listeners with NH and SNHL.

C. Approach taken in the current study

In an attempt to answer the questions raised in Secs. I A and I B, two experiments were conducted that aimed to relate patterns of perceptual weights to the factors of stimulus audibility and resolution. In experiment 1, we tested NH listeners with small (if any) differences in detection thresholds across frequency and listeners with SNHL exhibiting a range of threshold differences across frequency to more directly test the hypothesis that alterations in cross-frequency weights correspond to the frequency regions with more severe hearing loss. We used a weight-derivation paradigm that incorporated four key methodological differences from previous studies. First, the stimulus comprised a two-tone complex rather than a six-tone complex. The two frequencies tested generally corresponded to a region of better hearing (750 Hz) and a region of poorer hearing (3500 Hz) in listeners with sloping hearing loss, although the opposite was the case in a few listeners with rising configurations of hearing loss. Using two frequencies allowed us to avoid issues of “edge effects” (e.g., Joshi et al., 2016) given that both tones are “edges” in our experiment. It was expected that two brief tones gated on and off simultaneously would still foster synthetic listening (Buss, 2008) and that listener judgments could still be modeled as a weighted sum of the two tones. Second, in contrast to previous studies, we measured discriminability JND psychometric functions at each frequency. In one task (a referent discrimination task), we employed strict stimulus control by only presenting level differences corresponding to specific discriminability values for each listener and frequency. In this case, unlike prior studies, the “weights” were estimated based on regression coefficients associated with changes in signal levels rather than random level variations. We also tested another task more similar to past weighting studies in which there was less control over the trial-by-trial discriminability because the stimulus levels were randomly drawn from distributions (although the SDs of the distributions were tailored to listener discriminability ranges). Third, in the task with strict stimulus control, we tested listeners' weights across different stimulus dimensions. The weighting studies described earlier examined cross-frequency weights obtained for judgments of loudness. In the present study, we employed a level discrimination task as before, but we also tested duration discrimination and frequency discrimination to investigate the generality of weighting patterns. Fourth, given the previous literature indicating that overall level influences findings, relative weights were measured in equal SL conditions—where the levels for the two frequencies were set to 15 dB SL—and in equal SPL conditions—where the levels for the two frequencies were set to a high SPL, and the level used for the NH group equaled the average of levels used for the SNHL group.

Tailoring the presented stimulus differences to each listener's JNDs at each frequency in the task with strict stimulus control (and ensuring audibility at each frequency in the equal SL condition) helped us to evaluate obtained weights in terms of central rather than audibility or discriminability differences. Our reasoning was that, if we presented stimuli with no cross-frequency asymmetries in audibility or discriminability and if weights were still related to threshold and discriminability asymmetries across frequency (which tend to be greater in listeners with SNHL), then these weighting changes may represent long-term exposure to these asymmetries in daily listening. Presumably, this experience ultimately would influence how a listener weights cross-frequency information. Measuring the JNDs also allowed us to determine the percentages of trials that presented discriminable differences at each frequency using level sampling methods of prior studies and allowed us to determine—in our task with less stimulus control—the impact of asymmetries in cross-frequency discriminability by calculating weights for subsets of trials in which one frequency was more discriminable than the other.

In experiment 2, we further tested the generalizability of the obtained weights by evaluating the use of high-frequency information in a low-pass-filtered speech recognition task in listeners with SNHL. Listeners participated in a speech filtering experiment replicating Horwitz et al. (2008). A relationship between listeners' use of this high-frequency speech information as measured in experiment 2 and the relative weights as measured in experiment 1 would support the view that weights represent a general alteration in the use of information in certain frequency regions.

II. EXPERIMENT 1

A. Methods

1. Listeners

Nine young adults (mean age = 22.56 years, SD = 4.07) with NH (including E.R.) and 13 young adults (mean age = 27.15 years, SD = 7.87) with SNHL participated in experiment 1. To increase the number of listeners with SNHL and to examine the influence of degree and direction of unevenness of SNHL across frequency on weights, enrollment requirements were not stringent with respect to degree or configuration of SNHL. Characteristics of the listeners with SNHL, including age, symmetry of hearing loss, onset of hearing loss, etiology of hearing loss, hearing aid experience, daily hearing aid use, and Abbreviated Profile of Hearing Aid Benefit (APHAB) scores, are shown in Table I. The individual audiograms of these listeners with SNHL and the average audiogram of the NH listeners are shown in Fig. 1.

TABLE I.

Individual characteristics of all listeners with SNHL. The ordering of columns is as follows: listener ID (ID), age, symmetry of hearing loss (Sym) [symmetrical (Sym), asymmetrical (Asym), bilateral (Bil), or unilateral (Uni)], onset of hearing loss (Onset of HL), etiology of hearing loss (HL etiology), hearing aid experience (HA exp), daily hearing aid use (Daily HA use), and scores from the APHAB, where higher scores indicate more problems.

ID	Age	Sym	Onset of HL	HL etiology	HA exp	Daily HA use	APHAB unaided	APHAB aided	APHAB benefit (unaided − aided)
HI1	25	Bil, Sym	Age 5	Unknown	>10 years	8–16 h	49.25	24.5	24.75
HI2	26	Bil, Sym	Childhood	Suspected genetic	None	None	12.67	—	—
HI3	44	Bil, Asym	Known since 3rd grade	Unknown	>10 years	8–16 h	80.17	38.79	41.37
HI4	21	Bil, Sym	Congenital	Premature birth	>10 years	1–4 h	29.21	28.88	0.33
HI5	29	Bil, Sym	Age 6	Unknown	>10 years	8–16 h	78.04	48.29	29.75
HI6	22	Bil, Sym	Congenital	Unknown	>10 years	None	40.71	39.29	1.42
HI7	20	Uni	Diagnosed 2 years ago (age 18)	Suspected childhood virus	None	None	21.58	—	—
HI8	36	Bil, Sym	Grade school	Suspected genetic	None	None	21.58	—	—
HI9	28	Bil, Asym	Congenital	Suspected genetic	>10 years	8–16 h	74.5	48.25	26.25
HI10	21	Uni	Congenital	Possibly premature birth	1-10 years	1–4 h	21.96	19	2.96
HI11	39	Bil, Asym	2 years ago (age 37)	Autoimmune	6 wks-11 months	1–4 h	29.92	30.29	−0.37
HI12	22	Bil, Asym	Congenital	Possibly premature birth	>10 years	8–16 h	68.83	51.42	17.41
HI13	20	Bil, Sym	Known since 1st grade	Suspected genetic	1-10 years	4–8 h	51.83	47.75	4.08

FIG. 1.

Audiograms for the listeners in experiment 1. Filled squares are the average audiograms for listeners with NH. All other symbols are for listeners with SNHL. The SNHL symbol legend is shown to the right, where each symbol indicates the listener ID. All audiograms are for the left ear except for HI7, HI9, and HI11.

As is apparent in Fig. 1, the listeners with SNHL were heterogeneous with respect to their hearing loss degree and configuration. The threshold equalizing noise (TEN) test (Moore et al., 2000) was administered to the listeners with SNHL to determine whether cochlear dead regions were present and to adjust target frequencies to avoid dead regions. The results of the TEN test indicated that no dead regions were detected in any listeners at any frequencies where the test could be administered. The TEN test could not be administered at 2 and 4 kHz for HI3; at 0.5, 0.75, and 1 kHz for HI9; or at 3 kHz for HI12 due to level limits of the audiometer or listener discomfort. In the main portion of experiments 1 and 2, the left ear was tested in all listeners except for HI7 (unilateral right-ear hearing loss) and HI9 and HI11 (both due to listener preference). Across experiments 1 and 2, listeners were run in 6–8 sessions, each totaling 2 h, and were paid for their participation.

2. Equipment

Listeners were seated in a double-walled sound attenuating booth. For the TEN test and audiogram, listeners wore ER-3A insert earphones (Etymotic Research, Inc., Oak Grove, IL) and registered responses via a response button. The TEN test was administered as a built-in test of the GSI Audiostar audiometer (Grason-Stadler, Eden Prairie, MN). For all other experiments, stimuli were generated using matlab version 2017b (MathWorks Inc., Natick, MA) software at a sampling rate of 44.1 kHz and delivered to an RME (Haimhausen, Germany) HDSP 9632 24-bit soundcard [audio stream input/output (ASIO)] and presented to one Sennheiser (Wedemark, Germany) HD280 Pro headphone corresponding to the test ear (see above). Listeners were seated in front of a computer monitor and registered responses via computer mouse click on a matlab graphical user interface (GUI).

