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Randomized stimuli and the non-independence of successive responses at the visual threshold

William S. Verplanck and Donald S. Blough

A. Introduction
It has often been found that the sequence of responses to repeated stimuli having the same brightness near the absolute threshold is not random, but exhibits a serial correlation (1, 2, 6, 7, 8). Two effects may be distinguished: a response-to-response linkage, and a linkage that can be conceptualized as a variable controlling the probability of response and varying in time. It is possible that response-to-response linkage would be reduced if successive stimuli varied substantially and randomly with respect to brightness.

In areas other than vision, sequential dependencies have been found among responses to stimuli randomly ordered in intensity. Perhaps the most complete study is one by Fernberger on the differential threshold for weight. He found a contrast effect, i.e., the S tended to call a comparison weight in the region of uncertainty heavier than the standard weight if it followed a light stimulus, and lighter if it followed a heavy stimulus. As Fernberger put it: “It is very tempting to say that we have here a type of expectation which tends toward a reversal of judgment from one pair to the succeeding” (3).

More recently, Schafer investigated interdependence in data obtained using the method of constant stimuli to determine the noise-masked auditory threshold (4). He found that the entire psychometric function varied with the intensity of the preceding stimulus. A relatively intense preceding stimulus reduced the percentage of response, a less intense preceding stimulus increased it, and a preceding stimulus of the same intensity reduced it slightly. He offered an interpretation of these results in terms of “set”. Schafer did not concern himself, as Fernberger did, with the response to the preceding stimulus.

Negative sequential dependencies such as those found in Fernberger and Schafer do not conform to the results obtained by the method of single stimuli at the absolute visual threshold, where positive dependencies are generally found. It is not impossible, however, that negative dependencies will appear between responses to visual stimuli if the stimuli are varied in intensity from trial to trial.

The present experiment, then, is concerned with dependence of responses on both the preceding stimulus and the preceding response to visual stimuli near the absolute threshold. A modified method of constant stimuli permits comparison of the results with data in other modalities, and with data on the sequential effects previously reported among responses to stimuli near the absolute visual threshold.

B. Procedure
1. Subjects
Four paid male undergraduates served as Ss. All had visual acuity better than 20/25 and normal vision in other respects, as tested on the Bausch & Lomb Orthorater. None had had any previous experience in visual experimentation.

2. Apparatus

The apparatus employed has been described in detail elsewhere (5). The S was seated in the light-tight chamber of the apparatus, his head held in position by a highly restrictive headrest but without a biting board. Artificial pupils 6.40 mm. in diameter were used; the angle of the pupil plane to the vertical was 10 degrees. The stimulus patch subtended 3 degrees at the cornea and was located 5 degrees below a red fixation point.

3. Procedure

During experimental runs, a short “ready” buzz was presented to the S every 5 sec. Except when blanks were interposed in the stimulus series, a flash 0.27 sec. in duration illuminated the stimulus patch 1.0 sec. after each buzz. Ss responded by depressing one of two keys (“yes” and “no”), and the responses were manually recorded. This response record was checked against both an automatic polygraph record and electric counters.

Each S reported at the same hour on every experimental day. S dark-adapted for 20 min. in Polaroid red plastic goggles, then spent 10 min. in complete darkness in the light-tight chamber before any critical trials were made. During the following 10 min. of this period, S remained in darkness except that he responded to 60 “warm-up” flashes randomized in intensity.

4. Preliminary Sessions

At the beginning of his first day, S was seated in the chamber at normal room illumination, and the headrest and interpupillary distance were adjusted until S stated that he could see the stimulus patch and the fixation point with maximum clarity. S then spent 20 min. in red goggles, followed by 10 min. in the darkened chamber. Standard instructions were then read to S, and he had the opportunity to familiarize himself with the situation. He was never informed of the nature of the experiment. He was told simply to “press the right-hand key if you see a flash after the buzzer, and press the left-hand key if there is no flash after the buzzer.” After the first day, E told S only that the procedure was to be “the same as before” and reminded him, before each series of stimuli, “always keep your eyes on the red light.”

During the first day or two with each S the brightness required to produce approximately a 50 per cent frequency of seeing was determined by the method of limits. This value determined the range over which the brightnesses were randomized on the subsequent preliminary sessions and on the experimental days. Each S had at least five and not more than eight preliminary sessions, of which one or two involved stimuli constant in brightness, and the remainder, stimuli randomized with respect to brightness. By the time the experiment began all subjects were responding consistently and readily in the situation and were yielding a very small percentage of positive responses to blanks.

5. Experimental Sessions

After the completion of preliminary training, each S was run for eight experimental days. On these days the following procedure was employed: After the 60-trial “warm-up” period, four series of 91 stimuli each were given. The series were separated by 2 min. rest intervals. Each stimulus was presented at one of six fixed brightnesses, five of them differing in steps of approximately 0.14 log units, and the sixth was zero. One brightness fell near S‘s 50 per cent frequency of seeing, with two above and three (including zero) below. The values remained unchanged over the eight experimental days. The brightnesses of successive stimuli were presented in random order, but with the restriction that each one followed itself and each other brightness 10 times in a full day’s session. The same random series was used each day.

