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Individual loudness functions
J. Sotmd Vib. (1970) 11 (4), 399-410
INDIVIDUAL LOUDNESS FUNCTIONS CLARIBELM. DE BARBENZA,M. E. BRYANAND W. TEbIPEST
Audiology Research Unit, Department of Electrical Engineerhlg, University of Salford, Salford 5, Lancs, England (Received 24 February 1969) Individual loudness functions have been obtained by a form of magnitude estimation for 15 observers. The experiments took place over a period of five months and used two different procedures. The results show that most of the individual observers can produce a loudness function of consistent slope and that in many cases this slope is significantly different from the mean slope of the group. At the end of the loudness estimation procedure each observer was asked to complete the Minnesota multiphasic personality inventory (M.M.P.I.) test in its individual form. A comparison of the slopes of the loudness functions with a measure of individual excitability shows a correspondence between increasing excitability and increasing steepness of loudness function. It is concluded that the major cause of inter-individual differences is probably psychological rather than physiological.
1. INTRODUCTION The problems associated with attributing numbers to the loudness of sounds have exercised many research workers over a period of about the last 40 years. The early work (reviewed in detail in 1953 by Robinson [1]) seemed to demonstrate that, while observers using various procedures were certainly able to provide numbers associated with loudness, the loudness scales produced differed considerably from one experimenter to the next. More recent work (see, for example, reference 2) has narrowed down the variations in the results to some extent and we now have in existence standard procedures which can be used to relate loudness to intensity. It is not clear how much of the apparent improvement in accuracy is due to real improvements in technique, and how much is due to a reduction in the variety of loudness evaluation procedures in use (see, for example, references 3 and 4). There is, however, one aspect of the loudness scaling procedure which has perhaps received less attention than it deserves; this is the question of the importance of inter-individual differences in scaling. This topic has been mentioned, usually in passing, in a number of the earlier papers. For example Fletcher and Munson [5] stated that they found large variations between the judgments of individual observers, and concluded that the investigation must therefore be conducted on a statistical basis. Zwieker, Flottorp and Stevens [6] discussed variability in loudness matching experiments and found evidence of consistent inter-individual differences which they attributed to differences in subjective criteria. In his paper on the "Relation between the Soue and Phon scales of loudness", Robinson [I] pointed out that individuals, on the whole, maintain a constant tendency with regard to their departure from average in his loudness halving and doubling experiments. More recently, Hellman and Zwislocki [7] have made the comment that in their loudness estimation experiments some individuals do not deviate significantlyfrom the group median, but others deviate more substantially; they did not, however, take up this point in detail and the general tone of their paper is that individuals are able to make consistent loudness judgments without large inter-individual differences. The four papers quoted above demonstrate that the existence of inter-individual differences 27 399
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has been noticed by various experimenters, but does not seem to have been regarded as of enough importance to justify any specific investigation. The important questions: do signi. fieant inter-individual differences exist ? how might they affect established loudness evaluation procedures ? and, what are their causes ? are not answered by the work on group loudness. It seems likely that individual loudness functions have not been of very much concern to many of the workers, simply because the very existence of differences between individuals was not seriously taken up by experimental psychologists until about ten years ago. Since most of the basic loudness work was done more than ten years ago, it is not really surprising that (so far as we are aware) none of the workers went so far as to apply any tests to determine homogeneity of the group he used. Much of the work off inter-individual differences in scaling performance, dating from 1958 onwards, has been reviewed by Ekman, Hosman, Lindman, Ljungberg and Akesson [8] who conclude, from results mainly in modalities other than loudness, that inter-individual differences exist, and that they are due to a combination of both genuine differences in sensitivity and the effects of response bias. In the field of loudness scaling it appears that there are only three papers (up to the end of 1968) dealing specifically with the differences between individuals, these are McGill [9], Stevens and Guirao [10], and Reason [11]; of these three, only Stevens and Guirao was included in the review by Ekman et aL [8] in 1968. In view of the sparseness of the literature and the fact that the two papers cited first seem to reach different conclusions, it is perhaps worthwhile to outline briefly their methods and conclusions. In the work reported by McGill [9], observers were asked to scale the loudness of I000 Hz tones by making a pencil mark on a line six inches long. To quote McGill, "The line was an absolute rating scale whose left-hand end symbolized 'the weakest tone you could possibly hear', while the right-hand end was supposed to be the 'loudest tone you could possibly hear.' Each tone was rated on a separate line and prior ratings were covered from s i g h t . . . Loudness ratings are reported as the distance (in 1/64ths of an inch) from the left-hand end of the line to the pencil mark." Two experimental procedures were used: in one, tones of 10 dB intervals in the range 30 to I00 dB were presented in random order until a total of 60 assessments had been made. In the other procedure 60 stimuli at I dB intervals from 41 to I00 dB were presented five times over in random order. Using the first of the two methods outlined above, a number of observers performed the experiment twice, with an interval of approximately one week between. It was found that while the agreement between the two determinations by the same observer a week apart was not perfect, it was quite good. However, the inter-subject differences were quite marked. McGill described the individual loudness functions obtained as "highly stylized but reproducible," making the point that inter-individual differences were most marked at low intensities. He infers that the differences between subjects are not random but represent stable parameters. McGill goes on to consider possible transformations which could be used to reduce or eliminate the inter-subject differences, but concludes that there is a variation in the slope of the loudness function from individual to individual. He finds it hard to believe that the actual sensory process differs between individuals as much as his results suggest and he takes the view that the differences arise from some internal "transformation" process which affects both the slope of the loudness function and its reference point. He goes on to describe the loudness evaluation process as being similar to the use of a ruler which can be "stretched" and in this way give different slopes for different individuals. While McGill's work does seem to provide strong evidence for the existence of individual loudness functions, it suffers from one possible limitation, the use of a lengfh assessment intermediate between the loudness and the number. This procedure really turns the experiment into a cross-modality procedure, with the assumption that length and number can be
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assumed to be linearly related. A further minor limitation is that the method, or at least the data as presented, does not lend itself to applying significance tests to the inter-individual differences. The suggestion which he makes, of a "rubber-scale" phenomenon, seems rather to beg the question of why the individual slopes differ so much, by merely describing it in a different way. The work of Stevens and Guirao [10] employed a rather different procedure. They asked a number of observers (11 in aid to set up their loudness functions by a production-estimation procedure in which the observers set the 1000 Hz tone to a number of different levels of loudness and assigned a number to each of them. Each of the eleven observers performed the experiment twice, with an interval of from one to six months between the two determinations. The two interesting questions which may be asked about the results are, how much variability is there between individuals ? and, are individuals consistent in their first and second trials .9 The results were plotted by Stevens and Guirao as "estimates of loudness" on a logarithmic scale vs. sound pressure level in decibels. The slope of the loudness function defined in this way is fl, the exponent in the power law assumed to relate sensation to stimulus magnitude. The measured fl values ranged from 0.40 to 1.10 with a mean of 0.73 and a standard deviation of 0"19, demonstrating a considerable variability between observers. On the question of the consistency of the individual loudness data between the first and second experiments for each observer, Stevens and Guirao state the correlation coefficient between the first and second test to be r = 0.53. They conclude from this that observers are not particularly consistent over a period of time and that "the observer may come to differ from his own previous function almost as much as he does from any other observer's function." However, their data ([10] Table I, p. 2213) have now been re-calculated (Stevens [12]) with the result r = 0.74. A " t " test was then applied and it was found that the probability of such a high correlation arising by chance was no greater than P = 0.01. This revised estimate indicates that there is stronger evidence of a tendency for observers to give similar values