3. Stimuli and procedures

Across all stages of experiment 1, two tones were presented, either in isolation or simultaneously as a two-tone complex. The base (shortest duration) tones were 150 ms with 5-ms raised cosine-squared onset and offset ramps. Two base frequencies were used (one low and one high), 750 and 3500 Hz. However, for two listeners with SNHL, one of the base frequencies was adjusted so that at least one of the tone frequencies fell in a region with greater than a mild hearing loss. For HI7, the upper frequency was shifted from 3500 to 4000 Hz. For HI10, the lower frequency was shifted from 750 to 1000 Hz. There were two base level conditions—one in which the levels of the two tones were set to equal SL (15 dB) and one in which the levels were set to equal SPL. In the equal SPL condition, for the listeners with SNHL, the base level of the tone with the poorest threshold was set to 15 dB SL, and the base level of the other tone was increased to the equivalent SPL. For the listeners with NH, the two tones were set to 85 dB SPL to approximate the average presentation level for listeners with SNHL, which was 85.76 dB SPL (range 66.75–110 dB SPL).

a. Quiet thresholds.

In the first stage of experiment 1 (section 1 of Table II), detection thresholds were measured in quiet for the low- and high-frequency tones separately using a three-interval, three-alternative forced-choice procedure. The base frequencies and durations were used. On each trial, the tone was presented in one randomly selected interval, and the other two intervals contained silence the same duration as the stimulus. The inter-stimulus interval was 500 ms, and there was a 500-ms silent buffer before the first interval and following the final interval, yielding a total single-trial stimulus duration of 2450 ms. The three temporal intervals were marked visually on the GUI. The listener selected the interval that contained the tone and was given correct/incorrect visual feedback. The level of the tone was adjusted with a two-down, one-up tracking procedure to estimate 70.7% correct (Levitt, 1971). The step size was 5 dB for the first two reversals and 2 dB for the last eight reversals. Threshold was taken as the average of the levels from the final eight reversals. For each frequency, there were two separate adaptive blocks of trials, and the final threshold was taken as the average of the thresholds from the two blocks.

TABLE II.

Data collection outline.

1. Quiet thresholds	Low-frequency tone
	High-frequency tone
2. Discriminability JNDs	Equal SL	Level	Low-frequency tone
			High-frequency tone
		Duration	Low
			High
		Frequency	Low
			High
	Equal SPL	Level	Low
			High
		Duration	Low
			High
		Frequency	Low
			High
3. Relative weights	Referent discrimination task (run first without feedback and then with feedback)	Equal SL	Level
			Duration
			Frequency
		Equal SPL	Level
			Duration
			Frequency
	Two-interval discrimination task (level only)	Equal SL	Discrete levels
			Continuous distribution
		Equal SPL	Discrete levels
			Continuous distribution

b. JNDs.

In the second stage of experiment 1 (section 2 of Table II), JNDs were measured for three different stimulus dimensions (level, duration, and frequency), for each base tone frequency (low and high), and for each base level condition (equal SL and equal SPL) separately. For each condition, two separate adaptive blocks of trials were run in a two-interval, two-alternative forced-choice procedure. The average of the thresholds from the two blocks was taken as the result. In all cases, the inter-stimulus interval was 500 ms specified between the offset of the first stimulus and the onset of the second stimulus. There was also a 500 ms silent buffer preceding the onset of the first stimulus and following the offset of the second stimulus. In all tasks, the intervals were marked visually on the GUI. These visual markers were equal in duration, even in the case of duration discrimination so as not to provide a visual cue. For each condition, correct/incorrect response feedback was provided after each trial.

For the level JND, both intervals contained a single tone with the same base frequency (either low or high, depending on the block) and duration (150 ms). In one interval, the tone was set to the base level corresponding either to 15 dB SL or to the specified SPL. In the other interval, the tone was incremented in intensity. The order of these intervals was randomized on each trial. The listener was instructed to select the “louder” interval. The size of the level increment, expressed as the Weber fraction in decibels, 10 log (ΔI/I), was increased or decreased relative to the previous trial using a three-down, one-up tracking procedure estimating 79.4% correct (Levitt, 1971). For the first block, the starting increment was a Weber fraction of 0 dB (corresponding to a 3.01 dB level difference between intervals), and for the second block, the starting increment was 5 dB higher than the Weber fraction JND estimate of the first block. The increment step size was 5 dB for the first two reversals and 2 dB for the final eight reversals. The level JND from each block was the average of the Weber fraction increments at the last eight reversals, and the JNDs from the two blocks were averaged.

For the duration JND, both intervals contained a tone with the same base frequency (either low or high) and base level (either according to the SL or SPL setting). In one interval, the tone was set to the base duration of 150 ms, and in the other interval, the tone was increased in duration. The order of these intervals was randomized on each trial. The listener was instructed to select the “longer” duration interval. The duration difference between the tones in the two intervals was adjusted using a three-down, one-up procedure. For the first block, the starting duration difference was 60 ms, and for the second block, the starting duration was 5 ms longer than the duration JND estimate from the first block. The duration difference step size was 5 ms for the first two reversals [based on Fitzgibbons and Gordon-Salant (1994)] and 1 ms for the final eight reversals. The duration JND from each block was the average of the duration differences at the last eight reversals, and the JNDs from the two blocks were averaged.

For the frequency JND, both intervals contained a tone with the same base duration (150 ms) and base level (either according to the SL or SPL setting). In one interval, the tone frequency was set to either the low or high frequency depending on the block. In the other interval, the tone frequency was higher. The ordering of these intervals was randomized in each trial, and the listener selected the interval that was “higher in pitch.” The starting frequency of the higher tone was 18% of the base frequency for HI listeners or 6% of the base frequency for NH listeners. The higher tone frequency was adjusted by a factor of 1.2 for all ten reversals. The frequency JND from each block was the average of the last eight reversals, and the JNDs from the two blocks were averaged.

Following the estimation of the JNDs, initial psychometric functions were constructed from the adaptive blocks of trials for each base frequency (low or high), base level condition (according to SL or SPL setting), and stimulus dimension (level, duration, or frequency). This yielded 12 conditions in total for the NH listeners. For the SNHL group, there were nine unique conditions because in the equal SPL condition, one of the frequencies was set to the same level as the equal SL condition. To construct these functions, the level, duration, or frequency difference values on each trial were combined from both blocks. Prior to fitting the psychometric functions, some pre-processing of the data was performed to apply a consistent “binning” rule across listeners and conditions. The data were grouped into “bins” based on the size of the spacing between difference values. Specifically, the spacing between all unique data points was determined, and the size of each bin was fixed at the median spacing value. This ensured that the bin width would not be so large that it grouped all data together but not so small that there would be small numbers of trials per data point. Within each bin, the listener's responses were tallied, and percent correct was calculated. The psychometric functions were fitted with logistic functions using the “psignifit” function (Wichmann and Hill, 2001) in matlab version 2017b, which weights each data point by the number of trials. Values corresponding to 70%, 80%, and 90% correct were extracted from these initial fitted functions (referred to as JND₇₀, JND₈₀, and JND₉₀).

Next, these extracted JND₇₀, JND₈₀, and JND₉₀ values were presented in a two-interval, two-alternative forced-choice procedure on a fixed number of trials (30 trials each for JND₇₀, JND₈₀, and JND₉₀ values per frequency, level condition, and stimulus dimension). Either the equal SL or equal SPL condition was tested first, randomly selected for each listener. The ordering of the 30 repetitions of each JND value within a condition was randomized and then blocked into three blocks of 30 trials. The blocks were run in the following order: one block of the low tone level JND, then high tone level JND, followed by low tone duration JND, high tone duration JND, then low tone frequency JND, and high tone frequency JND. This ordering was repeated three times. Before each block, listeners were instructed to select either the “louder,” “longer,” or “higher pitched” interval. On each trial, the base stimulus was presented in either the first or second interval (with equal probability), and the other interval contained an increment stimulus based on JND₇₀, JND₈₀, or JND₉₀ in the selected stimulus dimension. For each condition, the proportion correct for each JND value was calculated, and the data points were added to the existing psychometric functions constructed from the adaptive blocks of trials. These final psychometric functions (consisting of data from the adaptive blocks and fixed-trial blocks; see Dai, 1995) were fit with logistic functions. More details about these logistic functions and goodness of fit are provided.¹ From these functions, JNDs corresponding to 70%, 80%, and 90% correct were extracted (to be referred to as JND_70final, JND_80final, and JND_90final).

c. Weighting of two-tone complexes.

In the third stage (section 3 of Table II), listeners were always presented with two-tone complexes on each trial, consisting of simultaneous low-frequency and high-frequency tones. Two types of tasks were used (schematized for level discrimination in Fig. 2). One task—referred to as “referent discrimination”—was a three-interval, two-alternative forced-choice procedure in which the first interval was the reference and the second and third intervals were comparison intervals [Fig. 2(A)].

FIG. 2.

Schematic of one trial for the two tasks used to measure weights in experiment 1. (A) The referent discrimination task. The base levels for each frequency (“Base”) are presented for all stimuli in all three intervals with the exception of one frequency in either interval 2 or 3, which is incremented based on one of the three JND values (“JND 70%,” “JND 80%,” “JND 90%”). (B) The two-interval discrimination task. Levels for both frequencies in each interval are randomly selected either from four discrete values (levels corresponding to “Base,” “JND 70%,” “JND 80%,” “JND 90%”) or from a continuous distribution with the same mean and SD as these four levels.

