Information Analysis of Choice Behavior in Producing Acoustical Signals

LETTERS TO THE EDITOR

Received 2 November 1971; revised 21 December 1971

Information Analysis of Choice Behavior in Producing Acoustical Signals

M•CUEL M. HUPET

Center of Experimental Psychology, University of Louvain, B-3041-Pdlenberg, Bdgium

Instead of presenting a perceptual stimulus to which a subject must assign a numerical response, he is given a number from 1 to N and must then generate a corresponding motor response. The amounts of information transmitted in producing acoustical signals varying in only one dimension, either their SPL (between 0 and 105 dB) or their frequency (between 50 and 6000 Hz), are compared to the amounts of transmitted information in identifying analogous signals.

4.15

INTRODUCTION

Several studies have explored the limits of the absolute judgment by testing how accurately people can identify various signals (Macrae, 1970). In all cases, stimuli were presented in such a way that they varied continuously or discretely in one or several dimensions; the subject's task being to classify them into a number of categories N, generally numbered from 1 to N. The maximum amount of transmitted information, known as the "channel capacity," can be calculated by varying N. Measures taken on various perceptive dimensions have led to the conclusion that rather small and equivalent capacities exist, ranging from 2 to 3 bits for unidimensional stimuli.

It must be noted, however, that all previous experiments on absolute judgment consider only the channel capacity for stimulus identification, by measuring the accuracy of judgment in situations requiring absolute judgments of various categories on a stimulus con- tinuum. It remains to be seen whether any different capacity can be obtained by manipulating response rather than stimulus categories. This question could be investigated by using the following procedure: instead of presenting a perceptual stimulus to v•hich a subject must assign a numerical response, he would be given a number from 1 to N and he would then have to generate a corresponding motor response. Using this new procedure, it would be possible to measure the maximum number of different categories of response which can be accurately used. In such an experiment indeed, the stimulus numbers from 1 to N are multidimensional stimuli

which can be identified without any risk of confusion; the only difficulty is to select the correct response category corresponding to the numerical stimulus.

We investigated this problem of the production of acoustical signals, starting with the most simple situa- tion in which the signals to be selected varied in only one dimension, either their sound-pressure level or frequency. First, it was hypothesized that the number of

unidimensional acoustical signals a subject is able to produce without any confusion is very small, and that channel capacity in producing signals is nearly the same as that in identifying analogous signals. Indeed, for the same channel, it seems safe to say that the repertory of categories is probably the same. Furthermore, the signals which are produced by the subject are controlled by feedback and this information is obviously limited by stimulus channel capacity. Nevertheless, the question can be asked: if the subject produces the signal categories himself, will substantial improvements in information transmission be found?

I. EXPERIMENT 1

A. Procedure

The level of bandpassed noise (500-2000 Hz) was systematically manipulated between 0 to 105 dB (re 0.0002 dyn/cm2). One subject at a time was seated in a soundproof room where the noise was sounded several times by a loudspeaker with a slowly increasing SPL. The subject was then given the following instruction: "Divide mentally the scale of intensity you have heard into 6 (7, 9, or 12) categories that you number from 1 to 6 (7, 9, or 12), from the least to the most intense noise. Every time I give you a number from 1 to 6 (7, 9, or 12), you will have to use these two buttons in order to produce a noise with the corresponding intensity; by press- ing one of them you will increase the intensity, while the other enables you to decrease it. It is not necessary to produce a noise with a definite fixed intensity in response to each number, but if I give you a higher number, you will have to produce a more intense noise than the one produced in response to smaller numbers. The stimulus number will appear on the screen' facing you. The noise will start with a randomly selected intensity level." The two buttons were actually connected to two lamps which were in a room adjacent to that of subject; all the sound-producing electronic equipment was in this

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room where the experimenter manipulated an atten- uator in order to increase or to decrease the SPL accord-

ing to which one of the lamps was lit. Thus the subject cannot appeal to any adjusting marks or kinesthesic or time cues in selecting the SPL he was required to produce.

The total number N of response categories was 6, 7, 9, and 12. The successive stimulus numbers xi given to the subjects were randomly selected; but over an entire experimental session, the number of presentations of each xi of the series was equal. For N=6 and N=7, each subject was required to produce each category 40 times; for N-9, 45 times for each category; and for N-- 12, 60 times each. The various experiments were run in counterbalanced order for the different subjects. Before each experiment, the subjects were given an initial practice session that they were allowed to con- tinue until they felt that no further improvement would result. Five normal-hearing subjects were used, ranging in age from 20 to 30 years.

B. Analysis of Data

The analysis of data is in terms of information transmission. First it consists of ranging the subject's responses, which are noted in attenuation decibel values, in their descending order, indicating for each of them the stimulus number xi which evoked it. The first response category then consists of the ni first responses (ni=number of times that the stimulus xi has been presented) which are supposed to correspond to the smallest stimulus number; and each other response category is similarly determined by each ni following response until the final ni responses, which are supposed to correspond to the highest stimulus number. The interversions are incorrect responses; for example, an interversion between the stimuli 3 and 5 will be noted

as a response 5 to the stimulus 3, and as a response 3 to the stimulus 5. In this way, it is finally possible to establish confusion matrices which have as many different response categories as different stimuli and from which the transmitted information can be calculated.

C. Results

The amounts of transmitted information as a function

of the input information are shown in Table I, where the T(x;y) values have been corrected by the Miller- Madow formula (in Macrae, 1971).