C. Results

The data have been analyzed to reveal the effect of two variables on the probability of a “yes”: the response to the preceding stimulus, and the brightness of the preceding stimulus. The data have also been arranged to test the difference between the “ascending” and “descending” thresholds. In this analysis, “ascending” runs include all responses to stimuli that were just one step brighter than the preceding stimulus, and “descending” runs are composed of responses to stimuli one step dimmer than the preceding stimulus.

In all figures, percentages of “yes” responses are plotted along the ordinate on a normal probability scale. In Figure 1 the abscissa represents absolute brightness; in the other figures the unit along the abscissa is a relative brightness “step.” Each step represents 0.14 log units. Step 3 was set on the basis of the preliminary runs of each S to correspond as nearly as possible to the S‘s 50 per cent threshold; consequently the steps represent different absolute values for each S (5). All functions are straight lines visually fitted to the experimental points.

1. PR as a function of Stimulus Brightness Alone

Absolute threshold functions for each of the four Ss, determined without regard to the preceding response or stimulus, are shown in Figure 1. Each point represents the percentage of “yes” responses given to the 480 stimuli presented during the eight experimental days at each brightness.

Figure 1
Absolute threshold functions for each S. Each point represents the percentage of “yes” responses to 480 stimuli of the brightness indicated on the abscissa.

2. PR as a Function of the Preceding Response

In Figure 2 two functions are plotted for each S: the percentage of “yes” obtained when the previous response was a “no” (triangles), and the percentage of “yes” when the previous response was a “yes” (circles). Each point represents the mean of eight values, one for each of the experimental days.

Figure 2
Percentage of “yes” responses obtained when the previous response was a “no” (triangles) compared to percentage of “yes” responses obtained when previous response was a “yes” (circles). The curves for successive subjects are shifted two steps to the right.2

For each S the number of “yes” responses appears to be larger when the responses follow “yes ” than when they follow “no”. In only one of the 20 possible comparisons is the point after “no” higher than the point after “yes.” By sign test this result would occur far less than 1 per cent of the time if the preceding response bore no systematic relationship to frequency of response. The slopes of the curves also differ. Thus the probability of a positive response is shown to be a function of the response to the preceding stimulus.

3. PR as a Function of the Preceding Brightness

When the brightness of the preceding stimulus is taken as the parameter, and the response to that stimulus ignored, six threshold functions are obtained


Pooled data of all S‘s, showing absence of effect of preceding stimulus brightness on frequency of seeing. Symbols for overlapping values have been shifted to right or left.

for each S, one for each of the stimulus brightnesses that could precede the stimuli used in determining the function. These curves were found to be almost identical for any given S, except for a small, apparently random, scatter of the points. Even when the data of all Ss are pooled, as shown in Figure 3, there is little evidence of any effect of preceding brightness.

4. PR as a Function of Both Preceding Stimulus and Preceding Response

Since the response parameter has two values and the stimulus parameter has six, a complete plot of the joint functions would involve 12 curves for each S. To clarify the presentation, only three values of the stimulus parameter have been presented in Figure 4, the lowest, the middle, and the highest intensities. Data of the four Ss have been combined into one plot. Each point in this plot represents the percentage of “yes” responses for the four Ss over all the experimental days. The number of responses represented by each point varies: it was impossible to plot a meaningful curve for a preceding response

Figure 4
Frequency of seeing as a joint function of preceding stimulus and preceding response. Each curve represents the mean threshold for all Ss following responses of “no” or “yes” to stimuli of brightness “1,” “3,” or “5.”

of “yes” to a preceding stimulus of “1” since very few stimuli of brightness level “1” elicited responses of “yes”. The probability of a “yes” response to stimuli following relatively intense stimuli is lower when the data are grouped according to preceding responses (Figure 4). That is to say, when the preceding response is controlled, PR shows to be a function of the intensity of the preceding stimulus. With the exception of a few scattered reversals, the data of theSs taken separately are consistent with this pattern.

5. “Ascending” and “Descending” Thresholds

During each experimental session a given stimulus was preceded by the next brighter stimulus on 10 trials, and by the next dimmer stimulus on 10 trials. These occasions duplicate the stimulus-to-stimulus relationship that exists when stimuli are presented in an intensity-ordered sequence, as by the method of limits.

We determined for each S a threshold curve that included only responses to stimuli preceded by the next brighter stimulus, and thus corresponded with the descending threshold in the method of limits. A second curve for each Sincluded only response to stimuli preceded by the next dimmer stimulus and corresponded to the ascending threshold in the method of limits.

No systematic difference was found between the ascending and descending thresholds so constructed–either for individual Ss or when the data of all were pooled. These data shed no light on the idiosyncrasies of data collected by the method of limits.