The listener was instructed to select the interval (either 2 or 3) that was “louder,” “longer,” or “higher pitched” depending on the stimulus dimension. This referent discrimination task paralleled that used by Lentz and Leek (2003) and Espinoza-Varas (2008). The other task—referred to as “two-interval discrimination”—was a two-interval, two-alternative forced-choice procedure [Fig. 2(B)]. The listener selected the “louder” interval on each trial. The two-interval discrimination task paralleled that used by Jesteadt et al. (2014) and Doherty and Lutfi (1996, 1999). Note that chance performance is the same for the two- and three-interval tasks used here (i.e., chance proportion correct of 0.5), but the across-interval comparisons available to the listeners—and consequently the possible decision strategies and memory demands—may differ. In the two-interval case, only a single direct comparison of the first with the second stimulus is possible. In the three-interval case, three comparisons across intervals are possible (i.e., interval 1 vs interval 2; interval 1 vs interval 3; and interval 2 vs interval 3) with each comparison providing enough information for the ideal observer to solve the task. These across-interval comparisons are separate from comparisons of a single stimulus to any learned long-term standards the listener may have established (see Durlach and Braida, 1969).

In the referent discrimination task, the first interval always contained 150-ms low-frequency and high-frequency tones. In the equal SL version, these tones were set to 15 dB SL. In the equal SPL version, these tones were set to 85 dB SPL for the NH listeners; for the listeners with SNHL, the tone with the poorest threshold was set to 15 dB SL, and the other tone was set to that equivalent SPL. In one of the other comparison intervals, the tones were set to the same frequencies, durations, and levels as the referent interval. In the other comparison interval, one of the frequencies was incremented in either frequency, level, or duration. For the duration task, the two tones in each interval had synchronous onsets, and the duration increment was added to the end of the stimulus. Whether this difference occurred in interval 2 or 3 was randomized on each trial. The dimension of the difference (level, duration, or frequency) was fixed within a block of trials. Each of the tone frequencies (low or high) was incremented in level, duration, or frequency based on JND_70final, JND_80final, and JND_90final separately on an equal number of trials (20 trials per JND value for each tone frequency), but the ordering was completely randomized across all trials and blocks. The 120 trials per stimulus dimension were arranged in 30-trial blocks, and all level discrimination blocks were run first, followed by duration and then frequency. In the initial planning of the study, we had aimed to examine the effects of feedback on weights obtained in the referent discrimination task (but see data analyses below²). The first set of blocks (just as described) was run without feedback. The same set of blocks (another 120 trials per condition) was repeated with feedback indicating the correct interval following the listener's response on each trial. This procedure was run for both the equal SL and equal SPL conditions. Either the equal SL or equal SPL condition was run first, randomly selected for each listener.

In the two-interval discrimination task, only the level discrimination dimension was tested. On each trial, the level of each frequency component in each interval was randomly and independently selected. Equal SL and equal SPL versions were run, and for each of these versions, two versions employing different methods of sampling levels were tested. In one method (“discrete”), levels were selected from four possible values at each frequency. These values corresponded to the base level (15 dB SL or the appropriate SPL) and the levels corresponding to JND_70final, JND_80final, and JND_90final for the relevant frequency and level conditions. This method of level selection was similar to the referent discrimination method. However, note that with this method of random selection, there was not always a “correct” answer (e.g., if the same level was selected in both intervals or if one frequency increased in level and the other decreased in level between interval 1 and 2). Accordingly, no feedback could be provided to the listeners. In the other method of level selection (“continuous”), a Gaussian distribution was constructed with the same mean and SD as the four values corresponding to the base level, JND_70final, JND_80final, and JND_90final for each frequency. On each trial, the level of each frequency in each interval was randomly selected from the corresponding Gaussian distribution. This continuous method was similar to the level sampling methods described in Doherty and Lutfi (1996, 1999). However, in the current study, the mean and SD of the distribution were unique to each listener and frequency. Both discrete and continuous level sampling methods were used to help ensure a range of discriminability of presented level differences. Ten blocks of 50 trials (500 total) were run for each of the four conditions—equal SL and equal SPL each with discrete and continuous level sampling methods. The trials from both sampling methods were used in an analysis of the effect of trial-by-trial discriminability on resulting calculated weights.

4. Data analyses

In each condition, the trial-by-trial responses and stimulus differences between intervals were used to perform a weighting analysis similar to that originally described in Berg (1989). Logistic regression analysis (Dye et al., 2005) was run separately for each condition using the “glmfit” function in matlab (specifying “binomial” and “logit” parameters). Listener response on each trial was regressed against either the level, frequency, or duration differences between intervals in each frequency band. In the referent discrimination task, the difference in level, duration, or frequency was taken between intervals 2 and 3 (see Lentz and Leek, 2003). The referent discrimination data shown in the results were based on coefficients from combined no-feedback and feedback trials (240 trials total²). In the two-interval discrimination task, the difference in level was taken between intervals 1 and 2.

Richards and Zhu (1994) demonstrated that regression coefficients can be used to estimate weights up to a proportionality constant but that this constant is irrelevant when cross-frequency coefficients are expressed in relative terms. Here, relative weights were calculated by taking the absolute value of the coefficient at each frequency divided by their sums (normalized to sum to 1; see Dye et al., 2005). Given that there were only two frequencies and the normalized weights at these two frequencies summed to 1, all information can be represented by the normalized weight of just one frequency. Thus, the weighting results will depict the normalized weight at the low frequency. Listener data were excluded from the results and statistical analyses if the correlation coefficients were not statistically significant at both frequencies. The data were still included in weighting analyses if a correlation coefficient was significant at only one frequency, and these cases are indicated in figures showing individual data throughout. Note that while the derivation of weights in the two-interval discrimination task is comparable to past weighting studies, there are aspects in the referent discrimination task that differ from the typical procedure. First, the “perturbations” were changes in signal strength. Recall that in this task, there was a level, duration, or frequency difference only at one frequency per trial. Thus, the coefficients are expected to be essentially scalars associated with the effect of level/duration/frequency changes (i.e., associated with the psychometric function). Furthermore, the stimulus differences, when present, were based on an even balance of JND_70final, JND_80final, and JND_90final at each frequency. As such, we expected the coefficients to be equivalent at the two frequencies—that is, equal weights at each frequency—unless other factors such as listener attention or signal uncertainty, etc., influence weights when both frequencies are present. That is, the end effect parallels procedures more typically used.

The relative low-frequency weights were compared across conditions using paired t tests and analyses of variance (ANOVAs). Detection thresholds and discriminability JNDs were compared using Pearson correlations, and predictors of relative low-frequency weights were tested using stepwise linear regression models. A Bonferroni adjustment of the p values was used to correct for multiple comparisons. Note that no additional adjustments of p values were made based on the initial analyses that determined significance of logistic regression coefficients or for the initial analysis.²

B. Results

1. Relationship between JNDs for discrimination and detection thresholds

To examine whether cross-frequency weights were related to differences in absolute detection thresholds across frequency and/or to discriminability of stimulus properties across frequency, it is important to determine first the relationship between detection thresholds and JNDs across frequencies. Presumably, cross-frequency threshold differences and cross-frequency JND differences could be informative with respect to the independent influence each exerts on weights; however, these relationships with weights can only be determined if threshold difference and JND difference are not themselves significantly correlated (e.g., multicollinearity of variables; Menard, 2002). There is a prior literature describing how JNDs in each dimension (level, duration, and frequency) are correlated with thresholds and/or presentation level across frequency (e.g., Schroder et al., 1994; Ruhm et al., 1966; Zurek and Formby, 1981), but it is much less clear from prior studies how listener-specific JND differences across frequency relate to detection threshold differences across frequency.

Figure 3 shows the relationship between detection threshold at each frequency and the measured JND for that frequency in each stimulus dimension for both equal SL and equal SPL presentation levels. Figure 4 shows the relationship between threshold differences and JND differences for the two frequencies (3500 Hz–750 Hz). The Pearson product-moment correlation coefficients and p values for each frequency, stimulus dimension, and level condition are indicated in each panel. All p values shown have been Bonferroni-corrected for the 18 correlations across Figs. 3 and 4. One NH listener, NH5 (shown as red symbols), was a clear outlier as revealed in a few of the panels, so this listener's data were excluded from all correlation coefficient calculations. Note that data from NH5 were also excluded from subsequent weighting statistical analyses involving comparisons with JNDs. This listener's weights are indicated in subsequent figures showing individual data.

FIG. 3.