for the slope of the loudness function on different occasions. Reason [11] was not directly concerned with individual loudness functions, but, in the course of work on the susceptibility of individuals to motion sickness, he obtained mean loudness scaling data for two groups, selected according to their susceptibility, and lack of susceptibility, to motion sickness. He found that the two groups differed significantly in the steepness of their loudness functions. He thus demonstrated that differences do exist and can be related to other measurable psychophysical factors. The work of McRobert et aL [3] on the magnitude estimation of loudness was not directly concerned with individual loudness functions, but involved the determination of a very large number of single estimates of relative loudness by different observers. The results were treated from the point of view of group mean data but the scatter of individual loudness estimates for the same loudness interval from different observers was very large, and raised the question of the extent to which group means represent the loudness estimates of individuals. The main conclusion from the work outlined above seems to be that there is some evidence of the existence of individual loudness functions, but the evidence is not entirely conclusive. Both McGill [9], and Stevens and Guirao [10] take the view that variations in the sensory process from individual to individual are not likely to cause the large differences found between loudness functions, a view with which the present authors are inclined to agree, although it is difficult to site any positive scientific evidence for this argument. However, having discarded, somewhat arbitrarily, what one might call the "physiological"explanation, the idea arose that it might be possible to relate loudness judgments to measurable psychological traits. The work to be described in this paper therefore sets out to answer two main questions:
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Do individual observers possess individual loudness functions 9.and, if the existence of individual loudness functions can be demonstrated, is it then possible to relate any features of them to individual psychological traits ? A third, and less important aim of the work, was to obtain some measure of the stability of the individual loudness functions by extending the measurements over a period of months and using two different loudness estimation procedures. 2. EXPERIMENTAL PROCEDURE The method employed is that of relative loudness estimation, in which the observer is presented with pairs of tones and asked to estimate the loudness of the second tone in relation to the first. The details of the procedure, and the arguments for it, have been presented at length in an earlier publication [3], but it would perhaps be worthwhile to outline them again here. The primary aim of the procedure is the avoidance of bias. Garner [13] has shown that when a range of stimuli is presented to an observer he appears to be biased towards the mid-point of the range available, in making half-loudness judgments. Garner's results suggested that in his, admittedly somewhat extreme, conditions, the effects of bias could completely over-ride the subjective judgment of the observer. These results led us to conclude that the constant-stimulus method, applied to fractional and multiple loudness judgments, was not reliable. The effects of constant stimulus bias can be avoided in the alternative loudness scaling procedure of magnitude adjustment, which has been investigated in some detail by Stevens and Poulton [14]. They asked observers to adjust a tone to half-loudness by means of a potentiometer and found that the potentiometer characteristic (i.e. the relation between intensity and angular rotation) had a large, and highly significant, effect on the half-loudness judgments. Although Stevens and Poulton suggested that, by a process of successive approximation, a "correct" potentiometer could be designed, the present authors are somewhat suspicious of the reliability of this procedure. The case of magnitude estimation, which now seems to be generally regarded as the best method of loudness scaling, eliminates both the constraints of the constant stimulus method and the apparatus difficulties of magnitude adjustment, by simply presenting the observer with a series of tones and asking him to describe their loudness compared to a reference tone. Hellman and Zwislocki [15] have shown that in this method the shape of the loudness function obtained depends on the number assigned to the reference tone. A further modification of this procedure, in the form of the abandonment of a fixed number for the reference tone, has been used by Stevens [16] and would appear to avoid the difficulty demonstrated by Hellman and Zwislocki. Although this form of magnitude estimation eliminates the sources of bias mentioned above, it may still suffer from a significant context error. This arises because all the judgments are made in a short space of time, and, as each judgment is made, another reference point is created in the mind of the observer. His later judgments will therefore be made with reference to all his previous estimates, rather than to the reference tone alone. This could be important in the case of levels which are far from the reference level, since the observer may make his judgment with reference to the nearest tone he has so far heard, rather than the reference level. By this process all his judgments are reduced to judgments of small intervals and it is not clear whether any real judgments over the larger intervals are ever made. Whether this context effect is important is difficult to say; Stevens [17] says "there is little doubt that the number the observer assigns to a tone is sometimes influenced by what he has called some previous tones", but does not accept that the effect is important. Garner's work
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on constant stimulus methods [13, 18] suggests, however, that context affects all judgments after the first, and that the effect is so great in some cases as to render the results meaningless. It would therefore seem wise, in the design of a magnitude estimation experiment, to eliminate this effect as far as possible. The experimental procedure adopted was therefore as follows. Tones were presented in pairs, the second tone being the more intense of the two. In the first experiment only one pair of tones was presented on any one day and the observer returned daily over a period of five months until he had judged each tone pair at least four times. In the second experiment all the tone-pairs were presented at least four times in a single listening session of about one hour. The tone pairs were presented in a different random order in each experiment and to each observer. Twelve pairs of tones ~ere used, all at I000 Hz, the sound pressure levels being 40]50, 50/60, 60/70, 70/80, 80/90, 40/60, 60/80, 40/70, 60/90, 40/80 50/90 and 40/90 (in dB re 0.0002 /~bar). Throughout the experiments the same instructions were given to the observers: "In this experiment you will hear a pair of tones. I want you to say how many times the second is louder than the first. You will be hearing the pairs of tones until you make your dccision." All the tones were presentcd binaurally under free-field conditions in a sound-insulated room (sce reference 19). Although the room was not fully anechoic it had a wall treatment which was highly absorbent at 1000 Hz. The tones were of 1 see duration with a 1 sec interval between tones, and had rise and fall times of approximately 20 msec to reduce audible starting and finishing transients. Tones were presented in an A-B-A-B sequence, always starting with the lower intensity of the pair, until the observer indicated that he had reached a decision. The sound pressure levels at the observer's ear position were checked daily with a calibrated microphone to ensure that the absolute levels remained constant throughout the experiment. Before the start of the loudness estimation experiments the audiogram of each observer was measured to make sure that all those taking part had normal hearing; no losses greater than 10 dB were found at 1000 Hz. After all the listening tests had been completed each observer was asked to complete the M.M.P.L (Minnesota multiphasic personality inventory) questionnaire in its individual form [20]. 3. RESULTS In order to perform a useful analysis of the loudness data obtained it was necessary to reduce each individual's data to as simple a form as possible, preferably to a single number and its variance. Most statistical procedures are based on normally distributed data, and as a first step an examination of the distribution of estimates was made. It was found that in general the distribution was highly skewed, with a long "tail" of high values. The transformation y = log,0 (observer's estimate) was therefore applied to all the data, and had the effect of making the distributions of estimates approximately normal. All subsequent computations were carried out on the transformed variable y. As a second step it was necessary to consider how each individual's data could best be combined. Most previous work on loudness has been concerned with the exponent of the loudness function which appears as the slope when y is plotted against intensity in dB, and this suggested immediately that the slope of the individual's loudness function was probably the most usefulparameter. The work of McGill [9] and others has shown that individual loudness functions are usually not straight, which implies that the slope must be some form of average over the range of measurement. A further complication of the present technique
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(discussed in more detail in reference 3) is that the estimate of relative loudness over the larger intervals (greater than 10 dB) can be arrived at by two or more routes involving one, two, or more estimates in combination, and that in most cases combining the estimates over several small intervals gives a larger value than the direct estimate over the whole interval.
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Figure I. Individual loudness functions for 15 observers obtained in the first experiment.
