Background Since the mid eighties, responsiveness is considered to be a separate property of health status questionnaires distinct from reliability and validity. The aim of the study was to assess the strength of the relationship between internal consistency reliability, referring to an instrument's sensitivity to differences in health status among subjects at one point in time, and responsiveness referring to sensitivity to health status changes over time.
Background
Since the mid eighties, responsiveness is considered to be a separate property of health status questionnaires distinct from reliability and validity. The aim of the study was to assess the strength of the relationship between internal consistency reliability, referring to an instrument's sensitivity to differences in health status among subjects at one point in time, and responsiveness referring to sensitivity to health status changes over time.Methods We used three different datasets comprising the scores of patients on the Barthel, the SIP and the GO-QoL instruments at two points in time. The internal consistency was reduced stepwise by removing the item that contributed most to a scale's reliability. We calculated the responsiveness expressed by the Standardized Response Mean (SRM) on each set of remaining items. The strength of the relationship between the thus obtained internal consistency coefficients and SRMs was quantified by Spearman rank correlation coefficients.
Methods
We used three different datasets comprising the scores of patients on the Barthel, the SIP and the GO-QoL instruments at two points in time. The internal consistency was reduced stepwise by removing the item that contributed most to a scale's reliability. We calculated the responsiveness expressed by the Standardized Response Mean (SRM) on each set of remaining items. The strength of the relationship between the thus obtained internal consistency coefficients and SRMs was quantified by Spearman rank correlation coefficients.Results Strong to perfect correlations (0.90 – 1.00) was found between internal consistency coefficients and SRMs for all instruments indicating, that the two can be used interchangeably.
Results
Strong to perfect correlations (0.90 – 1.00) was found between internal consistency coefficients and SRMs for all instruments indicating, that the two can be used interchangeably.Conclusion The results contradict the conviction that responsiveness is a separate psychometric property. The internal consistency coefficient adequately reflects an instrument's potential sensitivity to changes over time.
Conclusion
The results contradict the conviction that responsiveness is a separate psychometric property. The internal consistency coefficient adequately reflects an instrument's potential sensitivity to changes over time.

Background Responsiveness, a concept introduced in the mid-eighties by bio-medical researchers, is considered to be an essential measurement property of health status questionnaires, distinct from reliability and validity [ 1 ]. However, it can be questioned whether an instrument's sensitivity to differences between health status changes over time, which refers to responsiveness, is different from an instrument's sensitivity to differences in health among subjects at one point in time, which refers to the psychometric concept of parallel forms reliability from the framework of classical test theory [ 2 ]. A number of theorists have argued that responsiveness is not a separate psychometric attribute of health status instruments, but merely some form of construct validity [ 3 ]. The aim of the study is to provide empirical evidence of this notion by investigating the relationship between instrument responsiveness and the traditional psychometric concept of parallel forms reliability as embodied by the internal consistency coefficient [ 2 , 3 ].
Background