(Color online) Relationship between detection thresholds at each frequency and JNDs for that frequency [low frequency (circles) and high frequency (triangles)]. Open symbols, listeners with NH; filled symbols, listeners with SNHL. The equal SL conditions are shown in the left column, and the equal SPL conditions are shown in the right column. Top row, level JNDs; middle row, duration JNDs; bottom row, frequency JNDs. Pearson correlation coefficients and p values are indicated for each condition in each panel. p values have been Bonferroni-corrected for multiple comparisons.

FIG. 4.

Relationship between threshold difference (high-frequency threshold – low-frequency threshold) and JND difference (high-frequency JND – low-frequency JND). Open symbols, listeners with NH; filled symbols, listeners with SNHL. Left column, equal SL conditions; right column, equal SPL conditions. Top row, level JND differences; middle row, duration JND differences; bottom row, frequency JND differences. Pearson correlation coefficients and p values are indicated for each condition in each panel. p values have been corrected for multiple comparisons.

For frequency JNDs (bottom row of Fig. 3), there were significant positive correlations between thresholds and JNDs for both tone frequencies in the equal SPL condition and at the low frequency in the equal SL condition, such that listeners with poorer thresholds had larger frequency JNDs. This is consistent with findings reported in previous studies (e.g., Zurek and Formby, 1981; Tyler et al., 1983) and represents a suprathreshold deficit that co-varies with threshold elevation in listeners with SNHL and is fairly independent of presentation level. Threshold difference across frequency (bottom row of Fig. 4) was significantly positively correlated with JND difference across frequency in the equal SPL condition (but not in the equal SL condition), indicating that listeners with better low than high thresholds also showed better low than high JNDs.

For duration JNDs (middle row of Fig. 3) in the equal SL condition, there was a general negative trend in correlation with threshold such that poorer thresholds corresponded to better JNDs, although this did not reach statistical significance. This result appears to be driven by presentation level because the trends in correlations changed to have positive slopes in the equal SPL condition (when presentation levels were, on average, 85 dB SPL), although again this was not significant. It has previously been demonstrated that duration discrimination improves with higher SL/SPL (e.g., Ruhm et al., 1966). The finding of no significant correlation between threshold and JND in these young adult listeners is consistent with prior literature showing an effect of age but not of hearing loss on duration discrimination (Fitzgibbons and Gordon-Salant, 1994; Grose et al., 2004). The correlation between threshold difference and JND difference at the two frequencies (middle row of Fig. 4) was not significant for either equal SL or equal SPL conditions.

Finally, for level JNDs (top row of Fig. 3), thresholds were not significantly correlated with JNDs after correcting for multiple comparisons. Threshold differences at the two frequencies (top row of Fig. 4) were not correlated with differences in JNDs at the two frequencies. The prior studies described in the Introduction comparing weights between listeners with NH and SNHL all pertained to level/loudness discrimination, but individual level JNDs were not reported in those studies. The level JNDs shown in Fig. 3 give a sense for the individual variability that may be seen. Even after excluding the outlier (NH5), some listeners required level differences of approximately 4 dB to achieve 80% correct discrimination performance, whereas others required only 1 dB or less. In Sec. II B 2, we examined how often discriminable level differences were produced across frequencies and listeners using current and prior study methods (e.g., Doherty and Lutfi, 1996).

Overall, level and duration JNDs appeared not to be significantly associated with the degree of hearing loss. The differences between the JNDs for these two tasks at the two test frequencies were not significantly correlated with the differences between the detection thresholds at the two frequencies. However, the JNDs for frequency discrimination, which are thought to represent suprathreshold deficits related to SNHL, were positively correlated with the degree of hearing loss, and the differences in frequency JNDs between the two test frequencies were positively correlated with the detection threshold differences at the two frequencies in the equal SPL condition. The correlation coefficient for threshold difference vs frequency discrimination JND difference was <0.8 (below the cutoff for problematic multicollinearity; Menard, 2002), which will allow us to test these as separate predictors of weights in later analyses.

2. Influence of relative cross-frequency discriminability on weights

One design feature of the present study was tailoring the level, duration, and frequency differences presented on each trial not only to each listener but also for each constituent frequency comprising the multitone stimulus. The justification for this method would come from evidence that the derived weights could be influenced by the asymmetries in discriminability at the two frequencies. As theorized in the Introduction, if the listeners base their responses on the frequency where the stimulus difference is greater and presumably more salient perceptually and there are more trials that are discriminable at one frequency than the other, then this could result in an observed weight that changes depending on which frequency is more discriminable. This possibility is examined next.

a. What percentage of trials in the level discrimination task are discriminable?

First, we determined the percentage of trials for each task that fell into different discriminability ranges (<70%, 70%–80%, 80%–90%, and >90% discriminable) based on the JND_70final, JND_80final, and JND_90final values extracted from the psychometric functions for each listener, frequency, and level condition. This was done for the two-interval level discrimination task (combined discrete and continuous conditions, yielding 1000 trials total) and for the referent level discrimination task (combined feedback and no-feedback trials, yielding 240 trials). For each task and listener, the difference in level between intervals on each trial was calculated, and the absolute value of this difference was categorized as <70%, ≥70% and <80%, ≥80% and ≤90%, and >90% discriminable according to the listener- and frequency-specific JNDs.

Figure 5 shows the percentages of total trials that corresponded to each of the discriminability categories across tasks for both the low and high test frequencies. In the referent discrimination task, 50% of the trials at each frequency were <70% discriminable. This reflects the fact that on each trial, a level increment was only added to one frequency, and the number of trials with level differences was balanced across frequency, resulting in 50% of trials for each frequency with no level differences. The other 50% of the trials at each frequency were 70%–90% discriminable. Note that the 80%–90% category includes both end points (i.e., 80% and 90% discriminability); thus, 33.3% of the trials fall within this category (2/3 of the remaining 50% of discriminable trials). The 70%–80% category does not include 80% discriminability, and thus 16.7% of the trials fall within this category (1/3 of the remaining 50% of discriminable trials). The averaged results reflect the exact percentages for each listener, and the percentages of discriminable trials were completely balanced across frequency, as intended. In the two-interval discrimination task, there was less control over the discriminability of level differences presented. On average, across panels, between 50% and 60% of the trials were <70% discriminable. However, the two frequencies were not evenly matched in the number of discriminable trials.

FIG. 5.

Mean percentages of trials corresponding to different ranges of discriminability based on listener JNDs across tasks and NH and SNHL groups. Within each set, the left-to-right ordering of the four bars is equal SL low frequency (L), equal SL high frequency (H), equal SPL low frequency (L), and equal SPL high frequency (H).

To determine how these discriminability percentages compare to those that would be obtained by the methods of previous studies (Doherty and Lutfi, 1996, 1999; Jesteadt et al., 2014), we ran a simulation of level draws using the distributions used in those studies. For the simulation implemented here, four independent level draws—one corresponding to the low frequency in interval 1, one for the low frequency in interval 2, one for the high frequency in interval 1, and one for the high frequency in interval 2—were made on each trial (1 × 10⁵ total trials) from the appropriate level distributions. The low-frequency and high-frequency level distributions had mean levels set to the base level in either the equal SL or equal SPL condition for each listener, and the SDs were set to 5 dB. The levels selected in the simulations were never allowed to exceed 2.5 SDs from the mean (see Doherty and Lutfi, 1996). For each trial, the difference in levels between intervals was categorized as <70%, ≥70% and<80%, ≥80% and ≤90%, and >90% discriminable according to the listener- and frequency-specific JNDs. The mean results of this simulation (also shown in Fig. 5) indicated that more trials were classified as discriminable, on average, than in the two-interval and referent discrimination tasks of this study. In the simulation of prior study methods, between 60% and 80% of trials were classified as >90% discriminable at each frequency.

b. What percentages of trials contain uneven discriminability across frequency?

Next, we determined the percentages of trials that contained asymmetries in discriminability across the two frequencies. For each listener and in each condition, we categorized the level differences on each trial and at each frequency according to the discriminability categories shown in Fig. 5. We then tagged each trial according to whether the low- or high-frequency level difference fell into the more discriminable category. For example, if the low-frequency level difference was >90% discriminable, and the high-frequency level difference was 70%–80% discriminable, that trial was included in the low-frequency-more-discriminable-than-high-frequency (to be called “L > H”) subset of trials. Trials where the low frequency was less discriminable than the high frequency will be called “L < H.” Figure 6 shows the percentages of trials in each task that contained asymmetries in discriminability across frequency. In the referent discrimination task, half of the trials fell into each of the categories (100% of the trials contained asymmetries in discriminability) because the level differences were only present at one frequency at a time. In the two-interval discrimination task, between 25% and 40% of the trials contained asymmetries in discriminability. Moreover, the percentages of trials corresponding to the L > H and L < H categories were not evenly matched. In the simulation, between 20% and 30% of trials contained asymmetries in discriminability in either direction, and again, the directions of the asymmetries were not evenly matched. It should be noted that the simulation contained many trials that were >90% discriminable (see Fig. 5), and we did not examine asymmetries in discriminability when both frequencies were >90% discriminable (e.g., where one frequency was 92% discriminable and the other was 100% discriminable). Thus, the percentages of asymmetric discriminability in the simulation may actually be much higher.