With the above difficulties in mind, and the knowledge that if the analysis were to proceed some procedure must be devised, several different possibilities were considered. It was found that, if the results for each interval were combined (i.e. the estimates for, say, 40/50, 50/60, 60/70, 70/80 and 80/90 were all pooled), and the results plotted in the form mean y against intensity interval in dB, the function obtained was fairly linear and did not exhibit any consistent curvature. This procedure was therefore adopted and each individual's results plotted in this form. It is acknowledged that this procedure is to some extent arbitrary, and that a
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different procedure might well produce a slightly different loudness function. It is, however, a practical method o f combining an individual's estimates in order to extract a working value for the mean slope, and there is no reason to suppose that the method used is likely to invalidate inter-individual comparisons which are, after all, the main purpose o f this work. Having arrived at a procedure by which each individual's data could be plotted in a simple form the 15 sets o f data were considered from several points of view. The individual data for the 15 observers in the first experiment are shown in Figure 1. 3. I. A COMPARISONOF THE GROUPMEANDATAOBTAINEDIN EXPERIMENTS 1 AND 2 This comparison was made to establish the equivalence, or otherwise, of the two methods of magnitude estimation used. Figure 2 shows the mean data obtained for all the observers in the two experiments plotted in the form y vs. intensity interval. In calculating, say, the experiment 1 point for a 20 dB
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intensity interval, all the estimates o f all the observers over the various 20 dB intervals in the experiment were averaged, after the y = log10 (observer's estimate) transformation had been made. The lines on Figure 2 are least squares regression lines fitted to the mean data and the slope values are shown on the lines. A " t " test was applied to test the significance of the difference between the slopes and gave " t " = 1.26, indicating that the slopes are not significantly different (P = 0.25). 3.2. A COMPARISON
OF THE INDIVIDUAL DATA OBTAINED IN EXPERIMENTS
I AND 2
Having decided, on the basis of the mean results shown in Figure 2, that the two methods give extremely similar results for the slope o f the loudness function for a group of listeners, the second comparison becomes a measure o f the extent to which individuals can produce self-consistent data over a period of time. The individual results were therefore considered as follows. First a least squares regression line was fitted to each individual's data, which were expressed in the same form as in Figure 1. This calculation was performed for both the first and second experiments, the slopes being denoted as b I and b2, respectively. Table I shows the
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calculated values of bl and b2, the " t " value for the difference between bl and bz, and P, the probability range in which the " t " value falls (using the method described by Crow, Davies and Maxfield [21]). It is seen from this table that in no case is P less than 0.05, the level of probability usually regarded as denoting statistical significance. Three of the observers fall into the range 0.05 < P < 0.I0, three in the range 0"10 < P < 0.25 and the remaining seven give P > 0.25. This test therefore shows that observers in general give very similar slopes for their loudness functions in the two experiments. In addition to the " t " test computation, the values ofb~ and b2 were used to calculate the correlation coefficient " r " between the first and second experiments, the value of " r " was found to be 0.95, significant at the level P < 0.001. The results o f the " t " test, and the correlation coefficient, taken together, suggest that many observers can make self-consistent estimates o f relative loudness, and thus support the hypothesis that individual loudness functions exist, and can be determined. TABLE 1
Comparison of the slopes of the individual loudnessfimctions found fll experhnents I (bi) and 2 (b2) Observer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
bl 0.020 0.020 0.016 0-029 0.019 0.022 0.037 0.013 0.020 0.025 0.020 0.012 0-070 0.021 0.028
ba 0.024 0.028 0.020 0.038 0.019 0.030 0.043 0.012 R 0.030 0.022 0.018 0.068 0.018 --
t 1.65 1-80 1.09 2.20 0-17 2-22 0.46 0-21 R 1.22 0-85 2.27 0.24 1.60 --
P >0-1 >0-1 >0.25 >0.05 >0.50 >0.05 >0.50 >0-25 >0.25 >0-25 >0.05 >0.50 >0-10 --
3.3. COMPARISON OF THE INDIVIDUAL LOUDNESS D A T A W I T H THE GROUP M E A N DATA Since the calculations m a d e on the individual data show the observers to be selfconsistent
in their loudness estimates, the next step was to look for evidence o f any significant intersubject variation. In order to do this, using the data o f the first experiment, an analysis of variance [22] was applied to the variation about the individual slopes bl and between the slopes b,. The results o f this analysis were then used to calculate the ratio of variances F=2.56. This value for F h a s a probability o f less than 0.05 and it was therefore concluded that there is a specific inter-subject variation. This result implies that the group mean slope o f the loudness function is not entirely representative of the individual loudness functions, since some of them, at least, must differ significantly from the mean. In order to obtain a more detailed picture of the extent to which individuals differed from the group mean, the following procedure (which is acknowledged to lack statistical rigour) was adopted. A " t " test was applied to each difference between the individual value of bl, b2, etc., and the group mean b value for the first experiment. Table 2 shows that, i f P = 0.05 is taken as a test of a significant difference, then nine o f the observers differ from the mean, and eight of these differences are
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significant at the P = 0.025 level. This supports the results of the analysis o f variance that the individual observers' data do not form a homogeneous whole due to the existence of specific inter-subject differences. It should perhaps be noted here that, since a different randomized presentation was used for each observer in each experiment, and since the majority o f observers produced similar loudness functions in the two experiments, it does not seem possible that the inter-individual differences were mere artefacts due to the order in which the tone pairs were presented. TABLE 2
Comparison of tile slopes of the individualfimctions with the mean slope for tile group ( only P values < 0.05 are quoted) Observer
t
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2.07 1.34 3.23 1.33 3.72 1-19 3.07 7.16 2.99 0-01 3"47 7"90 6"74 2"13 1"32
P -<0.025 <0.025 -<0.025 <0-025 <0.025 <0-025 <0'025 <0-025 <0"05 --
3.4. COMPAlUSONOF TH~ SLOPESOF TIlE LOUDNESSFUNCTIONSWITH THE THRESHOLDDATA H o o d [23] in a recent paper has suggested that the loudness function o f an individual observer may be related to his threshold sensitivity. The data o f experiment 1 were therefore examined with this in mind. The correlation between the slope o f the loudness function and the threshold o f hearing at the same frequency was calculated and found to be 0.07, not a significant value. It was therefore concluded that this experiment does not support Hood's hypothesis that a steep loudness function is to be expected when the threshold is particularly sensitive. 3.5. COMPARISONOF THE LOUDNESSESTIMATES3,VITHTHE M.M.P.L TESTRESULTS The Minnesota multiphasic personality inventory (M.M.P.I.) is a personality inventory widely used by psychologists to estimate the extent to which a person shows a variety o f personality traits (see, for example, Stagner [24]). In the application o f the inventory the observer is presented with a total o f 550 statements to each o f which he records an answer "true .... false", or "cannot say". The replies are then used, according to what is essentially an empirical scheme, to calculate scores on a number o f scales representing different characteristics of personality. The scores obtained in this way then form a "profile" of the individual concerned. The first stage in interpreting the profiles, and considering how they might be related to the loudness scaling data, was to decide on a level at which a score could be regarded as o f significance. Hathaway [25] proposed that a score of more than 54 should be noted, but in
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this case a somewhat more severe criterion of 60 was adopted. Using this criterion it was found that 11 of the profiles showed significant scores on one or more ofthe following scales: depression (D), hysteria (Hy), and hypomania (Ma). The profiles were therefore initially grouped into four categories: (1) depressive, (2) hysterical, (3) hypomanic and (4) those without any of these traits, this last category comprising 3 persons. It was observed that none of the profiles with a significant D score was significant on either Hy or Ma, and that the combination Hy plus Ma occurred only once. The profiles were therefore re-grouped into three categories: (1) those with predominantly depressive traits; (2) those with predominantly hysterical and hypomanic traits, and (3) those with no predominant traits. This particular grouping is not entirely arbitrary, but has a basis in the established techniques available for outlining personality characteristics. It has been proposed (see reference 25) by Diamond, that one can obtain from M.M.P.I. data a measure of an "activity dimension" which is reflected at one extreme by depression and at the other by hypomania. The depressive type tends to be pessimistic, non-active, and has a low level of responsivity to external stimuli. The hypomanic types are characterized by their hyperactivity, exaggerated responsivity and tendency to elation. The hysterical type shares with the depressive a tendency to react to or be dependent on the human environment but in general much more closely resembles the hypomanie both in response to external stimuli and in a tendency to put into action, consciously or unconsciously, inner patterns and drives. It is therefore possible to describe hypomanic and hysterical types by the comprehensive term "excitable", this term combining both a responsivity and a tendency to hyperactivity. The depressive type is conversely described as having restricted excitability. In order to compare the results provided by the loudness experiments with those given by the M.M.P.I., the 14 observers who completed both were categorized as described above, but now labelled excitable (E), normal (N), or of restricted excitability (RE), and the classifications were compared with the loudness function slopes which are plotted in Table 3 in ascending order of steepness. It is clear from Table 3 that, in general, the observers with restricted excitability (RE) give low values of b (the slope of the loudness function), those TABLE3
Comparison of the M.M.P.L tests and the fltdividual loudness slopes Observer 12 8 3 5 1 2 9 11 14 6 10 15 4 7 13
Excitability rating RE RE RE N N N E E E'I" REt -E I" E E RE
Loudness slope 0.012 0"013 0"016 0'019 0.020 0.020 0"020 0.020 0"021 0-022 0"025 0.028 0"029 0-037 0"070
t Analysis of the M.M.P.I. data for the validity scales suggested that these observers were not reliable.
