NON‐INDEPENDENCE IN SUBJECTIVELY RANDOM BINARY SEQUENCES
Authors: Brown David Louis 
Published: August 2014

In experiments which require the production of binary sequences by subjects, it has been found repeatedly that the interpretation of experimental results depends critically upon the nature of nonrandom sequential patterning among successive responses. Examples from the literature are discussed, where an experiment was originally misinterpreted because interresponse patterning was not considered.

This patterning has become an object of study in itself. It has been suggested (Ross & Levy, 1958) that the length of the sequence of responses is an important determinant of the nature of the interresponse patterning.

Differences between subjects in the type of patterns produced have also been reported. In addition, the nature of patterning has been found to vary depending upon the instructions given and the experimental procedures used. The present study was designed to evaluate the importance of these three variables (sequence length, subjects, and instructions).

Two groups of university undergraduates (a total of 78 subjects) each wrote two sets of six “random” binary sequences of six different lengths, using X and 0 as the two responses. Instructions for one group were to “try to make the sequence look like the sort of result you would expect if a balanced coin were to be tossed on each trial.” The other group was instructed to match as closely as possible the results of a series of actual coin tosses.

Long‐term dependencies were found when the proportion of 0 responses was plotted as a function of the cumulative imbalance in the frequency of previous 0 and X responses. The form of the dependency was the same in both groups and for all six sequence lengths, but the strength of the dependency was greater in the short sequences.

Short‐term dependencies were found when the proportion of 0 responses was plotted as a function of the eight possible preceding patterns of responses, when response sequences were examined to a depth of three responses. The group curves were found to be adequately summarized by a simple three‐parameter linear model in which the effect of each previous response contributes to the probability of an 0 on subsequent responses in a manner which has the following properties: avoidance of response repetition even with intervening responses (negative recency); independent effects for the separate preceding responses (little interaction); and a decay in the influence of more remote responses. The nonrandom effects were stronger for the short sequences and were reflected in more extreme parameter values for these sequences.

Differences in these three parameters also accounted for the differences between subjects in response patterning.

A more general eight parameter model (linear in the parameters, but not in the responses) was also developed and was useful in comparing the differences in response patterning in different experimental situations. Patterns in an ESP experiment reported in the literature were similar to those in the present study.

Quite different types of response patterning were found when subjects in the present study were given a pattern completion task. The eight possible three‐long subsequences were presented to the subjects as an eight‐item test. The subject's task was to determine the pattern in the three‐symbol sequence and extend it one symbol further.

These data were found to require a quite different set of values for the eight parameters of the general equation. These results conformed to those reported in an experiment involving difficult psychophysical discriminations.

Substantial effects were found for all three variables (sequence length, subjects, and instructions) and were summarized as differences in parameter values in the linear equation.