Formal thinking about correlation

Abstract

Twenty‐five adults were administered two tasks involving the data of 12,2X2 matrices. In the first, subjects were invited to make decisions on the basis of data which was presented as involving causal, one‐way relationships. Four groups of subjects were distinguished in the level of their operational thinking. In task 2 the subjects were invited to make judgements on identical data, but presented as involving two‐way noncausal relationships. Results showed changes in the level of thought: subjects employing concrete operations in task 1 regressed to lower levels of thought; subjects employing transitional formal thought in task 1 advanced to fully formal thought in task 2. It was concluded that the first task imposed a ceiling effect on the thought levels of the latter subjects. Results showed that the level of thought employed was a function of the frequency of the data in the cells of the matrices and that the emergence of illogical thought was related to task difficulty.

A note on measurement of contingency between two binary variables in judgment tasks

“…The matrix was described to indicate that, if a relationship existed, it was a non causal one. Green et al (1979) comctly argued that, while M>R or M>c is an appropriate measure for the one-way problem, neither measure, in isolation, allows a precise calculation of association for the two-way problem. Further, they acknowledged the warning of Jenkins and Ward (1965) and Ward and Jenkins (1965) that t::.d should not be used if neither pair of marginal frequencies is equal.…”

“…These measures are examined, and the inappropriateness of some are noted. As well, it is argued that accurate judgments about related variables should not be used to infer that the judgments are based on the appropriate information.A number of studies in the psychological literature have been concerned with judgments of contingency or correlation between two binary variables (Allan & Jenkins, in press;Gray, 1976;Green, Jurd, & Seggie, 1979;Inhelder & Piaget, 1958;Seggie, 1975;Seggie & Endersby, 1972;Smedslund, 1963;. One purpose of the present note is to evaluate the various measures of contingency that have been used in these studies.…”

The judgment of covariation between binary variables: Some conditions that influence the process

“…This claim was made on the basis of research showing that "under some circumstances people do understand the concept of covariation and use information about instances appropriately to estimate covariations" (p. 282) (Alloy & Abramson, 1979;Inhelder & Piaget, 1958;Peterson, 1980;Ward & Jenkins, 1965). In addition to that work, Green, Jurd, and Seggie (1979), Seggie (1975), Seggie and Endersby (1972), and Seggie and Schofield (1987) also reported conditions under which subjects make highly appropriate judgments of covariation between binary variables.…”

“…Within the context of age and sex differences, subjects can use the binary relationships to make logical decisions. Although the decision making of subjects is less accurate when they are presented with data representing zero correlations (Green et al, 1979;Seggie, 1975;Seggie & Endersby, 1972), the Green et al study investigated the important consequences of the ceiling effect evident in the performance of subjects presented with correlated data. Green et al pointed out that the decision-making task asks the subjects to make a choice between the two values of one variable, a choice that may encourage the search for a one-way causal relationship (e.g., a particular treatment leading to a particular outcome).…”

“…It is also evident that there is no difference in accuracy of decision making as a function of level of correlation and that a ceiling effect was in operation. The consequences of such an effect for the diagnosis of the subjects' level of thought were addressed by Green et al (1979), who showed that accurate decisions can be made through the exercise of the penultimate level of formal operations. That subjects of the present experiment are at least capable of that level of thought in dealing with relationships beween dichotomous variables can be seen in Table 2.…”