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categorized as normal (N) give somewhat higher values, and those classed as excitable (E) give the highest b values. The one exception (No. 13) proved rather puzzling, and cannot be fully explained, however, on being questioned about the mental process by which he arrived at his estimates of relative loudness, he described a complex procedure, quite different from those reported by the other observers. It seems possible that this procedure was responsible for his atypical b value of 0.70. 3.6. THEIMPLICATIONSOFINDMDUALLOUDNESSFUNCTIONSTOLOUDNESSSCALINGPROCEDURES The main implication of the present work to loudness scaling procedures is contained in section 3.3. where it is shown that, since the individual results do not all belong to the same population, in the statistical sense, the concept of a group mean as representing the best estimate of the individual's performance is not strictly applicable. This implies that it would be more appropriate to postulate a range for the slope of the loudness function, and to maintain an awareness of the fact that the individual's loudness function can be expected to lie within the range, rather than at its mean value. This points to the introduction of a concept of susceptibility to loudness, rather similar to the concept of susceptibility to noise-induced hearing loss [26] where it is accepted that different individuals may be affected to a greater or lesser extent by the same stimulus.
4. CONCLUSIONS It has been demonstrated that, using a form of relative loudness estimation, individual observers can produce, in the majority of cases, a loudness function whose slope is highly consistent over a period of some months. It has also been shown that this slope is, in more than half the cases, significantly different from the mean slope of the group. From this it has been concluded that most observers possess an individual scale of relative loudness, and that these scales differ considerably from individual to individual. Comparison ofthe individual loudness functions with individual threshold data at the same frequency shows no evidence of any correlation, this result reinforcing the view that differences are not due primarily to physiological causes. A comparison of the results with estimates of observers' "excitability" derived from the M.M.P.I. test has shown some degree ofcorrespondence between excitability and steepness ofthe loudness function. Although the M.M.P.I. data does not lend itself to statistical analysis it is interesting to note that only 2 of the 14 observers who completed the test did not follow the general pattern of excitability versus steepness of the loudness function. It is therefore concluded that the experimental results support the view that differences in loudness estimation are largely psychological in origin. REFERENCES 1. D.W. ROBINSON1953 Acustica 3, 334. The relation between the sone and phon scales of loudness. 2. S. S. STEVENS1959 .L acoust. Soe. Am. 31, 995. On the validity of the loudness scale. 3. H. McRoBERT, M. E. BRYANand W. TEMPEST1965 J. Sound Vib. 2, 391. Magnitude estimation of loudness. 4. W. TEMPEST,H. McROBERTand M. E. BRYAN1965 Proc. 5th Int. Congr. AcoustlcsLidge. Paper B16. Estimation of relative loudness. 5. H. FLETCHER and W. A. MUNSON 1933 Z acoust. Soc. Am. 5, 82. Loudness, its definition, measurement and calculation. 6. E. ZWlCKER,G. FLOTTORPand S. S. STEVENS1957./. acoust. Soc. Am. 29, 548. Critical bandwidth in loudness summation. 7. R.P. HELLMANand J. J. ZW~SLOCKt1963.L acoust. Soc. Am. 35, 856. Monaural loudness function at 1000 cps and interaural summation. 8. G. EKMAN,B. HOSMAN,R. LINDMA~r,L. I.JUNGBERGand C. A. AKESSON1968 Percept. Mot. Skills 26, 815. Interindividual differences in scaling performance.
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9. W. J. McGILL 1960 Psychological Scaling, The slope of the loudness function. A puzzle. (eds H. Gulliksen and S. Messiek). New York: John Wiley. 10. J. C. STEVENSand M. GUIRAO 1964 J. acoust. Soc. Am. 36, 2210. Individual loudness functions. 11. J. T. R~ASON 1968 Br. J. PsycoL 59, 385. Relations between motion sickness susceptibility, the spiral after-effect, and loudness estimation. 12. J. C. STEVENS 1968 Private Communication. 13. w . R. G ARr~R ~9 54 J. ac~ust. S~c. Arn. 26~ 7 3. A technique and a sca~e f~r ~udness measurements. 14. S. S. STEVENS and E. C. POUL'rON 1956 J. exp. PsycoL 51, 71. The estimation of loudness by unpractised observers. 15. R. P. HELLMANand J. ZWISLOCKI 1961 J. acoust. Soc. Am. 33, 687. Some factors affecting the estimation of loudness. 16. S. S. STEVENS 1957 J. acoust. Soc. Am. 29, 603. Concerning the form o f the loudness scale. 17. S. S. STEVENs 1956 Am. J. PsychoL 69, 1. The direct estimation of sensory magnitudes-loudness. 18. W. R. GARNER 1958 J. acoust. Soc. Am. 30, 1005. Advantages o f the discriminability criterion for a loudness scale. i9. JACQUELINEA. MARSH,M. E. BRYAN and W. TEMPEST 1968 J. Sound Vib. 7, 1. An inexpensive free-field listening room. 20. S. R. HATHAWAY and J. C. McKINLEY 1951 Minnesota Multiphasic Personality Inventory Manual New York: The Psychological Corporation. 21. E. CRow, F. DAVIS and M. MAXFIELD 1960 Statistics Manual New York: Dover Publications. 22. A HALO 1952 Statistical Theory with Engineering Applications. New York: John Wiley. 23. J. D. H o o d 1968 J. acoust. Soc. Am. 44, 959. Loudness discomfort levels. 24. R. STAONER 1961 Psychology o f Personality. New York: McGraw-Hill. 25. W. G. DAHLSTROMand G. S. ~VELSH 1965 An M.M.P.I. Handbook. Minnesota: University of Minnesota Press. 26. D. W. ROBINSON1968 NPL Aero Report Ac32. The relationships between hearing loss and noise exposure.