6. Responses to Blanks

During the experimental sessions each S was presented with a total of 480 blanks. On these trials no stimulus light was presented after the ready signal. “Yes” responses to these blanks for each of the four Ss were 0.2 per cent, 1.3 per cent, 1.0 per cent, and 0.2 per cent.

D. Discussion

The analysis of the data with the preceding response as the parameter (Figure 2) indicates that, in our situation, randomizing stimulus intensities does not eliminate response-to-response dependencies. If an S reports one stimulus, he is more likely to report the next one. If he misses a stimulus, he is more likely to miss the next one.

At least two distinct processes can account for this type of response inter-dependency. Fluctuation in the S’s “sensitivity” over periods longer than the inter-trial interval would produce these results, as would a simple Markovian response-to-response dependency.

The analysis in terms of both preceding stimulus and response (Figure 4) enables us to make a tentative choice between these possibilities. If the preceding response alone affected the next response, no separation would be expected of the “after no” and “after yes” curves with different preceding stimulus intensities; a “no” in response to a “1” would be just as effective in reducing the probability of a “yes” to the next stimulus as a “no” in response to a “5.” However, a separation of these curves would be expected if sensitivity variation accounted (either in part or in full) for the serial dependency. A “no” in response to a bright “5” would be expected only if sensitivity were momentarily at a low level, and, if this were the case, the next response would probably also be a “no”–hence the relatively high threshold after a “no” in response to a “5”. A “no” in response to a dim “1” would occur even under conditions of relatively high sensitivity–hence the relatively low threshold after a “no” in response to a “1”.

The same argument applies to thresholds derived from responses following “yes.” Since a relatively higher sensitivity is necessary for the subject to respond “yes” to a “3” than to a “5,” on the average, the threshold following “yes” in response to a “3” would be lower and PR higher, than the threshold following “yes” in response to “5.” This was found to be the case; the inter-trial dependency varied in sensitivity.

The data obtained in these experiments are not similar to those of Schafer, in that they do not show any dependence of the threshold on the intensity of the preceding stimulus alone. But when the responses are grouped according to previous response, the functions resemble Schafer’s, in that a relatively intense stimulus is associated with a reduced probability of response of the next stimulus, below the value produced by a stimulus following a less intense stimulus.

The sequential dependencies found between responses are the reverse of those found by Fernberger. In Fernberger’s weight-lifting experiment, Ss tended to alternate responses; in this experiment, Ss tended to repeat responses.

A significant difference between ascending and descending thresholds has been reported (7) when stimulus flashes are presented by the method of limits (intensity-ordered). The similarity between ascending and descending thresholds constructed from the present data suggests that one-step dependence between trials is not the source of this difference.

E. Summary

In an investigation of the non-independence of successive responses to randomized near-threshold visual stimuli, it was found that: (a) These responses are not independent: Ss tend to repeat their “yes” and “no” responses. (b) Responses to stimuli of a given brightness appear to be independent of the brightness of the preceding stimuli. (c) Analysis of dependencies of successive responses suggest that in the present experiment such dependencies result in large part from the action of some superordinate variable, such as the fluctuation of a “sensitivity” factor. (d) One-step response-to-response dependencies do not seem to account for the differences obtained with intensity-ordered stimuli between ascending and descending thresholds.


1. Collier, G. Probability of response and inter-trial associations functions of monocular and binocular stimulation. Journal of Experimental Psychology, 1954, 47, pp. 75-83.

2. Cotton, J. W., & Verplanck, W. S. The dependence of frequencies of seeing on procedural variables: II. Procedure of terminating series of intensity-ordered stimuli. Journal of General Psychology, 1955, 53, pp. 49-57.

3. Fernberger, S. W. Interdependence of judgments within the series for the method of constant stimuli. Journal of Experimental Psychology, 1920, 3, pp. 126-150.

4. Schafer, T. H. Influence of the preceding item in measurements of the noise-masked threshold by a modified constant method. Journal of Experimental Psychology, 1950, 40, pp. 365-371.

5. Verplanck, W. S., & Blough, D. S. An apparatus for the presentation of visual stimuli at low intensities. Journal of General Psychology, 1955, 53, pp. 67-77.

6. Verplanck, W. S., Collier, G. H., & Cotton, J. W. Nonindependence of successive responses in measurements of the visual threshold. Journal of Experimental Psychology, 1952, 44, pp. 273-282.

7. Verplanck, W. S., & Cotton, J. W. The dependence of frequencies of seeing on procedural variables: I. Direction and length of series of intensity-ordered stimuli. Journal of General Psychology, 1955, 53, pp. 37-47.

8. Verplanck, W. S., Cotton, J. W. & Collier, G. H. Previous training as a determinant of response dependency at the threshold. Journal of Experimental Psychology, 1953, 46, pp. 10-14.

1 This research was supported by Contract N5ori-07639 between Harvard University and the Office of Naval Research (Project Nr140-253).

2 Slight shifts in the position of individual points correct for small constant errors in the setting of the stimulus.

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