FIG. 6.

Mean percentages of trials in which the low frequency contained a more discriminable level difference than the high frequency or the high frequency contained a more discriminable level difference than the low frequency across tasks. Error bars, SDs. x axis labels are the same as in Fig. 5.

c. Does uneven discriminability across frequency influence weights?

Finally, we determined how asymmetries in discriminability of the two frequencies on any given trial influenced the derived weights. From the two-interval discrimination data, we ran logistic regressions separately for trials corresponding to L > H and for trials corresponding to L < H (the categories shown in Fig. 6). Normalized weights were calculated in each condition from the low- and high-frequency regression coefficients. As indicated earlier, normalized low-frequency weights were still included in the figures and analyses if the coefficient for one frequency was statistically significant but the other was not.

Figure 7 compares relative low-frequency weights calculated from trials where L < H vs L > H. Weights calculated from all trials also are shown. Symbols are connected for each listener to facilitate comparisons. Relative low-frequency weights are shown in the top panel for the equal SL condition and in the bottom panel for the equal SPL condition. Open symbols show NH weights, and filled symbols show SNHL weights. To test the hypothesis that listeners place greater weight on the more discriminable frequency, we determined whether low-frequency weights were greater in the L > H than in the L < H condition (the first two connected symbols in each data set) using paired-sample one-tailed t tests. The t test comparing the L > H weights to the L < H weights for all listeners in the equal SL condition was not significant (applying Bonferroni corrections for two t tests): mean = 0.06, SD = 0.15, t(19) = 1.86, p = 0.08. Fifty-five percent of all listeners showed greater low-frequency weights in the L > H condition than in the L < H condition in the equal SL condition. However, the comparison of L > H and L < H weights in the equal SPL condition was statistically significant: mean = 0.08, SD = 0.17, t(21) = 2.19, p = 0.04, indicating greater low-frequency weights when L > H compared to L < H. Fifty-nine percent of all listeners showed greater low-frequency weights in the L > H condition than the L < H condition. Comparing the weights from all trials to the L < H and L > H weights, weights from all trials tended to be more similar to the L < H weights for the NH listeners in the equal SL condition. In the other cases (listeners with SNHL in the equal SL and equal SPL conditions and NH listeners in the equal SPL condition), weights from all trials were more similar to the L > H weights. This may be due to the percentages of total trials that are comprised of each of these asymmetries. Note that there was a greater percentage of L < H trials than L > H trials for NH listeners in the equal SL condition, but there was a greater percentage of L > H trials for NH listeners in the equal SL condition and for listeners with SNHL in both equal SL and equal SPL conditions (Fig. 6, Two-Interval Discrim). Another noteworthy finding apparent in Fig. 7 is that weights show greater variability across listeners with SNHL than listeners with NH.

FIG. 7.

Comparison of relative low-frequency weights for level discrimination for trials in which the low frequency contained a less discriminable level difference than the high frequency (L < H), vs when the low frequency was more discriminable than the high frequency (L > H), vs the weights from all trials. Top panel, weights for the equal SL condition; bottom panel, weights for the equal SPL condition. Open symbols, listeners with NH; filled symbols, listeners with SNHL. Triangles, weights for which both contributing regression coefficients were statistically significant. Squares, weights for which only one of the two coefficients was significant. Star symbols, results for listener NH5. Each listener's relative weights in each condition are connected to facilitate comparisons. Relative low-frequency weights >0.5 indicate a low-frequency bias, and weights <0.5 indicate a high-frequency bias.

Overall, there is some evidence from the preceding analysis in support of the proposition that listener weights change depending on which frequency component contains a more discriminable level difference. In the equal SPL condition, the low-frequency weights were significantly greater when the low frequency was more discriminable than when the high frequency was more discriminable, and 59% of the listeners showed this trend. All subsequent analyses of weights will examine the referent discrimination task weights where there was greater control over cross-frequency discriminability.

3. Effect of stimulus dimension and level on weights

In the referent discrimination task, listeners performed level, duration, and frequency discrimination to determine the consistency of weights across stimulus dimensions. The averaged relative low-frequency weights across conditions and groups are shown in Fig. 8. For comparison, the weights in the two-interval discrimination task from all trials also are shown. Qualitatively, the two-interval task weights—with less control over relative cross-frequency discriminability—deviated more from the 0.5 line in the NH listeners than did the referent discrimination level weights. The weights in the referent discrimination task were analyzed with a repeated-measures ANOVA with within-subject factors of stimulus dimension (level, duration, frequency) and level (equal SL vs equal SPL) and a between-subjects factor of group (NH vs SNHL). There was a significant effect of stimulus dimension [F(2,32) = 30.14, p < 0.001]. No other effects or interactions were significant.

FIG. 8.

Relative low-frequency weights across all conditions in the referent discrimination task and also for the two-interval discrimination task (measured for level discrimination only). The 0.5 line indicates equal weights given for low and high frequencies. Open symbols, listeners with NH; filled symbols, listeners with SNHL. Symbols above this line indicate greater low-frequency weight, and symbols below this line indicate greater high-frequency weight. Error bars, standard errors.

A correlation analysis comparing weights across stimulus dimensions revealed that the relationship between level and duration discrimination relative weights was statistically significant in the equal SL condition (r = 0.61, Bonferroni-adjusted p = 0.024) and the equal SPL condition (r = 0.57, adjusted p = 0.0480); the correlation between level and frequency discrimination relative weights was not significant in either equal SL (r = 0.26, adjusted p = 1) or equal SPL (r = –0.28, adjusted p = 1) conditions; and the relationship between frequency and duration discrimination relative weights was not significant in equal SL (r = 0.12, adjusted p = 1) or equal SPL (–0.02, adjusted p = 1) conditions. The finding that no significant correlation was observed in comparisons involving frequency discrimination weights was due to the trend for greater weight to be placed at the low-frequency component in the frequency discrimination task. These results indicated that weights for the discrimination of duration and level were related to one another, but neither of these was related to weights for the discrimination of frequency.

4. Effect of threshold asymmetry and JND asymmetry on weights

The analysis described in Sec. II B 3 revealed no significant effect or interaction involving group (NH vs SNHL) for relative weights across stimulus dimensions in the referent discrimination task. However, the listeners with SNHL in this study exhibited a range of threshold configurations (see Fig. 1). One question asked in this study was whether listeners with NH and SNHL differed in their relative weighting of different frequency regions as a result of variable degrees of “unevenness” of thresholds across frequency and/or feature discriminability across frequency. As described earlier, our aim was to modify the stimulus to account for audibility or suprathreshold deficits for the listeners tested in the present experiments. Thus, relative weights that differ across frequency after these compensations would suggest that the difference was not due to issues with audibility or discriminability of the stimulus as presented, but rather was due to long-term changes in the use of cross-frequency information as a result of these asymmetries.

To assess the viability of this “unevenness” hypothesis for both thresholds and discriminability, we conducted stepwise multiple linear regressions for the weights obtained in each stimulus dimension and level condition in the referent discrimination task where there was control over cross-frequency discriminability. The dependent variable was the relative low-frequency weight in each condition. There were two independent variables: threshold difference (high-frequency threshold – low-frequency threshold in dB) and difference in discriminability JNDs (high-frequency JND – low-frequency JND). The JNDs used in the difference calculations were for the same stimulus dimension and level as the independent variable weights and were the average of JND_70final, JND_80final, and JND_90final. Table III shows the results of the regression models in each weight condition. The rightmost column shows the relationship between the two predictors in the model (threshold difference and JND difference across frequency), which were also shown previously in Fig. 4. The p values have been Bonferroni-corrected for the six models tested. The only significant models were for equal SL level weights (R² = 0.616, p < 0.01) and equal SL duration weights (R² = 0.664, p < 0.01). For both models, only threshold difference was a significant predictor.³

TABLE III.

Results of multiple regression models for data in experiment 1 regressing the weight condition indicated in the left-most column onto threshold difference (1) and JND difference (2) predictors. Unstandardized coefficients (B) and Bonferroni-corrected p values are shown for the intercept and each predictor in each model. The R² and corrected p value are also shown for each overall model. The last column shows the correlation between the two predictors in the model to show that multicollinearity was not present. Bold numbers are statistically significant values.