TABLE I. Intensity. Transmitted information as a function of stimulus information in bits per stimulus for each subject and on an average.

r (•; y) N H(x) S• S2 S• S4 S5 X 6 2.6 2.4 2.5 2.2 2.3 2.3 2.2 7 2.8 2.4 2.3 2.4 2.3 2.2 2.3 9 3.2 2.4 2.4 2.2 2.3 2.3 2.2

12 3.6 2.3 2.4 2.8 2.4 2.3 2.3

TABLE II. Frequency. Transmitted information as a function of stimulus information in bits per stimulus, for each subject and on an average.

T (x; y) N H(x) S• S•. S• S4 •

7 2.8 2.4 2.3 2.3 2.5 2.4 9 3.2 2.4 2.4 2.4 2.6 2.4

12 3.6 2.5 2.5 2.4 2.5 2.5

The transmitted information increases to a level of

only about 2.3 bits; this value corresponds to perfect selection of only four or five categories of response which can be used without any risk of error. In a previous experiment on identification of tones, Garner (1953) found that the channel capacity for absolute judgments of loudness was about 2.3 bits. For this dimension, channel capacity is thus exactly the same in producing signals as that in identifying analogous signals. And this is in accordance with our first hypothesis.

II. EXPERIMENT 2

A. Experimental Conditions

In this second experiment, four subjects were given a pair of earphones wired for monaural listening. They were required to produce acoustical signals which were tones varying only in frequency between 50 and 6000 Hz. The sound-pressure level of the tones was approximately 80 dB (re 0.0002 dyn/cm•'); in order to reduce differential loudness cues, the voltage output of the signal generator (Beat-Frequency Oscillator, Radiom- eter H012) was varied so that the SPL of the tones varied randomly over 10 dB.

Using the same general procedure as in Expt. 1, the subjects were required to produce seven, nine, or 12 categories of tones. The total number of responses per subject was 280 for seven categories, 405 for nine categories, and 720 for 12 categories.

B. Results

The amounts of transmitted information are shown

in Table II, where the T(x; y) values have been corrected by the Miller-Madow formula. For this dimension, the transmitted information bends off toward an asymptote at about 2.4 bits, which is equivalent to perfect selection of only five or six categories. In a previous experiment by Pollack (1952) where the subjects were required to identify pitch of tones presented indi- vidually, the transmitted information leveled off at about 2.3 bits.

III. DISCUSSION

Under the conditions of measurement employed, an informational transfer of approximately 2.4 bits is the maximum obtained in situations requiring choice behavior in production of unidimensional acoustical sig-

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nals. The obtained results thus confirm the expected similarity in information transmission between the response production system and the stimulus identification one; and even though the subject produced his own signal categories, no additional information can be processed.

It could be argued, however, that the procedure employed is simply an additional method of varying the stimulus dimension, i.e., that the subject merely con- siders the acoustical response produced as stimulus information and proceeds to pair this with a subjectively determined response category corresponding to the numerical stimulus. In the two experiments reported, it could thus be considered that the subject did not generate a particular motor response but that he only

produced a variety of responses until the stimulus con- forms to the category. Using the method of production described, it would thus be interesting to investigate the limits of the categorical production of vocal sounds; the subject, having been given a particular number as stimulus, would be required to produce the appropriate vocal response in one discrete attempt, without assign- ing various signals to response categories.

ACKNOWLEDGMENTS

This research was supported by grants from the National Foundation of Science of Belgium. The author would like to thank Professor Dr. Jean Costermans for his frequent assistance and helpful suggestions.

REFERENCES

GARde. R, W. R. (1953). "An Informational Analysis of Absolute Judgments of Loudness," J. Exp. Psychol. 46, 373-380. MACRAY., A. W. (1070). "Channel Capacity in Absolute Judgment Tasks: An Artifact of Information Bias?" Psychol. Bull. 73, 112-121.

MACKAY., A. W. (1971). "On Calculating Unbiased Information Measures," Psychol. Bull. 75, 270-277.

POT.T.ACK, I. (1952). "The Information of Elementary Auditory Displays," J. Acoust. Soc. Amer. 24, 745-749.

Received 17 February 1971 4.3

Construction of a Dummy Head after New Measurements of Thresholds of Hearing

V. MELLERT

Drittes Physikalisches Institut, Universit•t, G•ttingen, West Germany

A dummy head was constructed after new measurements of thresholds of hearing. Correlated structures were found in the thresholds of hearing for all subjects. It was possible to average the identifiable structures and to adjust the frequency responses of the dummy-head to the average threshold of hearing.

An improved dummy head was constructed for sound transmission in head-related stereophony (cf. Damaske and Mellert, 1969). Its acoustical properties should resemble those of an "average" human listener. To achieve this, the geometry of the dummy head must be chosen properly. Particularly, the frequency responses of the microphones in the dummy head's ears, including their dependence on the angle of sound incidence, should correspond to those of the human ears. As Shaw and Teranishi (1968) showed on artificial ears, the coupling of several resonances of the outer ear to the free sound field depends on the direction of incidence. Therefore, audibility thresholds were measured for several angles of incidence of plane waves, using a sine-wave generator with automatically swept frequency. No such measurements were found in the literature, probably owing to the difficulties resulting from imperfect loudspeakers.

For the threshold measurement, reported here, an "ideal" loudspeaker was simulated in an anechoic chamber as follows. The loudspeaker is fed from a sine-wave generator, the frequency of which increases slowly from 200 Hz to 12 kHz in about 12 min. A condenser microphone at the ear level of the empty listener's seat controls the driving voltage for the

SPL

IOdB

0.2 0.5 I 2 5 kHz I0 15 •.• f

FiG. 1. SPL vs frequency, f, measured with a condenser microphone in the free sound field later used for threshold measurements: (a) 30 cm in the direction of the loudspeaker ahead of subject's place. (b) At subject's place. (c) 30 cm behind subject's place.

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Information Analysis of Choice Behavior in Producing Acoustical Signals