A study of the sensory threshold

This thesis is concerned with the problem of defining the processes by which a subject selects a response to a stimulus. Initially certain topics in two areas of research, sensory scaling and threshold measurement, are revived. In relation to the first the conflict between Fechner's law, which is derived from threshold measurements, and the more recent 'power law' given by 'direct methods' of scaling, is examined. It is shown that this conflict is due not to differences in the data from which the laws are derived, but to differences in the assumptions underlying the treatment of the data, and it is suggested that the logarithmic function may prove more useful for explaining a number of the findings in experiments on scaling, and that the same central effect of the stimulus say be considered to determine the response whether scales are being derived or thresholds measured. A short account of the development of models of the sensory discrimination process is then given, and evidence is reviewed which appears sufficient to justify applying the theory of signal-detection to the sensory threshold, and rejecting the neural quantum theory.
To investigate the threshold mechanism further it was decided to examine the effect of an accessory stimulus given in controlled temporal relation to a critical stimulus on the threshold for the latter. The first experiment was an attempt to confirm Motokawa's finding (Gebhard, 1953) that sensitivity to an electric phosphene is affected a preceding flash of light, reaching a maximum 1–3 seconds after the flash, the exact time depending on the colour of the light. The absolute threshold for the electric phosphene was measured by the method of limits at intervals of 1–9 seconds after a flash of blue or white light. Motokawa found that sensitivity was maximal when the interval between the stimuli was 2 seconds for the white light, or 3 seconds for blue light. Neither particular could be confirmed. There was no peak of sensitivity in the range studied, nor was there any marked difference in the curves relating threshold level to inter-stimulus interval for the two colours of light. Instead a monotonic relation between threshold and inter-stimulus interval was found, for this range, the threshold falling as the inter-stimulus interval decreased, slowly at long intervals and more rapidly at the shorter ones. This raised two questions: why could Motokawa's findings not be confirmed? and what was the nature of the effect which had been found?
The experimental technique of Motokawa and his colleagues is reviewed, and it is suggested that their findings mat be an artefact of certain features of their procedure, in particular the use of large steps where a threshold change is not expected, and small steps where a threshold is expected to appear.
Two possibilities are considered for the threshold-lowering effect: it might depend on the use of two visual stimuli and reflect a peripheral interaction at the retina, or it might be a central effect, not specifically visual. To investigate this the light flash was replaced, in the second experiment, by the ring of a bell of the same duration and given at the same inter-stimulus intervals. The same threshold-lowering effect of the accessory stimulus was found as in the first experiment, showing that the effect could be produced by an accessory stimulus in another modality. Further support for this conclusion was provided by Experiment 3, in which both the light-flash and the bell were used, the former at the same intervals as in Experiment 1, but the latter always preceding the critical stimulus by 1 second. Here the threshold did not vary significantly: there was little or no residual effect of the light when the bell was given at a shorter inter-stimulus interval. It appeared that it was the interval of time since the most recent accessory stimulus, whatever its modality, that mainly determined the degree to which the threshold fell.
In Experiment 4 the generality of the threshold-lowering effect was examined further. Using a visual accessory and auditory critical stimulus the possibility that the effect would occur only with visual critical stimuli was excluded.
These findings raised two questions: What processes underlie the change in threshold? What determines the relation between threshold level and inter-stimulus interval? Possible answers to the first question were suggested in terms of the analysis offered by signal detection theory. In this theory it is assumed that the decision whether or not a stimulus has been administered is made by a process equivalent to comparing the afferent input with a criterion, and the criterion is computed in a way which may take account of the parameters, the variance (σ2) and mean (M), of the 'noise' and 'signal + noise' distributions. The possibilities considered were that a change was produced in the functioning of the afferent paths at the time that the message from the critical stimulus was travelling along them, equivalent to a reduction in σN or MN, with a consequent change in the value of the criterion, c, computed by the subject (a 'distribution effect'), or that the computation of c was affected directly (a 'criterion effect').
Two hypotheses were proposed in answer to the second question (the relation between threshold level and inter-stimulus interval): (a) The accessory stimulus might have an 'arousing' or 'alerting' effect, causing an immediate central change with a small latency, which then decayed with time. (b) The subject might make use of the accessory stimulus as a 'temporal reference point' or 'warning'. By virtue of temporal information which he might possess he could use the accessory stimulus to determine when he could expect the critical stimulus to arrive. Here two subsidiary hypotheses might be suggested: (i) The subject lovers his threshold for the whole of the 'waiting time'. (ii) He may lover his threshold only when he expect the critical stimulus. Since his time-keeping ability is of limited precision, and the range of error will be greater for long times than for short, the 'range of expectation', if he allows for this, will be smaller the shorter the inter-stimulus interval. In either case, if the reduction in threshold is inversely related to the period for which it is reduced, a relation between threshold level and inter-stimulus interval of the sort found would be produced.
In Experiment 5 an attempt was made to test the 'warning' hypothesis directly by using a small range of randomly varied inter-stimulus intervals instead of a single fixed interval as previously, in order to see whether a fall in threshold daring the 'range of expectation' could be demonstrated. Ranges of 0.5–1.5 seconds were used but no consistent effect was found. In Experiment 6 the same procedure was used but the inter-stimulus intervals were varied at random over a large range – 5 seconds – to prevent the accessory stimulus providing temporal information. Though it was found that the fall in threshold previously shown o^er this range disappeared, the possibility that this was due to 'habituation' of an 'arousal response' could not be excluded.