Responsiveness, a concept introduced in the mid-eighties by bio-medical researchers, is considered to be an essential measurement property of health status questionnaires, distinct from reliability and validity [ 1 ]. However, it can be questioned whether an instrument's sensitivity to differences between health status changes over time, which refers to responsiveness, is different from an instrument's sensitivity to differences in health among subjects at one point in time, which refers to the psychometric concept of parallel forms reliability from the framework of classical test theory [ 2 ]. A number of theorists have argued that responsiveness is not a separate psychometric attribute of health status instruments, but merely some form of construct validity [ 3 ]. The aim of the study is to provide empirical evidence of this notion by investigating the relationship between instrument responsiveness and the traditional psychometric concept of parallel forms reliability as embodied by the internal consistency coefficient [ 2 , 3 ].Methods We used three datasets comprising the scores of patients on three widely used health status instruments on two moments in time in order to assess health changes. The first dataset was from a randomized clinical trial investigating the effects of arm and leg rehabilitation training on the functional recovery of stroke survivors using the 10-item Barthel (basic) activities of daily living scale [ 4 ]. Patients (n = 89) were rated one week and 12 weeks after stroke. A Barthel scale score ranges from zero to 20 points with higher scores indicating more independent functioning. The second dataset comprised the scores on the 45-item physical component of the Sickness Impact Profile (SIP) of 227 patients with myocardial infarction [ 5 ](on average 2 year interval between assessments), 120 patients with stroke [ 6 ] (3 year interval between assessments) and 141 patients scheduled for a carotid endartectomy surgical procedure [ 7 ] (3 months time interval). The SIP physical items are scored on a dichotomous scale with 1 point for each endorsed item statement. The scale ranges from 0 to 45 points with higher scores indicating higher levels of sickness related dysfunction. The third dataset contained the scores of 164 patients with Graves' ophthalmopathy scored on the 8-item psychosocial dimension of the Graves' ophthalmopathy quality of life (GO-QOL) instrument [ 8 ]. The GO-QOL scale items are scored on a 1 to 3 point rating scale. Overall scores are transformed to a 0–100 scale with higher scores indicating better psychosocial functioning. Patients completed the instrument before and three or six months after radiotherapy or eye surgery. Only subjects with no missing values at baseline or follow-up were included in the analysis. The Barthel dataset had no missing values, the SIP datasets had 13 % (16/120), 28% (64/227) and 0.7% (1/141) missing values respectively and the GO-QOL had 0.6% (1/164) missing values. For the SIP datasets, there was a mean deterioration in health (1 point), for the Barthel and GO-QOL scales patients were improved at follow-up (Table  1 ). Table 1 Score statistics and reliabilities (α) at baseline and follow-up. Barthel N = 89 SIP N = 407 GO-QOL N = 163 Baseline score (SD, IQR 1 ) 7.98 (4.52, 5–12) 5.12 (6.28, 1–7) 59.32 (24.64, 44–81) Follow-up score (SD, IQR) 14.25 (5.06, 10–19) 6.13 (7.57, 0–9) 65.22 (24.17, 50–81) Mean change score (SD) 2 6.27 (3.21) 1.01 (4.36) 5.90 (17.13) SRM 3 1.95 0.23 0.34 Chronbach's α time 1 0.86 0.92 0.83 Chronbach's α time 2 0.89 0.94 0.84 1) Distribution of change scores was approximately normal for all three datasets 2) IQR = interquartile range 3) SRM = Standardized Response Mean (see statistical analysis section) Statistical analysis The analysis aimed to assess the strength of the relationship between internal consistency reliability (Cronbach α or Kuder-Richarson-20) reflecting sensitivity to differences in health status among patients [ 3 ], and the Standardized Response Mean effect size (SRM) indicating an instrument's sensitivity to change. The SRM is calculated as the mean of the change scores divided by the standard deviation of the change scores [ 3 , 9 ]. In a stepwise procedure, we reduced the baseline internal consistency by removing the item contributing most to the internal consistency coefficient until 0.60 was reached, which was considered as the minimum standard for reliability [ 10 ]. For the 45-item SIP physical scale, two items were removed at every step. For the other instruments, one item was removed at each step. Using the remaining items at each item reduction step, we calculated the SRM. The thus decreasing internal consistency coefficients and associated SRMs were plotted and the strength of the relationship was calculated using Spearman rank correlation coefficients. All analyses were performed with SPSS 11.0, a commercially available software package.
