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The Dependence of Frequencies of Seeing on Procedural Variables: II. Procedure of Terminating Series of Intensity-Ordered Stimuli

Departments of Psychology, Northwestern University and Stanford University

John W. Cotton and William S. Verplanck

A. The Problem

The first paper (5) in this series presented experimental evidence that the visual thresholds obtained with the intensity-ordered stimuli when only ascending series are presented are lower than those obtained when only descending series are presented. The slope (“SD”) of the frequency of seeing curves obtained did not vary as a function of the direction of the brightness change. These results mean that Ss tend to say “yes” more often to stimuli that appear near the beginning of sets of ascending series than to the stimuli of the same intensities when ascending and descending series are alternated. Under specified stimulating conditions something has acted to alter the probability that a “yes” will be given. Converse effects occur in descending series.

One class of variable known to produce alternations in the probability of a response in other situations includes events which have repeatedly followed the response in question in the past (“positive and negative reinforcing stimuli”). This suggests that the events that follow the termination of a series may produce shifts in the frequencies of response such as we have observed. For example, in those procedures using ascending series only, at the end of each series (i.e., when the subject has said “yes” three items) the next stimulus presented is a weak one that invariably produces a “no.” Perhaps this stimulus, with its high probability of evoking a “no,” operates to increase the probability that the stimuli which preceded it (as specified by their intensities) will produce “yeses” when they are next presented. The introduction of a long delay before the next series is begun, or the experimenter’s announcement of a rest period at the end of a series might also operate in this way.

To state it another way, if the behavior of S is changed at the end of a series, the responses preceding that change will tend to occur with higher frequency when the situation recurs. This should cause the 50 per cent threshold obtained in a set of descending series to be higher than that obtained in ascending series, since in the respective cases “noes” and “yeses” become more probable. Similarly, the longer the series, the greater the effect. This post hoc hypothesis accounts for the results already reported.

According to the hypothesis, a delay at the end of a series should increase the tendency for descending thresholds to be greater than those obtained without a delay. We might also expect that the threshold obtained from descending series should be higher if the criterion for series termination were changed from three successive “noes” to one “no,” because the consequence of the termination becomes nearer in time to the stimulus-values to which “yes” has been given.

These two predictions have been tested in the experiment reported here. It is designed to verify the original finding with respect to ascending and descending series, and to determine whether these findings can be accentuated by introducing time interval delays at the end of a series or by changing the criterion for series termination.

Six different procedures of stimulus presentation are compared: an ascending procedure, an ascending-and-descending procedure, three descending procedures with different inter-series intervals, and a descending procedure with a criterion of only one “no” response for terminating a run. Our speculations suggest that the lowest 50 per cent thresholds will be found with the ascending procedure, intermediate thresholds with the descending-and ascending procedure, and the highest thresholds with the three descending procedures. Among the descending procedures, as the inter-series delay increases, the threshold should increase. Consequently, a rank order of 50 per cent thresholds for five of our procedures can be predicted. The sixth procedure, which employs a changed criterion for terminating a run, may be expected to produce a higher 50 per cent threshold than a comparable descending procedure involving the original criterion, but an exact prediction of its rank cannot be made.

B. Apparatus and Procedure

1. Apparatus

The Hecht-Shlaer Model III Adaptometer used in our previous study was also employed in this experiment. All time intervals except those at the end of series were controlled automatically by a 4-sec. interval programmer. The Adaptometer has been described fully elsewhere (3, 4).

2. Subjects

Six paid undergraduate men served as subjects. Each S met or exceeded Service visual norms for near and far acuity, phoria, and depth perception, as measured by the Bausch and Lomb Orthorater. No S had previous experience in investigations of the visual threshold, and the same training procedure described in our previous paper (5) was used before the experiment itself began. Experimental Ss were run between the hours of 8 a.m. and 6 p.m. Some variation in hour of running occurred for one subject; otherwise the time of experimentation was stable for each subject.

3. Dark Adaptation and Darkroom Procedure

A six-by-six Latin square design was used to counterbalance three variables: individual differences among Ss, day-to-day variations, and the procedures on each experimental day, and every S served with a different procedure on each successive day. Twenty series of stimulations were presented in each experimental session regardless of the procedure used. Time intervals at the end of series were fixed by the different procedures used, except that a 1 to 21/2 min. rest period was given each day, generally between the tenth and eleventh series.

The six procedures are labeled as LA4/3 (long ascending method with 4-sec. inter-series delays and a 3 “yes” response criterion for series termination), LAD4/3 (long ascending and descending series alternated with 4-sec., inter-series delays and a 3 “yes” or “no” response criterion for termination of ascending and descending series, respectively), LD4/3 (long descending series with 4-sec. inter-series delays and a 3 “no” response criterion for series termination). These three procedures duplicate those reported in the preceding paper. Procedure LD8/3 and LD16/3 differed from LD4/3 only in that an 8- and 16-sec. delay, respectively, were introduced between series. The final procedure, LD4/1, differed from LD4/3 in that one “no” response was the criterion for series termination.

Other properties of the procedures correspond exactly to those in the first experiment.

One day was spent in training each S before the six experimental days began. On this day, each S responded through the five series with each of the six variations of the methods of limits being used, plus 50 consecutive single luminance stimulations at 2.5 log mmL.