Weight condition	Intercept		1. Threshold difference		2. JND difference		Overall model		1 vs 2 Multicollinearity?
	B	p	B	p	B	p	R 2	p	Multiple R
Level SL	0.658	<0.01	−0.007	<0.01	−0.001	1	0.616	<0.01	0.247
Level SPL	0.618	<0.01	−0.001	1	−0.061	1	0.076	1	0.520
Duration SL	0.564	<0.01	−0.007	0.02	0.005	1	0.557	<0.01	0.348
Duration SPL	0.514	<0.01	0.002	1	−0.001	1	0.226	1	0.163
Frequency SL	0.795	<0.01	−0.001	1	0.124	1	0.279	1	0.384
Frequency SPL	0.854	<0.01	0.000	1	0.072	1	0.078	1	0.677

Figure 9 (“Equal SL” heading) shows the correlation between equal SL level or duration weights and threshold differences and JND differences. The lines plotted in each panel were based on the intercept and B values in Table III. For both level and duration weights in the equal SL condition, relative low-frequency weights were greatest for listeners with poorer low-frequency than high-frequency thresholds and were smallest for listeners with poorer high-frequency than low-frequency thresholds. Thus, for either level discrimination or duration discrimination tasks, listeners weight the frequency in the region of poorer threshold more when there are large detection threshold asymmetries. However, in the equal SPL condition, the weights were not significantly related to threshold difference [see Table III and Fig. 9 (“Equal SPL” heading)]. The flat regression slope for threshold difference vs equal SPL level weights suggests the significant correlation in the equal SL condition was due to differences in presentation levels at the two frequencies.

FIG. 9.

Associations between threshold difference (high frequency – low frequency) or discrimination JND difference (high frequency – low frequency) and relative low-frequency weights. Top row, weights for level discrimination; bottom row, weights for duration discrimination. Lines, the regression slopes from regression models that regressed weights onto predictors of threshold difference and JND difference. The variance explained by each predictor of that weight is indicated in each panel (R²). Only the threshold difference predictor is shown in the equal SPL condition to demonstrate how the relationships between weights and threshold difference changed from the equal SL condition. Open symbols, listeners with NH; filled symbols, listeners with SNHL. Circles, weights for which contributing coefficients were statistically significant at both frequencies. Squares, weights for which only one coefficient was significant. Star symbols, data for NH5.

III. EXPERIMENT 2

One of the goals of this study was to establish whether the cross-frequency weights obtained from experiments using multitone complexes generalize to other types of stimuli and tasks. Specifically, we aimed to determine whether listeners who apply less weight to higher frequency information in a multitone complex in a discrimination task (experiment 1) would also underutilize the high-frequency content of speech in a speech recognition task. It should be acknowledged that careful experimental control over the discriminability of stimulus features across listeners is inherently more difficult with speech stimuli than for the relatively simple two-tone complexes used as stimuli in experiment 1. Here, we conducted an experiment that followed, as closely as possible, one reported by Horwitz et al. (2008). That study examined the importance of high-frequency information for speech recognition in NH listeners and in listeners with high-frequency SNHL by systematically low-pass filtering speech tokens. In our implementation of the filtered-speech experiment, we selected a subset of the cutoff frequencies used by Horwitz et al. to examine the importance of frequency information above 3000 Hz for speech recognition. Nonsense syllables were low-pass filtered at either 5600 or 3000 Hz and thus either contained speech information in the region of 3500 Hz (one of the target cross-frequencies in experiment 1) or did not. The target stimuli were presented in quiet and in a speech-shaped noise. Listeners with SNHL were presented with stimuli that were amplified with individualized frequency-specific gain. This procedure was similar to the individualized gain reported by Horwitz et al. (2008). However, unlike Horwitz et al. (2008), who presented NH listeners with stimuli in threshold-matching noise (to mimic audiograms of the SNHL group) and applied gain, the NH listeners in this experiment were presented the stimuli without amplification or spectral shape modifications. The changes in performance as a function of bandwidth were compared to AI-based predictions, and comparisons were made to the results from experiment 1.

A. Methods

1. Listeners

The majority of listeners from experiment 1 also participated in experiment 2. Due to listener time constraints, HI5, HI7, and HI11 did not take part in experiment 2.

2. Equipment, stimuli, and procedures

The experimental apparatus used in experiment 2 was the same as that used in experiment 1. The stimuli were syllables consisting of combinations of 20 consonants /b, tʃ, d, f, g, k, l, m, n, ŋ, p, r, s, ʃ, t, θ, v, w, j, z/ with 3 vowels /ɑ, i, u/, yielding 57 consonant-vowel and 54 vowel-consonant syllables (see Horwitz et al., 2008; Dubno and Schaefer, 1992; Dubno et al., 2003). Each syllable was spoken in isolation by a male and a female talker, resulting in 222 unique tokens. These stimuli were selected with the goal of isolating the salience of information in a specific frequency region without the confound of linguistic/contextual cues.

The speech was low-pass filtered with cutoff frequencies of 3000 or 5600 Hz. The digital low-pass filters were generated by first creating a 2048-sample vector representing frequencies from 0 to 20 000 Hz and zeroing out frequencies above the desired cutoff frequency. The inverse fast Fourier transform was taken of this vector, and then a Hanning window was applied. The resulting impulse response was applied to the signal using the “fftfilt” function in matlab version 2017b. The speech was presented either in quiet or in low-pass-filtered speech-shaped noise⁴ with the same cutoff frequencies as the speech. For the listeners with SNHL, individualized NAL-RP gain (Byrne et al., 1991) was applied to each stimulus. The stimulus level (pre-gain) was 70 dB SPL. The noise was presented at 65 dB SPL (SNR = 5 dB). Prior to testing, the final stimuli were checked for listener comfort and signal fidelity. For listener HI9, the target stimulus level was lowered to 64 dB SPL to avoid peak clipping. For listener HI1, the target stimulus level was lowered to 65 dB SPL to achieve listener comfort. In both cases, the noise levels also were lowered to maintain a SNR of +5 dB.

Within a condition (cutoff frequency, quiet, or noise), the 222 items were presented in random order for each listener in four blocks of 55 or 56 trials to minimize listener fatigue; all listeners ultimately heard and responded to all 222 items. All blocks without noise (eight total) were tested first, with the cutoff frequency of each block randomized, followed by the eight noise blocks with randomized cutoff-frequency block order. The listener's task on each trial was to select the consonant heard (from 20 consonant response alternatives) by registering a response on the visual display of the 20 response options organized in a 4 × 5 grid. No feedback was provided. Prior to testing, listeners were first shown the grid listing all consonants, and an example of each test syllable was played with the corresponding consonant button highlighted. Listeners were then given 20 practice trials of identifying consonants in quiet with a 5600 Hz cutoff frequency.

3. Data analysis

For each listener and condition, an AI value was calculated using a procedure similar to that described in Horwitz et al. (2008), which is based on the ANSI (1969, 1997) standard. This procedure involved using both the frequency-importance function and the transfer function relating the AI to consonant recognition developed specifically for the NST materials and the speech peaks measured for these specific stimuli in 1/3 octave bands (Dirks et al., 1990). To determine audibility in the AI calculation for each listener, thresholds were measured in dB SPL for pure tones in 1/3 octaves from 200 to 6300 Hz using the experimental equipment and headphones. For the listeners for whom time did not permit thresholds to be measured in the experimental booths, clinical audiometric thresholds were used and converted from dB hearing loss to dB SPL. These thresholds were converted to equivalent internal noise levels, and these levels were compared to the speech and noise levels in the same 1/3 octave bands to quantify audibility [as in Horwitz et al. (2008)]. The speech levels were calculated from the long-term average spectrum of all level-scaled NST syllables. The noise levels were calculated from the average spectrum of two of the syllables spoken by the female talker (to be consistent with the noise stimulus used in the experiment⁴). Listener-specific NAL-RP gain was applied for the listeners with SNHL, just as in the perceptual experiment. The target and noise spectra were shaped by an inverse headphone filter to represent the response at the eardrum. These stimuli were then filtered into 21 1/3 octave bands using brickwall filters in the frequency domain, and the average level in each band was determined. These levels were then expressed as level re: the overall level. After summing the importance-weighted audibility across bands to calculate the AI and determining predicted consonant recognition using the AI-recognition transfer function shown as the solid line in Fig. 10 (Dirks et al., 1990), predicted and observed consonant-recognition scores in percent correct were converted to rationalized arcsine units (rau; Studebaker, 1985).

FIG. 10.

Consonant recognition scores (in rau) plotted against AI values in each condition. Solid line, the transfer function relating the AI to consonant recognition; dotted lines, ±2 SDs, from Dirks et al. (1990). Observed scores are shown by symbols, connected by dashed lines for the 3000 and 5600 Hz cutoff frequencies for each listener. Circles, quiet conditions; triangles, noise conditions. Left panel, data from listeners with NH; right panel, data from listeners with SNHL loss. Star symbols in the left panel, data from NH5.