INDIVIDUAL LOUDNESS FUNCTIONS CLARIBELM. DE BARBENZA,M. E. BRYANAND W. TEbIPEST
Audiology Research Unit, Department of Electrical Engineerhlg, University of Salford, Salford 5, Lancs, England (Received 24 February 1969) Individual loudness functions have been obtained by a form of magnitude estimation for 15 observers. The experiments took place over a period of five months and used two different procedures. The results show that most of the individual observers can produce a loudness function of consistent slope and that in many cases this slope is significantly different from the mean slope of the group. At the end of the loudness estimation procedure each observer was asked to complete the Minnesota multiphasic personality inventory (M.M.P.I.) test in its individual form. A comparison of the slopes of the loudness functions with a measure of individual excitability shows a correspondence between increasing excitability and increasing steepness of loudness function. It is concluded that the major cause of inter-individual differences is probably psychological rather than physiological.
1. INTRODUCTION The problems associated with attributing numbers to the loudness of sounds have exercised many research workers over a period of about the last 40 years. The early work (reviewed in detail in 1953 by Robinson [1]) seemed to demonstrate that, while observers using various procedures were certainly able to provide numbers associated with loudness, the loudness scales produced differed considerably from one experimenter to the next. More recent work (see, for example, reference 2) has narrowed down the variations in the results to some extent and we now have in existence standard procedures which can be used to relate loudness to intensity. It is not clear how much of the apparent improvement in accuracy is due to real improvements in technique, and how much is due to a reduction in the variety of loudness evaluation procedures in use (see, for example, references 3 and 4). There is, however, one aspect of the loudness scaling procedure which has perhaps received less attention than it deserves; this is the question of the importance of inter-individual differences in scaling. This topic has been mentioned, usually in passing, in a number of the earlier papers. For example Fletcher and Munson [5] stated that they found large variations between the judgments of individual observers, and concluded that the investigation must therefore be conducted on a statistical basis. Zwieker, Flottorp and Stevens [6] discussed variability in loudness matching experiments and found evidence of consistent inter-individual differences which they attributed to differences in subjective criteria. In his paper on the "Relation between the Soue and Phon scales of loudness", Robinson [I] pointed out that individuals, on the whole, maintain a constant tendency with regard to their departure from average in his loudness halving and doubling experiments. More recently, Hellman and Zwislocki [7] have made the comment that in their loudness estimation experiments some individuals do not deviate significantlyfrom the group median, but others deviate more substantially; they did not, however, take up this point in detail and the general tone of their paper is that individuals are able to make consistent loudness judgments without large inter-individual differences. The four papers quoted above demonstrate that the existence of inter-individual differences 27 399
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has been noticed by various experimenters, but does not seem to have been regarded as of enough importance to justify any specific investigation. The important questions: do signi. fieant inter-individual differences exist ? how might they affect established loudness evaluation procedures ? and, what are their causes ? are not answered by the work on group loudness. It seems likely that individual loudness functions have not been of very much concern to many of the workers, simply because the very existence of differences between individuals was not seriously taken up by experimental psychologists until about ten years ago. Since most of the basic loudness work was done more than ten years ago, it is not really surprising that (so far as we are aware) none of the workers went so far as to apply any tests to determine homogeneity of the group he used. Much of the work off inter-individual differences in scaling performance, dating from 1958 onwards, has been reviewed by Ekman, Hosman, Lindman, Ljungberg and Akesson [8] who conclude, from results mainly in modalities other than loudness, that inter-individual differences exist, and that they are due to a combination of both genuine differences in sensitivity and the effects of response bias. In the field of loudness scaling it appears that there are only three papers (up to the end of 1968) dealing specifically with the differences between individuals, these are McGill [9], Stevens and Guirao [10], and Reason [11]; of these three, only Stevens and Guirao was included in the review by Ekman et aL [8] in 1968. In view of the sparseness of the literature and the fact that the two papers cited first seem to reach different conclusions, it is perhaps worthwhile to outline briefly their methods and conclusions. In the work reported by McGill [9], observers were asked to scale the loudness of I000 Hz tones by making a pencil mark on a line six inches long. To quote McGill, "The line was an absolute rating scale whose left-hand end symbolized 'the weakest tone you could possibly hear', while the right-hand end was supposed to be the 'loudest tone you could possibly hear.' Each tone was rated on a separate line and prior ratings were covered from s i g h t . . . Loudness ratings are reported as the distance (in 1/64ths of an inch) from the left-hand end of the line to the pencil mark." Two experimental procedures were used: in one, tones of 10 dB intervals in the range 30 to I00 dB were presented in random order until a total of 60 assessments had been made. In the other procedure 60 stimuli at I dB intervals from 41 to I00 dB were presented five times over in random order. Using the first of the two methods outlined above, a number of observers performed the experiment twice, with an interval of approximately one week between. It was found that while the agreement between the two determinations by the same observer a week apart was not perfect, it was quite good. However, the inter-subject differences were quite marked. McGill described the individual loudness functions obtained as "highly stylized but reproducible," making the point that inter-individual differences were most marked at low intensities. He infers that the differences between subjects are not random but represent stable parameters. McGill goes on to consider possible transformations which could be used to reduce or eliminate the inter-subject differences, but concludes that there is a variation in the slope of the loudness function from individual to individual. He finds it hard to believe that the actual sensory process differs between individuals as much as his results suggest and he takes the view that the differences arise from some internal "transformation" process which affects both the slope of the loudness function and its reference point. He goes on to describe the loudness evaluation process as being similar to the use of a ruler which can be "stretched" and in this way give different slopes for different individuals. While McGill's work does seem to provide strong evidence for the existence of individual loudness functions, it suffers from one possible limitation, the use of a lengfh assessment intermediate between the loudness and the number. This procedure really turns the experiment into a cross-modality procedure, with the assumption that length and number can be
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assumed to be linearly related. A further minor limitation is that the method, or at least the data as presented, does not lend itself to applying significance tests to the inter-individual differences. The suggestion which he makes, of a "rubber-scale" phenomenon, seems rather to beg the question of why the individual slopes differ so much, by merely describing it in a different way. The work of Stevens and Guirao [10] employed a rather different procedure. They asked a number of observers (11 in aid to set up their loudness functions by a production-estimation procedure in which the observers set the 1000 Hz tone to a number of different levels of loudness and assigned a number to each of them. Each of the eleven observers performed the experiment twice, with an interval of from one to six months between the two determinations. The two interesting questions which may be asked about the results are, how much variability is there between individuals ? and, are individuals consistent in their first and second trials .9 The results were plotted by Stevens and Guirao as "estimates of loudness" on a logarithmic scale vs. sound pressure level in decibels. The slope of the loudness function defined in this way is fl, the exponent in the power law assumed to relate sensation to stimulus magnitude. The measured fl values ranged from 0.40 to 1.10 with a mean of 0.73 and a standard deviation of 0"19, demonstrating a considerable variability between observers. On the question of the consistency of the individual loudness data between the first and second experiments for each observer, Stevens and Guirao state the correlation coefficient between the first and second test to be r = 0.53. They conclude from this that observers are not particularly consistent over a period of time and that "the observer may come to differ from his own previous function almost as much as he does from any other observer's function." However, their data ([10] Table I, p. 2213) have now been re-calculated (Stevens [12]) with the result r = 0.74. A " t " test was then applied and it was found that the probability of such a high correlation arising by chance was no greater than P = 0.01. This revised estimate indicates that there is stronger evidence of a tendency for observers to give similar values for the slope