C. Results

The relative frequencies of “yeses” given to each stimulus brightness, in log mmL, were plotted on arithmetic probability paper and a straight line was visually fitted to the experimental points (1), yielding a conventional PR or frequency of response function. The “standard deviation,” or slope, was determined as before. Table 1 presents mean values of the 50 per cent thresholds and slope values, or “standard deviation,” for the several methods, subjects, and days. The variations in mean thresholds and “slope” as a function of these variables have been evaluated by means of the analyses of variance summarized in Table 2.

Table 2 shows that mean values of the 50 per cent threshold and of the SD s both exhibit significant differences in individual Ss’ performance (1 per cent level of confidence ) and in performance under the different procedures (5 per cent level of confidence).

Mean Values of 50 Per Cent Threshold and “SD”s

Analyses of Variance 50 Per Cent Thresholds and “Standard Deviations”

Since the procedures were shown to affect the threshold values in this experiment, our hypothesis regarding the effects of various methods was then evaluated on the basis of t tests between pairs of methods. Fifteen t tests were performed, one between each possible pair of methods. The standard error of the difference was estimated by Fisher’s procedure (2, pp. 73-74). The results of these tests, which are summarized in Table 3, are unequivocal: The thresholds obtained with long ascending series (LA4/3) differed significantly (2 per cent level or better) from the thresholds obtained with every other method, and no significant differences appeared in the t tests performed between thresholds for other methods. Consequently, the significance of methods-differences observed in the analysis of variance appears to arise solely from the fact that the long ascending method (LA4/3) produces significantly lower thresholds than do the other methods.

Since the analysis of variance showed that SD values also vary as a function of the particular procedure employed, 15 t tests of mean “SD”s for pairs of procedures were performed in the same manner as those for threshold differences. The results of these tests are summarized in Table 4. On the basis of these t tests, we can assert that the long ascending method (LA4/1) differs at the 5 per cent level or better from all the other methods except the long ascending-and-descending method (LAD4/3) and that the long descending-and ascending method (LAD4/3) differs from the long descending, 16-sec. method (LD16/4) at better than the 5 per cent level in the threshold measures yielded.

D. Discussion

The experimental data reported above corroborate our previous finding that the ascending method of limits procedure employed yields lower thresholds than the descending method. An investigation of the differences between pairs of methods indicates that only one method, the long ascending method (LA4/3) results in mean thresholds significantly different from other methods. On statistical grounds, then, we cannot assert that our predicted changes in threshold occurred as a function of method. An examination of means for the various methods shows some correspondence between group behavior and theory. The hypothesis being tested predicts that the methods should be arranged in order from low to high thresholds as follows: LA4/3, LAD4/3, LD4/3, LD8/3, and LD16/3, with LD4/1 to fall somewhere above LD4/3. Only one deviation from this predicted order occurs in the data: The LD8/3 procedure gave a lower threshold than LD4/3.

Apparently the predictions have been somewhat successful even though no statistical confidence can be placed in these observed trends. If further experimentation should show statistically significant threshold trends of the type noted in this experiment, the hypothesis would appear useful even though the magnitude of the differences is small.

Results of t Tests Between Mean 50 Per Cent Thresholds for the Six Procedures

Results of t Tests Between mean “SD”s for the Six Procedures

The present experiment indicates that the SD is also a function of the specific method of limits used. As in the case of the threshold a constant trend exists from procedure to procedure, although the major differences appear to lie between the ascending procedure and other procedures. The SD decreases in order from LA4/3 to LAD4/3, LD4/3, LD8/3, and LD16/3. The sixth procedure, LD4/1, yields a mean “SD” equal to that of LD8/3.

This covariation of threshold and “SD” values is interesting. No significant changes were observed in “SD” values as a function of method in our first study (5) of the method of limits. In that study the mean “SD”s were also greatest for the ascending methods and least for the descending methods, but the differences were not significant.

The changes in “SD”s as a function of method in this experiment are not explainable by our hypothesis: the differential reinforcement of response changes that we postulated should change the placement of the threshold curve but not necessarily its shape. No new hypothesis which would lead to the prediction of the parallel changes we have observed in thresholds and SD s as a function of the methods used in this experiment.

E. Summary

Six Ss were given one day of thresholds training prior to serving for six days, each one day under each of six variations of the method of limits. The six variations, selected on the basis of predictions derived from results of a previous experiment, yielded mean thresholds that differed in the directions predicted, but the mean thresholds obtained with only one procedure differed significantly from thresholds obtained with other procedures.

Significant changes in SD values were also found from method to method. In general, mean SD s were large for methods where mean thresholds were low and vice versa. No explanation for the changes in SD values is proposed.


1. Beck, L. H. An experimental investigation of binoculars as an aid to night vision. (Unpublished Ph.D. Dissertation, Brown University), 1945.

2. Fisher, R. A. The Design of Experiments. (4th ed.) Edinburgh: Oliver & Boyd, 1947.

3. Hecht, S., & Shlaer, S. An adaptometer for measuring human dark adaptation. J. Opt. Soc. Amer., 1938, 28, 269-275.

4. Verplanck, W. S., Collier, G. H., & Cotton, J. W. Nonindependence of successive responses in measurements of the visual threshold. Journal of Experimental Psychology, 1952, 42, 273-282.

5. 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, 37-47.

Department of Psychology Department of Psychology
Northwestern University Stanford University
Evanston, Illinois Stanford, California


* Received in the Editorial Office on August 7, 1953.

1 The experiment reported in this paper was performed in the Department of Psychology, Indiana University, under ONR Contract N6ori-180, T.O. IV, Project 143-253, and with support from a grant by the Graduate School of Arts and Sciences.

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