Methods
We used three datasets comprising the scores of patients on three widely used health status instruments on two moments in time in order to assess health changes. The first dataset was from a randomized clinical trial investigating the effects of arm and leg rehabilitation training on the functional recovery of stroke survivors using the 10-item Barthel (basic) activities of daily living scale [ 4 ]. Patients (n = 89) were rated one week and 12 weeks after stroke. A Barthel scale score ranges from zero to 20 points with higher scores indicating more independent functioning. The second dataset comprised the scores on the 45-item physical component of the Sickness Impact Profile (SIP) of 227 patients with myocardial infarction [ 5 ](on average 2 year interval between assessments), 120 patients with stroke [ 6 ] (3 year interval between assessments) and 141 patients scheduled for a carotid endartectomy surgical procedure [ 7 ] (3 months time interval). The SIP physical items are scored on a dichotomous scale with 1 point for each endorsed item statement. The scale ranges from 0 to 45 points with higher scores indicating higher levels of sickness related dysfunction. The third dataset contained the scores of 164 patients with Graves' ophthalmopathy scored on the 8-item psychosocial dimension of the Graves' ophthalmopathy quality of life (GO-QOL) instrument [ 8 ]. The GO-QOL scale items are scored on a 1 to 3 point rating scale. Overall scores are transformed to a 0–100 scale with higher scores indicating better psychosocial functioning. Patients completed the instrument before and three or six months after radiotherapy or eye surgery.Only subjects with no missing values at baseline or follow-up were included in the analysis. The Barthel dataset had no missing values, the SIP datasets had 13 % (16/120), 28% (64/227) and 0.7% (1/141) missing values respectively and the GO-QOL had 0.6% (1/164) missing values. For the SIP datasets, there was a mean deterioration in health (1 point), for the Barthel and GO-QOL scales patients were improved at follow-up (Table  1 ).Score statistics and reliabilities (α) at baseline and follow-up.1) Distribution of change scores was approximately normal for all three datasets2) IQR = interquartile range3) SRM = Standardized Response Mean (see statistical analysis section)Statistical analysis The analysis aimed to assess the strength of the relationship between internal consistency reliability (Cronbach α or Kuder-Richarson-20) reflecting sensitivity to differences in health status among patients [ 3 ], and the Standardized Response Mean effect size (SRM) indicating an instrument's sensitivity to change. The SRM is calculated as the mean of the change scores divided by the standard deviation of the change scores [ 3 , 9 ]. In a stepwise procedure, we reduced the baseline internal consistency by removing the item contributing most to the internal consistency coefficient until 0.60 was reached, which was considered as the minimum standard for reliability [ 10 ]. For the 45-item SIP physical scale, two items were removed at every step. For the other instruments, one item was removed at each step. Using the remaining items at each item reduction step, we calculated the SRM. The thus decreasing internal consistency coefficients and associated SRMs were plotted and the strength of the relationship was calculated using Spearman rank correlation coefficients. All analyses were performed with SPSS 11.0, a commercially available software package.
Statistical analysis
The analysis aimed to assess the strength of the relationship between internal consistency reliability (Cronbach α or Kuder-Richarson-20) reflecting sensitivity to differences in health status among patients [ 3 ], and the Standardized Response Mean effect size (SRM) indicating an instrument's sensitivity to change. The SRM is calculated as the mean of the change scores divided by the standard deviation of the change scores [ 3 , 9 ]. In a stepwise procedure, we reduced the baseline internal consistency by removing the item contributing most to the internal consistency coefficient until 0.60 was reached, which was considered as the minimum standard for reliability [ 10 ]. For the 45-item SIP physical scale, two items were removed at every step. For the other instruments, one item was removed at each step. Using the remaining items at each item reduction step, we calculated the SRM. The thus decreasing internal consistency coefficients and associated SRMs were plotted and the strength of the relationship was calculated using Spearman rank correlation coefficients. All analyses were performed with SPSS 11.0, a commercially available software package.Results Figures  1 ,  2  and  3  show the spearman rank correlations between the internal consistency coefficients and the SRM using the scores on the Barthel, the SIP and the GO-QOL respectively. The spearman rank correlations ranged between 0.90 for the Barthel index to 1.00 for the GO-QoL indicating strong to perfect relations between internal consistency and responsiveness. Figure 1 Barthel – Relation between the internal consistency reliability (alpha) and the SRM  (Spearman's r = 0.90) Figure 2 SIP – Relation between the internal consistency reliability (alpha) and the SRM  (Spearman's r = 0.99) Figure 3 GO-QOL – Relation between the internal consistency reliability (alpha) and the SRM  (Spearman's r = 1.00)