of the loudness function on different occasions. Reason [11] was not directly concerned with individual loudness functions, but, in the course of work on the susceptibility of individuals to motion sickness, he obtained mean loudness scaling data for two groups, selected according to their susceptibility, and lack of susceptibility, to motion sickness. He found that the two groups differed significantly in the steepness of their loudness functions. He thus demonstrated that differences do exist and can be related to other measurable psychophysical factors. The work of McRobert et aL [3] on the magnitude estimation of loudness was not directly concerned with individual loudness functions, but involved the determination of a very large number of single estimates of relative loudness by different observers. The results were treated from the point of view of group mean data but the scatter of individual loudness estimates for the same loudness interval from different observers was very large, and raised the question of the extent to which group means represent the loudness estimates of individuals. The main conclusion from the work outlined above seems to be that there is some evidence of the existence of individual loudness functions, but the evidence is not entirely conclusive. Both McGill [9], and Stevens and Guirao [10] take the view that variations in the sensory process from individual to individual are not likely to cause the large differences found between loudness functions, a view with which the present authors are inclined to agree, although it is difficult to site any positive scientific evidence for this argument. However, having discarded, somewhat arbitrarily, what one might call the "physiological"explanation, the idea arose that it might be possible to relate loudness judgments to measurable psychological traits. The work to be described in this paper therefore sets out to answer two main questions:
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Do individual observers possess individual loudness functions 9.and, if the existence of individual loudness functions can be demonstrated, is it then possible to relate any features of them to individual psychological traits ? A third, and less important aim of the work, was to obtain some measure of the stability of the individual loudness functions by extending the measurements over a period of months and using two different loudness estimation procedures. 2. EXPERIMENTAL PROCEDURE The method employed is that of relative loudness estimation, in which the observer is presented with pairs of tones and asked to estimate the loudness of the second tone in relation to the first. The details of the procedure, and the arguments for it, have been presented at length in an earlier publication [3], but it would perhaps be worthwhile to outline them again here. The primary aim of the procedure is the avoidance of bias. Garner [13] has shown that when a range of stimuli is presented to an observer he appears to be biased towards the mid-point of the range available, in making half-loudness judgments. Garner's results suggested that in his, admittedly somewhat extreme, conditions, the effects of bias could completely over-ride the subjective judgment of the observer. These results led us to conclude that the constant-stimulus method, applied to fractional and multiple loudness judgments, was not reliable. The effects of constant stimulus bias can be avoided in the alternative loudness scaling procedure of magnitude adjustment, which has been investigated in some detail by Stevens and Poulton [14]. They asked observers to adjust a tone to half-loudness by means of a potentiometer and found that the potentiometer characteristic (i.e. the relation between intensity and angular rotation) had a large, and highly significant, effect on the half-loudness judgments. Although Stevens and Poulton suggested that, by a process of successive approximation, a "correct" potentiometer could be designed, the present authors are somewhat suspicious of the reliability of this procedure. The case of magnitude estimation, which now seems to be generally regarded as the best method of loudness scaling, eliminates both the constraints of the constant stimulus method and the apparatus difficulties of magnitude adjustment, by simply presenting the observer with a series of tones and asking him to describe their loudness compared to a reference tone. Hellman and Zwislocki [15] have shown that in this method the shape of the loudness function obtained depends on the number assigned to the reference tone. A further modification of this procedure, in the form of the abandonment of a fixed number for the reference tone, has been used by Stevens [16] and would appear to avoid the difficulty demonstrated by Hellman and Zwislocki. Although this form of magnitude estimation eliminates the sources of bias mentioned above, it may still suffer from a significant context error. This arises because all the judgments are made in a short space of time, and, as each judgment is made, another reference point is created in the mind of the observer. His later judgments will therefore be made with reference to all his previous estimates, rather than to the reference tone alone. This could be important in the case of levels which are far from the reference level, since the observer may make his judgment with reference to the nearest tone he has so far heard, rather than the reference level. By this process all his judgments are reduced to judgments of small intervals and it is not clear whether any real judgments over the larger intervals are ever made. Whether this context effect is important is difficult to say; Stevens [17] says "there is little doubt that the number the observer assigns to a tone is sometimes influenced by what he has called some previous tones", but does not accept that the effect is important. Garner's work
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on constant stimulus methods [13, 18] suggests, however, that context affects all judgments after the first, and that the effect is so great in some cases as to render the results meaningless. It would therefore seem wise, in the design of a magnitude estimation experiment, to eliminate this effect as far as possible. The experimental procedure adopted was therefore as follows. Tones were presented in pairs, the second tone being the more intense of the two. In the first experiment only one pair of tones was presented on any one day and the observer returned daily over a period of five months until he had judged each tone pair at least four times. In the second experiment all the tone-pairs were presented at least four times in a single listening session of about one hour. The tone pairs were presented in a different random order in each experiment and to each observer. Twelve pairs of tones ~ere used, all at I000 Hz, the sound pressure levels being 40]50, 50/60, 60/70, 70/80, 80/90, 40/60, 60/80, 40/70, 60/90, 40/80 50/90 and 40/90 (in dB re 0.0002 /~bar). Throughout the experiments the same instructions were given to the observers: "In this experiment you will hear a pair of tones. I want you to say how many times the second is louder than the first. You will be hearing the pairs of tones until you make your dccision." All the tones were presentcd binaurally under free-field conditions in a sound-insulated room (sce reference 19). Although the room was not fully anechoic it had a wall treatment which was highly absorbent at 1000 Hz. The tones were of 1 see duration with a 1 sec interval between tones, and had rise and fall times of approximately 20 msec to reduce audible starting and finishing transients. Tones were presented in an A-B-A-B sequence, always starting with the lower intensity of the pair, until the observer indicated that he had reached a decision. The sound pressure levels at the observer's ear position were checked daily with a calibrated microphone to ensure that the absolute levels remained constant throughout the experiment. Before the start of the loudness estimation experiments the audiogram of each observer was measured to make sure that all those taking part had normal hearing; no losses greater than 10 dB were found at 1000 Hz. After all the listening tests had been completed each observer was asked to complete the M.M.P.L (Minnesota multiphasic personality inventory) questionnaire in its individual form [20]. 3. RESULTS In order to perform a useful analysis of the loudness data obtained it was necessary to reduce each individual's data to as simple a form as possible, preferably to a single number and its variance. Most statistical procedures are based on normally distributed data, and as a first step an examination of the distribution of estimates was made. It was found that in general the distribution was highly skewed, with a long "tail" of high values. The transformation y = log,0 (observer's estimate) was therefore applied to all the data, and had the effect of making the distributions of estimates approximately normal. All subsequent computations were carried out on the transformed variable y. As a second step it was necessary to consider how each individual's data could best be combined. Most previous work on loudness has been concerned with the exponent of the loudness function which appears as the slope when y is plotted against intensity in dB, and this suggested immediately that the slope of the individual's loudness function was probably the most usefulparameter. The work of McGill [9] and others has shown that individual loudness functions are usually not straight, which implies that the slope must be some form of average over the range of measurement. A further complication of the present technique
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C. M. DE BARBENZA, M. E. BRYAN AND W'. TEMPEST
(discussed in more detail in reference 3) is that the estimate of relative loudness over the larger intervals (greater than 10 dB) can be arrived at by two or more routes involving one, two, or more estimates in combination, and that in most cases combining the estimates over several small intervals gives a larger value than the direct estimate over the whole interval.