The exact relation between the fall in threshold and the inter-stimulus interval was next considered. It was suggested that a close and simple relation between the threshold and the 'just noticeable difference' for time discrimination would be difficult to reconcile with the arousal hypothesis, and would constitute evidence for the hypothesis of a 'range of expectation' Studies of temporal discrimination were briefly reviewed; it appeared that few results were in agreement, save that Weber's law had usually been found not to hold Since no reliable measures of the temporal differential threshold were available two experiments were performed to measure the j.n.d. in a situation as similar to Experiments 1, 2, and 4 as possible. In each case Weber's law was found to apply for a range of intervals from 0.5 to 9 seconds. These experiments also provided new evidence on the causation of the classical 'indifference interval', and this was examined further in Experiment 9.
It was found that the fall in threshold could be described as an inverse function of either the j.n.d. or the inter-stimulus interval itself, with the latter giving a possibly somewhat better fit. This suggested that the 'range of expectation' might be a constant proportion of the inter-stimulus interval, though the inverse function found was not necessarily incompatible with an arousal explanation.
A threshold reduction consequent on a decrease in 'noise' (and 'signal + noise') variance should show a corresponding fall in threshold variance, whereas the variance might be expected to be constant if the threshold reduction were secondly to a change in MN or directly due to a change in c. In Experiment 10 this was examined using the method of constant stimuli. No significant decrease in the threshold variance was found; it appeared to be constant and there we evidence that rises might occur as the threshold fell. Explanations were offered for this finding. It was also shown that the fall in threshold could not be attributed to an increase in 'guessing'.
The 'distribution' and 'criterion' hypotheses were tested, farther in Experiments 11, 12, and 14. On the 'distribution hypothesis' the threshold curve would be expected to show a minimum, with a rise in threshold at shorter intervals, due to the latency of any reflex effect on the afferent paths evoked by the accessory stimulus. In Experiment 11 inter-stimulus intervals ranging front 0.0–1.5 seconds were used, but the threshold fell continuously to the zero interval. Experiment 12 tested the possibility that this was an artefact due to temporal information or arousal provided or caused by the pre-warning; but despite the use of pre warnings varied randomly over a range of 2–7 seconds the fall in threshold at the zero interval was confirmed. It remained possible that the conduction of part at least of the afferent message from the critical stimulus might have been sufficiently slow to be affected by a rapid response to the simultaneous accessory stimulus. This was excluded by Experiment 14, which showed that an accessory stimulus administered as much as 500 msec. after the critical stimulus could lover the threshold for the latter. Thus it appeared that a direct effect was exerted on the computation of the criterion, and that stimulus traces could be kept in a short-term peripheral store for 0.5–1.0 seconds, and could then benefit by a lowered decision criterion. Certain experiments in the literature bearing on the short-term store were discussed.
The 'warning' and 'arousal' hypotheses were tested by an experiment for which the 'arousal' and 'waiting time' hypotheses on the one band and the 'range of expectation' hypothesis on the other made different predictions. In Experiment 13 thresholds determined with fixed inter-stimulus intervals were compared with the thresholds given when the inter-stimulus intervals were randomly varied over a small range, 1 second. On the assumption that subjects lowered their thresholds for a range of time about the expected time of arrival of the stimulus, it was predicted that the threshold would fall as the longer intervals decreased, but would be relatively constant at the shorter intervals. This prediction, which was not made by the 'arousal' or 'waiting time' hypotheses, was confirmed.
Both arousal and warning hypotheses et a reduced threshold-lowering effect of accessory stimuli which are themselves within the absolute threshold range. A review of some relevant experiments showed that such an effect had not been satisfactorily established. In Experiment 15 its occurrence was demonstrated and a model was proposed to explain certain features of these and other results. Changes in the intensity of supraliminal accessory stimuli would not affect their value as temporal reference points, but would seem likely to alter the decree of arousal caused by them. In Experiment 16 the threshold changes induced by a barely supraliminal and a moderately intense accessory stimulus were compared. No significant differences in the falls in threshold produced by them could be shown, though significant differences in reaction time were found.
Finally it was assumed that the temporal reference hypothesis applied, and that the subject computed a criterion would tend to keep the probability of his making false positive responses when the stimulus was expected at or below a minimal rate; this allowed the extent of the changes in frequency of response to a stimulus as the inter-stimulus interval was varied to be predicted. When these predictions were compared with the results of earlier experiments it wan found that the agreement between them was in most cases satisfactorily close. The agreement appeared slightly better it was assumed that the 'range of expectation' was a constant proportion of the inter-stimulus interval than when it was related to the differential threshold for duration.
It is concluded that the evidence appears to be sufficient to accept that the subject reduces his threshold about the expected time of arrival of the stimulus, for a period which is related to the inter-stimulus interval, and that the threshold reduction is produced by lowering the criterion applied to threshold judgments for that period. It also appears possible that the range of expectation may be a constant proportion of the inter-stimulus interval, and that the subject may reduce his criterion to an extent calculated to maintain the probability of hie making a false positive response to an input during the range of expectation at or below a limiting value.

Advisor: Oldfield, R