Results
Figures  1 ,  2  and  3  show the spearman rank correlations between the internal consistency coefficients and the SRM using the scores on the Barthel, the SIP and the GO-QOL respectively. The spearman rank correlations ranged between 0.90 for the Barthel index to 1.00 for the GO-QoL indicating strong to perfect relations between internal consistency and responsiveness.Discussion Our results contradict the conviction that responsiveness is a separate psychometric property of health scales. Internal consistency reliability, reflecting a scale's sensitivity to cross-sectional differences in health, closely coincided with the instruments' sensitivity to change as measured with the standardized response mean. Our results also reflect what is already known within the framework of classical test theory. A test score cannot correlate more highly with any other variable than its own true score [ 2 ]. This implies that the maximum correlation between an observed test score and any other variable, i.e. its validity, is the square root of its reliability [ 2 ]. Thus, the more reliable a test, the more potential for validity, in this case responsiveness, there exists. We used nested versions of the same test, which are highly correlated with each other, to illustrate this phenomenon. It is likely, however, that the results will also apply with different instruments measuring similar health constructs that are highly inter-correlated. It should also be noted that the results apply to one-dimensional psychometric scales and not to instruments containing so-called "causal" variables, for example disease symptoms [ 3 ] since these instruments are not strictly one-dimensional. We used the SRM effect size that uses the standard deviation the change scores and therefore includes all information about the changes on the selected instruments. The results can not generalized to alternative effect sizes such as Cohen's effect size or Guyatt's responsiveness statistic [ 1 ] because these largely depend on the variability of scores at baseline or the variability in scores obtained from a separate, not improved, sample. In a frequently cited paper, Guyatt et al. [ 1 ] made the distinction between discriminative instruments, whose purpose it is to measure differences between subjects and evaluative instruments, designed to examine change over time. This in contrast to most of the scales used in clinical medicine (blood pressure, cardiac output), which are assumed to work well in both discriminative and evaluative roles. To corroborate his arguments, he used the hypothetical example of two health status instruments designed to evaluate therapeutic interventions in patients with chronic lung disease that were presented to the same patient sample (Table  2 ). "Evaluative" instrument A showing poor test-retest reliability because of small between subject score variability but excellent responsiveness, and "discriminative" instrument B with excellent reliability because of large between-subject score variability and poor responsiveness. From Table  2 , however, it can be seen that this representation of instrument behaviour in clinical research is logically inconsistent, since it does not explain how two instruments, both measuring the same health construct show such divergent score distributions at baseline. According to instrument A the sample is highly homogeneous, while it is highly heterogeneous according to instrument B. In Appendix 1 (see  additional file 1 ), we show that the above representation is not impossible, but highly unlikely since it occurs only in extreme situations. Table 2 Representation of the scores on "evaluative" instrument A and "discriminative" instrument B in a randomized clinical trial [1] Instrument A Time 1 Time 2 Intervention Time 3 Difference score Exercise test Result Subject 1 8 9 Verum 15 +6 Much improved Subject 2 9 8 “” 15 +7 Much improved Subject 3 8 9 “” 15 +6 Much improved Subject 4 9 8 “” 15 +7 Much improved Subject 5 8 9 Placebo 8 -1 Unchanged Subject 6 9 8 “” 9 +1 Unchanged Subject 7 8 9 “” 8 -1 Unchanged Subject 8 9 8 “” 9 +1 Unchanged Instrument B Time 1 Time 2 Time 3 Difference score Exercise test Result Subject 1 5 5 Verum 5 0 Much improved Subject 2 9 9 “” 9 0 Much improved Subject 3 13 13 “” 13 0 Much improved Subject 4 17 17 “” 17 0 Much improved Subject 5 5 5 Placebo 5 0 Unchanged Subject 6 9 9 “” 9 0 Unchanged Subject 7 13 13 “” 13 0 Unchanged Subject 8 17 17 “” 17 0 During the past 20 years, clinimetric research has resulted in about 25 definitions and 30 measures of instrument responsiveness, sometimes referred to as sensitivity to change or longitudinal validity [ 11 ]. Moreover, it is evaluated in literally hundreds of published papers on the validation of health status instruments. Our results show that responsiveness, as measured with the SRM, mirrors the traditional concept of parallel test reliability as embodied by the internal consistency coefficient. When comparing instruments measuring similar health constructs, an instrument sensitive to health differences among subjects is also likely to be sensitive to therapy-induced change as well. However, further empirical data will be needed to confirm the relationship between internal consistency and responsiveness, e.g., by reviewing studies in which health status instruments were compared on their responsiveness.