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With the above difficulties in mind, and the knowledge that if the analysis were to proceed some procedure must be devised, several different possibilities were considered. It was found that, if the results for each interval were combined (i.e. the estimates for, say, 40/50, 50/60, 60/70, 70/80 and 80/90 were all pooled), and the results plotted in the form mean y against intensity interval in dB, the function obtained was fairly linear and did not exhibit any consistent curvature. This procedure was therefore adopted and each individual's results plotted in this form. It is acknowledged that this procedure is to some extent arbitrary, and that a
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different procedure might well produce a slightly different loudness function. It is, however, a practical method o f combining an individual's estimates in order to extract a working value for the mean slope, and there is no reason to suppose that the method used is likely to invalidate inter-individual comparisons which are, after all, the main purpose o f this work. Having arrived at a procedure by which each individual's data could be plotted in a simple form the 15 sets o f data were considered from several points of view. The individual data for the 15 observers in the first experiment are shown in Figure 1. 3. I. A COMPARISONOF THE GROUPMEANDATAOBTAINEDIN EXPERIMENTS 1 AND 2 This comparison was made to establish the equivalence, or otherwise, of the two methods of magnitude estimation used. Figure 2 shows the mean data obtained for all the observers in the two experiments plotted in the form y vs. intensity interval. In calculating, say, the experiment 1 point for a 20 dB
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intensity interval, all the estimates o f all the observers over the various 20 dB intervals in the experiment were averaged, after the y = log10 (observer's estimate) transformation had been made. The lines on Figure 2 are least squares regression lines fitted to the mean data and the slope values are shown on the lines. A " t " test was applied to test the significance of the difference between the slopes and gave " t " = 1.26, indicating that the slopes are not significantly different (P = 0.25). 3.2. A COMPARISON
OF THE INDIVIDUAL DATA OBTAINED IN EXPERIMENTS
I AND 2
Having decided, on the basis of the mean results shown in Figure 2, that the two methods give extremely similar results for the slope o f the loudness function for a group of listeners, the second comparison becomes a measure o f the extent to which individuals can produce self-consistent data over a period of time. The individual results were therefore considered as follows. First a least squares regression line was fitted to each individual's data, which were expressed in the same form as in Figure 1. This calculation was performed for both the first and second experiments, the slopes being denoted as b I and b2, respectively. Table I shows the
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c.M. DE BARBENZA,M. E. BRYANAND W. TEMPEST
calculated values of bl and b2, the " t " value for the difference between bl and bz, and P, the probability range in which the " t " value falls (using the method described by Crow, Davies and Maxfield [21]). It is seen from this table that in no case is P less than 0.05, the level of probability usually regarded as denoting statistical significance. Three of the observers fall into the range 0.05 < P < 0.I0, three in the range 0"10 < P < 0.25 and the remaining seven give P > 0.25. This test therefore shows that observers in general give very similar slopes for their loudness functions in the two experiments. In addition to the " t " test computation, the values ofb~ and b2 were used to calculate the correlation coefficient " r " between the first and second experiments, the value of " r " was found to be 0.95, significant at the level P < 0.001. The results o f the " t " test, and the correlation coefficient, taken together, suggest that many observers can make self-consistent estimates o f relative loudness, and thus support the hypothesis that individual loudness functions exist, and can be determined. TABLE 1
Comparison of the slopes of the individual loudnessfimctions found fll experhnents I (bi) and 2 (b2) Observer 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
bl 0.020 0.020 0.016 0-029 0.019 0.022 0.037 0.013 0.020 0.025 0.020 0.012 0-070 0.021 0.028
ba 0.024 0.028 0.020 0.038 0.019 0.030 0.043 0.012 R 0.030 0.022 0.018 0.068 0.018 --
t 1.65 1-80 1.09 2.20 0-17 2-22 0.46 0-21 R 1.22 0-85 2.27 0.24 1.60 --
P >0-1 >0-1 >0.25 >0.05 >0.50 >0.05 >0.50 >0-25 >0.25 >0-25 >0.05 >0.50 >0-10 --
3.3. COMPARISON OF THE INDIVIDUAL LOUDNESS D A T A W I T H THE GROUP M E A N DATA Since the calculations m a d e on the individual data show the observers to be selfconsistent
in their loudness estimates, the next step was to look for evidence o f any significant intersubject variation. In order to do this, using the data o f the first experiment, an analysis of variance [22] was applied to the variation about the individual slopes bl and between the slopes b,. The results o f this analysis were then used to calculate the ratio of variances F=2.56. This value for F h a s a probability o f less than 0.05 and it was therefore concluded that there is a specific inter-subject variation. This result implies that the group mean slope o f the loudness function is not entirely representative of the individual loudness functions, since some of them, at least, must differ significantly from the mean. In order to obtain a more detailed picture of the extent to which individuals differed from the group mean, the following procedure (which is acknowledged to lack statistical rigour) was adopted. A " t " test was applied to each difference between the individual value of bl, b2, etc., and the group mean b value for the first experiment. Table 2 shows that, i f P = 0.05 is taken as a test of a significant difference, then nine o f the observers differ from the mean, and eight of these differences are
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significant at the P = 0.025 level. This supports the results of the analysis o f variance that the individual observers' data do not form a homogeneous whole due to the existence of specific inter-subject differences. It should perhaps be noted here that, since a different randomized presentation was used for each observer in each experiment, and since the majority o f observers produced similar loudness functions in the two experiments, it does not seem possible that the inter-individual differences were mere artefacts due to the order in which the tone pairs were presented. TABLE 2
Comparison of tile slopes of the individualfimctions with the mean slope for tile group ( only P values < 0.05 are quoted) Observer
t
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2.07 1.34 3.23 1.33 3.72 1-19 3.07 7.16 2.99 0-01 3"47 7"90 6"74 2"13 1"32
P -<0.025 <0.025 -<0.025 <0-025 <0.025 <0-025 <0'025 <0-025 <0"05 --
3.4. COMPAlUSONOF TH~ SLOPESOF TIlE LOUDNESSFUNCTIONSWITH THE THRESHOLDDATA H o o d [23] in a recent paper has suggested that the loudness function o f an individual observer may be related to his threshold sensitivity. The data o f experiment 1 were therefore examined with this in mind. The correlation between the slope o f the loudness function and the threshold o f hearing at the same frequency was calculated and found to be 0.07, not a significant value. It was therefore concluded that this experiment does not support Hood's hypothesis that a steep loudness function is to be expected when the threshold is particularly sensitive. 3.5. COMPARISONOF THE LOUDNESSESTIMATES3,VITHTHE M.M.P.L TESTRESULTS The Minnesota multiphasic personality inventory (M.M.P.I.) is a personality inventory widely used by psychologists to estimate the extent to which a person shows a variety o f personality traits (see, for example, Stagner [24]). In the application o f the inventory the observer is presented with a total o f 550 statements to each o f which he records an answer "true .... false", or "cannot say". The replies are then used, according to what is essentially an empirical scheme, to calculate scores on a number o f scales representing different characteristics of personality. The scores obtained in this way then form a "profile" of the individual concerned. The first stage in interpreting the profiles, and considering how they might be related to the loudness scaling data, was to decide on a level at which a score could be regarded as o f significance. Hathaway [25] proposed that a score of more than 54 should be noted, but in
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this case a somewhat more severe criterion of 60 was adopted. Using this criterion it was found that 11 of the profiles showed significant scores on one or more ofthe following scales: depression (D), hysteria (Hy), and hypomania (Ma). The profiles were therefore initially grouped into four categories: (1) depressive, (2) hysterical, (3) hypomanic and (4) those without any of these traits, this last category comprising 3 persons. It was observed that none of the profiles with a significant D score was significant on either Hy or Ma, and that the combination Hy plus Ma occurred only once. The profiles were therefore re-grouped into three categories: (1) those with predominantly depressive traits; (2) those with predominantly hysterical and hypomanic traits, and (3) those with no predominant traits. This particular grouping is not entirely arbitrary, but has a basis in the established techniques available for outlining personality characteristics. It has been proposed (see reference 25) by Diamond, that one can obtain from M.M.P.I. data a measure of an "activity dimension" which is reflected at one extreme by depression and at the other by hypomania. The depressive type tends to be pessimistic, non-active, and has a low level of responsivity to external stimuli. The hypomanic types are characterized by their hyperactivity, exaggerated responsivity and tendency to elation. The hysterical type shares with the depressive a tendency to react to or be dependent on the human environment but in general much more closely resembles the hypomanie both in response to external stimuli and in a tendency to put into action, consciously or unconsciously, inner patterns and drives. It is therefore possible to describe hypomanic and hysterical types by the comprehensive term "excitable", this term combining both a responsivity and a tendency to hyperactivity. The depressive type is conversely described as having restricted excitability. In order to compare the results provided by the loudness experiments with those given by the M.M.P.I., the 14 observers who completed both were categorized as described above, but now labelled excitable (E), normal (N), or of restricted excitability (RE), and the classifications were compared with the loudness function slopes which are plotted in Table 3 in ascending order of steepness. It is clear from Table 3 that, in general, the observers with restricted excitability (RE) give low values of b (the slope of the loudness function), those TABLE3
Comparison of the M.M.P.L tests and the fltdividual loudness slopes Observer 12 8 3 5 1 2 9 11 14 6 10 15 4 7 13
Excitability rating RE RE RE N N N E E E'I" REt -E I" E E RE
Loudness slope 0.012 0"013 0"016 0'019 0.020 0.020 0"020 0.020 0"021 0-022 0"025 0.028 0"029 0-037 0"070
t Analysis of the M.M.P.I. data for the validity scales suggested that these observers were not reliable.
