Abstract Experiments on the absolute identification of pure tones were conducted at a single frequency in order to explore several effects. We measured the change in transmitted information as the stimulus range was varied, and we also measured the change in transmitted information as the number of categories within a fixed range was increased. In the former case, we found that information increased with increasing range. In the latter case, we found that information increased with increasing number of categories, but the increase was due to a purely mathematical effect. Transmitted information was estimated by means of computer simulation designed to overcome, in part, small sample bias. This simulator is of potential use to others by helping them calculate transmitted or mutual information accurately using a minimum number of experimental trials. The graph of calculated information against number of trials was found to assume a characteristic shape. Garner and Hake (1951) and Garner (1953) demonstrated how one could quantify the information transmitted to a participant who was required to judge the loudness of tones of a fixed frequency. The experimental paradigm is well known. The continuum of sound intensities between two fixed intervals (dB HL) could be divided into an arbitrary number of loudness categories (Garner used 4, 5, 6, 7, 10 and 20). The participant was trained to identify a tone as belonging to a specific category. He or she was then presented with a large number of tones of unknown intensity, and was required to sort them as well as he or she was able into the correct categories. The data were entered into a matrix, which is known as a confusion matrix, and, using the methods of Shannon and Weaver (1949), the mean information transmitted per stimulus was calculated (Attneave 1959, Norwich, 1993). A problem encountered in the measurement of channel capacities is the large number of trials that must be conducted in order to obtain accurate values. A trial is a single presentation to a participant of a tone whose intensity is unknown to him or her. Houtsma (1983) introduced the idea of obtaining plausible values by extending data through computer simulation. Studies of this type are referred to as one-dimensional because, for example, the tone was permitted to vary only in loudness and not in pitch (Garner, 1962). It was discovered by Miller (1956) that such one-dimensional stimuli could transmit to the participant no more than about 2.5 bits, or 1.75 natural units of information per stimulus. A natural unit of information is just information calculated using natural logarithms. It can be obtained from the information in bits by multiplying by 0.693... Earlier investigators have begun the exploration of the effects of stimulus range and number of stimulas categories on transmitted information. Braida and Durlach (1972), working within the framework of a theoretical model of loudness perception, have derived a relationship between information and sensitivity which, in turn, can be related to range. Luce, Weber and Green (1976) explored the effect of varying stimulus categories over a range fixed about a central intensity. Essentially, transmitted information was found to increase with both range and number of categories, saturating at a value not greater than approximately 2.5 bits. It has not been clear how these two variables independently cause the transmitted information to increase. OBJECT OF STUDY Our experiments were designed to study three effects. (a) By means of computer simulation, we explored the change in the calculated information (including the small sample bias) as the number of trials increases from zero to, say, 20,000. (b) We examined the change in transmitted information associated with differences in the total range of stimuli. For example, does the transmitted information differ when stimuli are selected over the range 1-90 dB HL as compared with 1-70 dB HiL? …
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