Discussion
Our results contradict the conviction that responsiveness is a separate psychometric property of health scales. Internal consistency reliability, reflecting a scale's sensitivity to cross-sectional differences in health, closely coincided with the instruments' sensitivity to change as measured with the standardized response mean. Our results also reflect what is already known within the framework of classical test theory. A test score cannot correlate more highly with any other variable than its own true score [ 2 ]. This implies that the maximum correlation between an observed test score and any other variable, i.e. its validity, is the square root of its reliability [ 2 ]. Thus, the more reliable a test, the more potential for validity, in this case responsiveness, there exists. We used nested versions of the same test, which are highly correlated with each other, to illustrate this phenomenon. It is likely, however, that the results will also apply with different instruments measuring similar health constructs that are highly inter-correlated. It should also be noted that the results apply to one-dimensional psychometric scales and not to instruments containing so-called "causal" variables, for example disease symptoms [ 3 ] since these instruments are not strictly one-dimensional.We used the SRM effect size that uses the standard deviation the change scores and therefore includes all information about the changes on the selected instruments. The results can not generalized to alternative effect sizes such as Cohen's effect size or Guyatt's responsiveness statistic [ 1 ] because these largely depend on the variability of scores at baseline or the variability in scores obtained from a separate, not improved, sample.In a frequently cited paper, Guyatt et al. [ 1 ] made the distinction between discriminative instruments, whose purpose it is to measure differences between subjects and evaluative instruments, designed to examine change over time. This in contrast to most of the scales used in clinical medicine (blood pressure, cardiac output), which are assumed to work well in both discriminative and evaluative roles. To corroborate his arguments, he used the hypothetical example of two health status instruments designed to evaluate therapeutic interventions in patients with chronic lung disease that were presented to the same patient sample (Table  2 ). "Evaluative" instrument A showing poor test-retest reliability because of small between subject score variability but excellent responsiveness, and "discriminative" instrument B with excellent reliability because of large between-subject score variability and poor responsiveness. From Table  2 , however, it can be seen that this representation of instrument behaviour in clinical research is logically inconsistent, since it does not explain how two instruments, both measuring the same health construct show such divergent score distributions at baseline. According to instrument A the sample is highly homogeneous, while it is highly heterogeneous according to instrument B. In Appendix 1 (see  additional file 1 ), we show that the above representation is not impossible, but highly unlikely since it occurs only in extreme situations.Representation of the scores on "evaluative" instrument A and "discriminative" instrument B in a randomized clinical trial [1]During the past 20 years, clinimetric research has resulted in about 25 definitions and 30 measures of instrument responsiveness, sometimes referred to as sensitivity to change or longitudinal validity [ 11 ]. Moreover, it is evaluated in literally hundreds of published papers on the validation of health status instruments. Our results show that responsiveness, as measured with the SRM, mirrors the traditional concept of parallel test reliability as embodied by the internal consistency coefficient. When comparing instruments measuring similar health constructs, an instrument sensitive to health differences among subjects is also likely to be sensitive to therapy-induced change as well. However, further empirical data will be needed to confirm the relationship between internal consistency and responsiveness, e.g., by reviewing studies in which health status instruments were compared on their responsiveness.Authors' contributions Robert Lindeboom conceived the idea for the manuscript, Mirjam Sprangers and Robert Lindeboom wrote the manuscript, Koos Zwinderman provided the mathematics and rewrote parts of the manuscript in earlier drafts
Authors' contributions
Robert Lindeboom conceived the idea for the manuscript, Mirjam Sprangers and Robert Lindeboom wrote the manuscript, Koos Zwinderman provided the mathematics and rewrote parts of the manuscript in earlier draftsSupplementary Material Additional File 1 Appendix 1: Is it possible to have one high reliable scale with low 'responsiveness', and a low reliable scale with high 'responsiveness' measuring the same construct? Click here for file
Supplementary Material
Additional File 1
Appendix 1: Is it possible to have one high reliable scale with low 'responsiveness', and a low reliable scale with high 'responsiveness' measuring the same construct?Click here for file


A fresh look at classic work of Thomas Gold on how the inner ear processes sound