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categorized as normal (N) give somewhat higher values, and those classed as excitable (E) give the highest b values. The one exception (No. 13) proved rather puzzling, and cannot be fully explained, however, on being questioned about the mental process by which he arrived at his estimates of relative loudness, he described a complex procedure, quite different from those reported by the other observers. It seems possible that this procedure was responsible for his atypical b value of 0.70. 3.6. THEIMPLICATIONSOFINDMDUALLOUDNESSFUNCTIONSTOLOUDNESSSCALINGPROCEDURES The main implication of the present work to loudness scaling procedures is contained in section 3.3. where it is shown that, since the individual results do not all belong to the same population, in the statistical sense, the concept of a group mean as representing the best estimate of the individual's performance is not strictly applicable. This implies that it would be more appropriate to postulate a range for the slope of the loudness function, and to maintain an awareness of the fact that the individual's loudness function can be expected to lie within the range, rather than at its mean value. This points to the introduction of a concept of susceptibility to loudness, rather similar to the concept of susceptibility to noise-induced hearing loss [26] where it is accepted that different individuals may be affected to a greater or lesser extent by the same stimulus.
4. CONCLUSIONS It has been demonstrated that, using a form of relative loudness estimation, individual observers can produce, in the majority of cases, a loudness function whose slope is highly consistent over a period of some months. It has also been shown that this slope is, in more than half the cases, significantly different from the mean slope of the group. From this it has been concluded that most observers possess an individual scale of relative loudness, and that these scales differ considerably from individual to individual. Comparison ofthe individual loudness functions with individual threshold data at the same frequency shows no evidence of any correlation, this result reinforcing the view that differences are not due primarily to physiological causes. A comparison of the results with estimates of observers' "excitability" derived from the M.M.P.I. test has shown some degree ofcorrespondence between excitability and steepness ofthe loudness function. Although the M.M.P.I. data does not lend itself to statistical analysis it is interesting to note that only 2 of the 14 observers who completed the test did not follow the general pattern of excitability versus steepness of the loudness function. It is therefore concluded that the experimental results support the view that differences in loudness estimation are largely psychological in origin. REFERENCES 1. D.W. ROBINSON1953 Acustica 3, 334. The relation between the sone and phon scales of loudness. 2. S. S. STEVENS1959 .L acoust. Soe. Am. 31, 995. On the validity of the loudness scale. 3. H. McRoBERT, M. E. BRYANand W. TEMPEST1965 J. Sound Vib. 2, 391. Magnitude estimation of loudness. 4. W. TEMPEST,H. McROBERTand M. E. BRYAN1965 Proc. 5th Int. Congr. AcoustlcsLidge. Paper B16. Estimation of relative loudness. 5. H. FLETCHER and W. A. MUNSON 1933 Z acoust. Soc. Am. 5, 82. Loudness, its definition, measurement and calculation. 6. E. ZWlCKER,G. FLOTTORPand S. S. STEVENS1957./. acoust. Soc. Am. 29, 548. Critical bandwidth in loudness summation. 7. R.P. HELLMANand J. J. ZW~SLOCKt1963.L acoust. Soc. Am. 35, 856. Monaural loudness function at 1000 cps and interaural summation. 8. G. EKMAN,B. HOSMAN,R. LINDMA~r,L. I.JUNGBERGand C. A. AKESSON1968 Percept. Mot. Skills 26, 815. Interindividual differences in scaling performance.
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9. W. J. McGILL 1960 Psychological Scaling, The slope of the loudness function. A puzzle. (eds H. Gulliksen and S. Messiek). New York: John Wiley. 10. J. C. STEVENSand M. GUIRAO 1964 J. acoust. Soc. Am. 36, 2210. Individual loudness functions. 11. J. T. R~ASON 1968 Br. J. PsycoL 59, 385. Relations between motion sickness susceptibility, the spiral after-effect, and loudness estimation. 12. J. C. STEVENS 1968 Private Communication. 13. w . R. G ARr~R ~9 54 J. ac~ust. S~c. Arn. 26~ 7 3. A technique and a sca~e f~r ~udness measurements. 14. S. S. STEVENS and E. C. POUL'rON 1956 J. exp. PsycoL 51, 71. The estimation of loudness by unpractised observers. 15. R. P. HELLMANand J. ZWISLOCKI 1961 J. acoust. Soc. Am. 33, 687. Some factors affecting the estimation of loudness. 16. S. S. STEVENS 1957 J. acoust. Soc. Am. 29, 603. Concerning the form o f the loudness scale. 17. S. S. STEVENs 1956 Am. J. PsychoL 69, 1. The direct estimation of sensory magnitudes-loudness. 18. W. R. GARNER 1958 J. acoust. Soc. Am. 30, 1005. Advantages o f the discriminability criterion for a loudness scale. i9. JACQUELINEA. MARSH,M. E. BRYAN and W. TEMPEST 1968 J. Sound Vib. 7, 1. An inexpensive free-field listening room. 20. S. R. HATHAWAY and J. C. McKINLEY 1951 Minnesota Multiphasic Personality Inventory Manual New York: The Psychological Corporation. 21. E. CRow, F. DAVIS and M. MAXFIELD 1960 Statistics Manual New York: Dover Publications. 22. A HALO 1952 Statistical Theory with Engineering Applications. New York: John Wiley. 23. J. D. H o o d 1968 J. acoust. Soc. Am. 44, 959. Loudness discomfort levels. 24. R. STAONER 1961 Psychology o f Personality. New York: McGraw-Hill. 25. W. G. DAHLSTROMand G. S. ~VELSH 1965 An M.M.P.I. Handbook. Minnesota: University of Minnesota Press. 26. D. W. ROBINSON1968 NPL Aero Report Ac32. The relationships between hearing loss and noise exposure.