For the data set for listeners with SNHL, observed vs AI-predicted scores were regressed linearly onto predictors of relative low-frequency weights from experiment 1 (as a possible indicator of central use of cross-frequency information), frequency discrimination JNDs from experiment 1 (to account for peripheral suprathreshold deficits not accounted for by the AI), and self-reported unaided or aided communication difficulties (as indicated by APHAB scores). For the weight predictor, the level weights in the equal SL condition of experiment 1 were used for the following reasons. The relative weights in the equal SPL condition, in which the tones at both frequencies were set to equal levels, would presumably be inappropriate for the present comparison because the speech in experiment 2 does not have equal energy in all frequency bands. Moreover, the equal SL condition of experiment 1 seems a more appropriate comparison to experiment 2 in which gain was applied to the speech stimuli to improve audibility across all frequencies. The level weights were selected in lieu of the frequency weights because the frequency weights in experiment 1 did not show sufficient inter-listener variability. Level and duration weights in the equal SL condition were significantly correlated, so it was assumed that they would act as equivalent predictors. The frequency discrimination JNDs were used as an index of peripheral suprathreshold deficit (instead of the level and duration JNDs) because they were less influenced by presentation level effects, and they showed clear effects of hearing loss (see Fig. 3).

B. Results

Figure 10 shows the relationship between AI and predicted and observed consonant recognition (in rau). The predicted relationship is taken from the transfer function relating the AI to consonant recognition (solid line); dotted lines are ±2 SDs. Observed consonant recognition for each listener is plotted as symbols. The symbols connected by dashed lines represent observed scores for the two cutoff frequencies for each listener. Thus, each pair of connected symbols shows the change in consonant recognition between cutoff frequencies of 3000 and 5600 Hz in relation to the corresponding predicted change as shown by the solid (mean) line. Consonant recognition scores and changes in scores for the listeners with NH (left panel) generally fit within ±2 SDs of the predicted scores. This was expected given that these predictions were generated from data from listeners with NH. For the observed scores and score changes for listeners with SNHL (right panel), some listeners fell within the predicted range, whereas others fell more than 2 SDs below the predicted scores, meaning that their observed scores were significantly poorer than scores predicted by the AI. Furthermore, there appeared to be some variability in the slopes of the lines connecting the symbols relative to the predicted slopes, indicating that there were individual differences in the use of speech information between 3000 and 5600 Hz. These two dimensions of the data for each listener—differences in observed and AI-predicted scores and differences in observed and predicted change with increasing bandwidth—will be used as dependent variables in the comparison of results from experiments 1 and 2.

First, we examined the extent to which certain predictors could explain the variance in a listener's overall speech recognition relative to that predicted by the AI. The observed minus predicted score in the widest bandwidth (5600 Hz cutoff) for the noise condition was used as the dependent variable. The quiet condition was not also examined as a dependent variable because of the statistically significant correlation between the observed minus predicted scores in quiet vs in noise [r(10) = 0.93, p < 0.001]. Theoretically, a listener's frequency JND relative to an expected JND for listeners with NH could be indicative of suprathreshold stimulus distortions related to SNHL (Nelson and Freyman, 1986; and see Fig. 3 in this study) and may reflect aspects of speech recognition performance not accounted for by the audibility-based AI. The predicted NH frequency JNDs were calculated for the low and high frequencies used in experiment 1 based on the SL, tone duration, and d′ of 1.61 [from the Micheyl et al. (2012) equation and mode maximum-likelihood parameters in Table II of that study, p. 6]. The predicted NH JND for 750 Hz is 5.25 Hz, and the predicted JND for 3500 Hz is 30.31 Hz. The logarithm of all observed frequency JNDs was taken (as in Fig. 3), and the logarithm of the predicted JNDs was taken. The difference in observed minus predicted log(JNDs) at the low and high frequency for each listener with SNHL was averaged and entered into the model as a single predictor. We also theorized that observed minus predicted consonant-recognition scores could be related to a listener's perceived unaided or aided communication difficulties in real-world scenarios. The APHAB aided score (or unaided score if the listener does not wear hearing aids) was entered into the model as another predictor. The results of this model are shown in the first row of Table IV. The frequency JND was not a significant predictor (unstandardized coefficient B = –19.37, p = 0.24); nor was the APHAB score (B = 0.74, p = 0.108).

TABLE IV.

Results of two regression models for data in experiment 2. The first row shows the model that regresses the observed-predicted consonant recognition in the 5600 Hz cutoff in noise condition (dependent variable; DV) against observed-predicted frequency discrimination JND and against the APHAB score. The second row shows model results for change in consonant recognition score from 3000 to 5600 Hz cutoffs divided by AI predicted change regressed against observed-predicted frequency discrimination JND at 3500 Hz and against the relative low-frequency weight in the equal SL level condition from experiment 1. Unstandardized coefficients (B) and Bonferroni-corrected p values are shown for the intercept and each predictor in each model. The R² and the corrected p value are also shown for the overall model.

	Intercept		Frequency JND		APHAB		Overall model
DV	B	p	B	p	B	p	R 2	p
Speech recognition	−23.05	0.196	−19.37	0.242	0.744	0.108	0.718	0.158
	Intercept		Frequency JND		Low-frequency weight		Overall model
DV	B	p	B	p	B	p	R 2	p
Change in speech recognition	1.80	0.624	0.530	1	−0.117	1	0.028	1

Next, we examined each listener's change in consonant recognition score in noise from the 3000 to 5600 Hz cutoff divided by the AI-predicted change [akin to the “efficiency” measure used in Hogan and Turner (1998)]. Again, the underlying hypothesis is that any additional suprathreshold deficits in the frequency region between 3000 and 5600 Hz may explain some of the variance in observed vs predicted differences in consonant recognition with the change in speech bandwidth. The difference between observed minus predicted frequency JND at 3500 Hz as calculated earlier (a frequency contained in the wider speech bandwidth but not the narrower speech bandwidth) was included as a predictor. The relative low-frequency weight in the equal SL level condition of experiment 1 was also included as a predictor to test the extent to which relative weighting of low vs high frequencies influences the benefit obtained from high frequencies in speech. The results of this model are shown in the second row of Table IV. Contrary to the hypotheses stated earlier, this analysis revealed that neither weights (B = 0.53, p = 1) nor high-frequency JNDs (B = –0.12, p = 1) were significant predictors of the benefit obtained from high-frequency speech content relative to AI-predicted benefit.

IV. DISCUSSION

This study was an examination of weights and weighting differences between NH and SNHL, with the aim of addressing questions and uncertainties from the existing literature. Specifically, we aimed to determine whether certain stimulus factors, such as the discriminability of differences across frequency, or differences in presentation level across listeners might affect weights and influence the weighting differences observed between groups. We also aimed to determine the extent to which weights derived from pure-tone experiments generalize across stimulus dimensions and correlate with the use of cross-frequency information in speech. Overall, the goal was to determine whether cross-frequency weights are different between listeners with NH and SNHL, whether weights correspond to the region of greater hearing loss, or whether weights can be explained by stimulus factors.

A. Do stimulus discriminability differences across frequencies alter weights?

For the two-interval discrimination task of experiment 1, we analyzed trials in which one frequency contained a more discriminable level difference than the other frequency. There was evidence that listeners placed greater weight on the low frequency when the low-frequency level difference was more discriminable than the high-frequency level difference, at least in the equal SPL condition. This suggests that there are conditions in which listeners may indeed be responding based on the relative discriminability of the components of a complex stimulus; that is, the weight is influenced by the relationship between the presented stimulus difference and the JND at each frequency. In the equal SL condition, though, there was no significant difference in weights overall that was related to the direction of asymmetry in discriminability across frequency. However, the listeners with NH showed a trend toward increased low-frequency weights in trials with more discriminable low-frequency level differences, but the listeners with SNHL appeared to be too variable to reach a conclusion (see Fig. 7). Note that it was reported in Sec. II B 4 that level weights in the referent discrimination task were strongly correlated with threshold asymmetry and presentation level asymmetry in the equal SL condition. It is possible that the presentation level asymmetry in the equal SL condition (which was greater for listeners with SNHL) obscured any influence of cross-frequency discriminability asymmetry on weights.

The current data indicate that that perceptual weights may be driven by relative cross-frequency stimulus discriminability even within the range of stimulus difference values typically used to derive weights, which represents a potential confound for measuring weights. That is, if listeners adopt the strategy of placing more weight on the more discriminable frequency, the end result could depend on the proportion of trials that were more discriminable at one frequency than another. To minimize this potential confound, it may be important to match discriminability across frequency for each listener or to individually balance the proportion of discriminable differences of the constituent components across frequency (as we did in the present study in the referent discrimination task).

It is important to point out that the relationship between relative cross-frequency stimulus discriminability and derived weights found here was based on a stimulus with only two components that were widely spaced in frequency. It is plausible that the influence of uneven discriminability across frequencies is of less concern in weighting studies with stimuli that include larger numbers of components than were used here. Specifically, resolving (or “hearing out”) simple stimulus differences for individual components embedded in large-N multicomponent stimuli is likely much more difficult than for the two-component stimulus used here, so perhaps the relationship between cross-frequency discriminability of level differences and calculated weights would be reduced. Currently, the evidence is insufficient to support a firm conclusion. Regardless of which method is employed for addressing this potential confound, it still may be necessary first to determine JNDs for each frequency and listener to ensure that there are not large percentages of trials with asymmetries in discriminability across frequency. As a cautionary note, we determined from a simulation using distributions of levels typically employed to derive weights that, on average, between 20% and 30% of trials contained asymmetries in discriminability favoring either the low frequency or the high frequency. The final weight estimate may depend on which asymmetry (L < H or L > H) makes up a higher percentage of total trials.