Sitting in the enveloping quietness of an anechoic chamber, or other quiet spot, you soon become aware that the ear makes its own distinctive sounds. Whistling, buzzing, hissing, perhaps a chiming chorus of many tones—such continuous sounds seem remarkably nonbiological to my perception, more in the realm of the electronic.Even more remarkable, put a sensitive microphone in the ear canal and you will usually pick up an objective counterpart of that subjective experience. Now known in auditory science as spontaneous otoacoustic emission, the sound registered by the microphone is a clear message that the cochlea uses active processes to detect the phenomenally faint sounds—measured in micropascals—that our ears routinely hear. If the ear were more sensitive, we would need to contend with the sound of air molecules raining upon our eardrums.What is that process—the mechanical or electrical scheme that Hallowell Davis in 1983 called the ‘cochlear amplifier’ ( Davis 1983 )—which energises the pea-sized hearing organ buried in the solid bone of our skull?That question has engaged my curiosity since the late 1970s, when English auditory physicist David Kemp first put a microphone to an ear and discovered the telltale sounds of the cochlea at work ( Kemp 1978 ). Siren-like, the sounds have drawn me into the theory and experiment of cochlear mechanics, now as part of a PhD course at the Australian National University in Canberra. I am studying the micromechanics of this process from a theoretical point of view, and investigating whether a resonance picture of some kind can be applied to the faint but mysterious sounds most cochleas emit.Kemp's discoveries are rightly viewed as opening a fresh path to auditory science, and to the tools and techniques for diagnosing the functional status of the cochlea. But in terms of fundamental understanding, a key paper remains that of Thomas Gold more than half a century ago ( Gold 1948 ). Still cited widely today, this paper deals with the basic question of how the cochlea works to analyse sound into its component frequencies. Two prominent theories—sympathetic resonance, proposed by  Hermann Helmholtz (1885) , and travelling waves, proposed by  Georg von Békésy (1960) —need to be distinguished ( Figure 1 ). In a nutshell, are there tiny, independently tuned elements in the cochlea, like the discrete strings of a piano, that are set into sympathetic vibration by incoming sound (Helmholtz), or is the continuously graded sensing surface of the cochlea hydrodynamically coupled so that, like flicking a rope, motion of the eardrum and middle ear bones causes a travelling wave to sweep from one end towards the other (von Békésy)?The first option, sympathetic resonance, has the advantage of allowing vanishingly small energies to build up, cycle by cycle, into an appreciable motion—like boosting a child on a swing. The second, travelling wave, has the weight of von Békésy's extensive experiments behind it. At the same time, one of the drawbacks of the travelling wave theory is the difficulty of accounting for the ear's exquisite fine tuning: trained musicians can easily detect tuning differences of less than 0.2%. Even von Békésy himself notes, on page 404 of his classic book, that ‘the resonance theory of hearing is probably the most elegant of all theories of hearing’.Gold's work, done in collaboration with RJ Pumphrey ( Gold and Pumphrey 1948 ), was the first to consider that the ear cannot act passively, as both Helmholtz and von Békésy had thought, but must be an active detector. Gold was a physicist who had done wartime work on radar, and he brought his signal-processing knowledge to bear on how the cochlea works. He knew that, to preserve signal-to-noise ratio, a signal had to be amplified before the detector, and that ‘surely nature can't be as stupid as to go and put a nerve fibre—that is a detector—right at the front end of the sensitivity of the system’. He therefore proposed that the ear operated like a regenerative receiver, much like some radio receivers of the time that used positive feedback to amplify a signal before it was detected. Regenerative receivers were simple—one could be built with a single vacuum tube—and they provided high sensitivity and narrow bandwidth. A drawback, however, was that, if provoked, the circuit could ‘take off’, producing an unwanted whistle. Gold connected this with the perception of ringing in the ear (tinnitus), and daringly suggested that if a microphone were put next to the ear, a corresponding sound might be picked up. He experimented, placing a microphone in his ear after inducing temporary tinnitus with overly loud sound. The technology wasn't up to the job—in 1948 microphones weren't sensitive enough—and the experiment, sadly, failed.Gold's pioneering work is now acknowledged to be a harbinger of Kemp's discoveries. But there is one aspect of Gold's paper that is not so widely considered: Gold's experiments led him to favour a resonance theory of hearing. In fact, the abstract of his 1948 paper declares that ‘previous theories of hearing are considered, and it is shown that only the resonance theory of Helmholtz… is consistent with observation’.Gold and Pumphrey did psychophysical experiments in which hearing thresholds were determined for listeners