B. Are weights generalizable/universal?

The weights that were obtained in experiment 1 were significantly correlated for level and duration discrimination tasks, suggesting that there were some cases where the weights did generalize from one task to another. Note that these quantities are both elements of sound energy and thus naturally are related. However, weights for level and duration discrimination were unrelated to weights for frequency discrimination, a task that may be considered qualitatively different from the other two. The lack of a correlation with frequency weights appears to be due to the tendency of virtually all listeners to place much greater weight on the low-frequency tone. It has been reported in past studies that pitch perception relies heavily on the lower resolved harmonics of a complex periodic sound (Moore et al., 1985; Oxenham, 2012). Even more closely related to the current findings, Dai (2000) measured cross-frequency weights for a task of pitch discrimination, similar to what was done in the present study, but his investigation included the first 12 harmonics of complex tones with fundamental frequencies ranging from 100 to 800 Hz. That study showed that the strongest weight was applied to a narrow frequency region around 600 Hz in all cases, with virtually no weight applied to the other frequencies. The frequency weights we obtained for a stimulus with only 750 and 3500 Hz components are consistent with these other findings—the weights were strongly biased toward the low frequency with little-to-no influence of the high-frequency tone in the complex. It appears that the strong low-frequency biases inherent to frequency discrimination override any additional individual variations in cross-frequency weights. Thus, with respect to weights obtained among the pure-tone discrimination measures, there was some evidence in support of idiosyncratic patterns that generalized across measures (level and duration weights). The fact that weights in those measures did not relate to frequency weights may have been due to the strong low-frequency bias inherent to pitch perception.

Moving beyond the pure-tone experiments, the patterns of weights obtained in this study were not related to the use of the high-frequency content of filtered speech in listeners with SNHL. This could indeed be because cross-frequency weights for level discrimination simply do not tap the same mechanisms responsible for effectively integrating cross-frequency information in speech. However, there may be alternative explanations for the lack of a relationship. First, it is possible that suprathreshold pure-tone results do not relate to consonant recognition scores because of the redundancy of speech information across frequency. According to that perspective, listeners do not rely exclusively on any particular narrow frequency region for consonant recognition in the same way that they make use of narrow frequency regions in pure-tone weighting tasks. We predicted that by using simple consonant-vowel stimuli, filtering the speech to either include information above 3000 Hz (containing the 3500 Hz frequency used in the weighting experiment) or not, and comparing observed changes in consonant recognition to AI-predicted changes, we could reduce the influence of this redundancy. However, current evidence is insufficient to rule out this possibility. Also, the 3000-Hz cutoff frequency included speech information from 3000 to 5600 Hz, which simply may be poorly related to weights for a pure tone at 3500 Hz.

Second, a careful attempt was made in experiment 1 to correct for any individual differences in audibility or suprathreshold discriminability of the relevant feature when measuring the pure-tone weights. However, it was not possible in experiment 2 to implement equally precise corrections to the speech stimulus. Although we applied individualized frequency-specific gain for the listeners with SNHL to increase audibility, and the regression models considered the observed scores relative to the AI predictions (which take into account audibility of the stimulus in each frequency band), there may be other suprathreshold SNHL-related deficits that still influenced the consonant recognition scores. We included each listener's measured frequency JND as a predictor representing suprathreshold deficits in the regression model, but this factor was not significant, possibly because it was only an incomplete indicator of the degree of suprathreshold deficit. Other studies have also reported that measures of spectral resolution did not predict consonant recognition scores relative to AI predictions (Dubno and Dirks, 1989; Dubno and Schaefer, 1992). Third, unfortunately, our sample size of listeners with SNHL in experiment 2 was relatively small (N = 10) and diverse with respect to etiology and audiometric configuration (see Table I and Fig. 1). It is possible that a stronger relationship between weights and recognition of filtered speech could be revealed with a larger sample size.

Related to the preceding discussion about the extent to which weights generalize to multiple tasks is the question of whether weights are fixed and invariant or are flexible and under a listener's explicit control. Previously, Doherty and Lutfi (1999) demonstrated that perceptual weights could be altered via the instructions/exposure to the stimulus provided to the listeners. In their study, they encouraged listeners to attend to a particular target tone within the complex by presenting 100 target-alone trials prior to the task, which was shown to increase the weight given to the target component. This suggests that listeners can modify, to some degree, how they weight cross-frequency information. They reported that, even after this exposure/instruction, differences between listeners with NH and SNHL remained with respect to the relative weight they gave to low- vs high-frequency tones. In the present study, providing correct/incorrect response feedback did not appear to result in differences in relative weights obtained in the referent discrimination task.² The number of trials for feedback and no-feedback conditions was small, however, and insufficient in several cases to yield significant coefficients in both feedback and no-feedback conditions. Thus, it remains an open question as to whether feedback could have yielded changes in relative weights for these listeners and methods had the experiments extended over a larger number of trials and over a longer period of time. There are other pieces of evidence from the current study indicating weights are not fixed and invariant. We showed earlier that weights could change depending on which frequency contained the more discriminable level difference (Fig. 7) and that weights changed from equal SL to equal SPL conditions (listeners may put greater weight on stimulus with higher presentation level; Fig. 9). This evidence, coupled with prior studies showing that weights change with increasing average presentation level when all tones are at the same level (Leibold et al., 2009), suggests that weights are, to some extent, flexible and perhaps under listener control based on stimulus changes.

C. Do cross-frequency weights differ between listeners with NH and SNHL?

In the present study, we measured weights both in an equal SL condition (both tones set to 15 dB SL in all listeners) and in an equal SPL condition (in listeners with SNHL the poorer threshold tone set to 15 dB SL and the better threshold tone set to that equivalent SPL; in listeners with NH both tones set to 85 dB SPL, which was the average of the presentation levels for listeners with SNHL). The presented stimulus differences were tailored to listener- and frequency-specific JNDs. The results showed that level and duration weights were significantly correlated with threshold asymmetry in the equal SL condition such that greater weight was placed on the frequency with greater hearing loss. At first glance, this appears to be consistent with past weighting studies showing greater weight in the high frequencies in listeners with high-frequency SNHL (Doherty and Lutfi, 1996, 1999). Those studies did not tailor the presented level differences according to listener- or frequency-specific discriminability. They also used stimuli with equal SPL across frequencies, but the mean SPL was higher for listeners with SNHL than for those with NH, which may explain the group differences in weights they observed [see related in Leibold et al. (2009)]. In the current study, weights were not significantly correlated with threshold asymmetry, and there was no effect of hearing loss on weights in the equal SPL condition, when all listeners and frequencies were presented the same average levels. This implies that the relationship seen in the equal SL condition likely was due to asymmetries in presentation levels rather than to the long-term consequences of asymmetries in degree of hearing loss.

These past and current weighting results are not consistent with the conclusion from other studies that listeners with SNHL always place greater weight on the frequency regions with better hearing (e.g., Moore and Vinay, 2009; Seldran et al., 2011; Varnet et al., 2019). The results also are not consistent with a previous study from our group that measured the ability of listeners with NH and SNHL to attend to different frequency regions in performing a pattern discrimination task, which showed that listeners with SNHL were markedly biased in attending to low-frequency information (Roverud et al., 2020). The results of the present study suggest that these inconsistencies among studies may exist because measured weighting differences between listeners with NH and SNHL are dominated by stimulus factors and therefore may not be indicative of more generalizable group differences in the use of cross-frequency information.

V. SUMMARY

• •After systematic controls, there were no group differences in the patterns of weights between listeners with NH and SNHL. Listeners with greater differences in thresholds across frequency weighted the poorer hearing frequency more when stimuli were presented at equal SLs. However, when stimuli were presented at equal SPLs across frequencies and listeners, there were no differences between listeners with NH and SNHL or effects of threshold difference across frequency on weights.
• •Although the weights for level discrimination and duration discrimination were related, those weights did not generalize to the task of frequency discrimination. Furthermore, none of the pure-tone discrimination weights were related to recognition of low-pass-filtered consonants in noise.
• •In some cases, the weights appeared to be influenced by the degree to which the stimulus differences were discriminable across frequency. This raises methodological issues for deriving weights in general, especially for listeners with SNHL, where JNDs are known to vary across frequency.
• •Weights appear to be highly influenced by stimulus and methodological factors, which makes it difficult to generalize the patterns of weights obtained in one task to other tasks or to real-world listening scenarios.