first for continuous pure tones and then for increasingly briefer stimuli of the same frequency. Gold and Pumphrey showed that their results could only be accounted for by considering the cochlea as a set of resonators, each of which responds to a narrow frequency range.In a second neat experiment, listeners had to detect differences between the sound of repetitive tone pips (series one) and those same stimuli but with the phase of every second pip inverted (series two, in which compressions replaced rarefactions and vice versa). Out-of-phase pips should counteract the action of in-phase pips and, following the child-on-swing analogy, rapidly bring swinging to a halt. Therefore, the argument goes, the two series should sound different. By increasing the silent interval between pips until the difference disappeared, the experimenters could infer how long the vibrations (or swinging) appeared to persist and could then put a measure on the quality factor  (Q),  or narrowness in frequency range, of the presumed underlying resonance.(Q),From the first experiment, Gold and Pumphrey derived values of  Q  of 32 to 300, meaning that the range of response was as little as 1/300-th of the imposed frequency—based on the picture of a broad travelling wave. The second experiment gave comparable results. However, their resonance interpretation has been dismissed because of a methodological flaw in the second experiment: the spectral signatures of the two series are not the same and provide additional cues. Nevertheless, it is not widely appreciated that the first experiment seems methodologically sound, and its results remain persuasive.QI think the resonance theory deserves reconsideration. The evidence of my ears tells me that the cochlea is very highly tuned, and an active resonance theory of some sort seems to provide the most satisfying explanation. Furthermore, as well as Gold's neglected experiment, we now know from studies of acoustic emissions that the relative bandwidth of spontaneously emitted sound from the cochlea can be 1/1000 of the emission's frequency, or less. My research, guided by Professors M. V. Srinivasan and N. H. Fletcher, has centred on finding an answer to that most fundamental question: if the cochlea is resonating, what are the resonant elements?A point of inspiration for me is Gold's later discussion of cochlear function ( Gold 1987 )—some nine years after Kemp's discoveries had been made. Gold draws a striking analogy for the problem confronting the cochlea, whose resonant elements—whatever they are—sit immersed in fluid (the aqueous lymph that fills the organ). To make these elements resonate is difficult, says Gold, because they are damped by surrounding fluid, just like the strings of a piano submerged in water would be. He concludes that, to make ‘an underwater piano’ work, we would have to add sensors and actuators to every string so that once a string is sounded the damping is counteracted by positive feedback. ‘If we now supplied each string with a correctly designed feedback circuit,’ he surmises, ‘then the underwater piano would work again.’My research is investigating what Gold's underwater piano strings might be. A suggestion put forward in a recent paper ( Bell and Fletcher 2004 ) is that resonance might occur in the space between the cochlea's geometrically arranged rows of outer hair cells. These cells are both effectors (they change length when stimulated) and sensors (their stereocilia detect minute displacements), so a positive feedback network can form that sets up resonance between one row of cells and its neighbour. The key is to transmit the feedback with the correct phase delay, and the new paper describes how this can be done using ‘squirting waves’ in the gap occupied by the outer hair cell stereocilia. The paper suggests that the outer hair cells create a standing wave resonance, from which energy is delivered to inner hair cells (where neural transduction takes place). In this way, the input signal is amplified before it is detected—an active system functioning just like Gold's regenerative receiver.With a prime candidate in place for the resonating elements, this should, I think, prompt us to re-evaluate resonance theories of hearing, which were first put forward by the ancient Greeks and which, irrepressibly, keep resurfacing. The best-known resonance theory was that formulated by Helmholtz, but at that time no satisfactory resonating elements could be identified, and it lapsed until Gold's attempt to revive it. There are other difficulties in reviving a resonance theory of hearing, but I think they can be overcome.If there really are resonant elements in the ear, the outstanding question would be, how are they stimulated? It is conceivable that motion of the conventional travelling wave sets them off, in which case we have an interesting hybrid of travelling wave and resonance. The other possibility, which I favour, is that outer hair cells are stimulated by the fast pressure wave that sweeps through all of the cochlear fluid at the speed of sound in water (1,500 m/s). If that is the case, and outer hair cells are primarily pressure sensors, not displacement detectors, then the ear is a fully resonant, pressure-driven system. New life, perhaps, to that old resonance idea.