Introduction
The world is full of many variables and relationships among the variables. When people make judgments and decisions, they do so often on the basis of what they believe about the relationships among variables, especially when predicting of one variable on the basis of a set of other variables (e.g., Anderson, 1981; Norman, 1974). For example, with price and quality, we may know that as quality goes up, so will price. From this, we may infer that as price goes up, so does quality, even though it is not necessarily true. This inference is one of bi-directionality; and it is often true for both correlational and deterministic relationships if there are no mitigating forces.
A second type of inference is transitivity. Given a set of three variables, A, B, and C, if B increases with A and C increases with B, then we might infer that C increases with A. Again, this is not necessarily true and one can think of many counterexamples; but in many situations transitivity is appropriate.
Most studies on the relationships of variables and inferences about them have been in context of multivariate relationships such as BrunswikÕs lens model (Brunswik, 1955) and HammondÕs social judgment model (Hammond, Stewart, Brehmer, Steinmann, 1975). In these examples, one variable is deemed the criterion variable and the rest are referred to as cues or predictor variables. But in many situations, there are only sets of variables and imperfect knowledge about their inter-relationships. We may use this partial knowledge concerning the inter-relationship between some variables to infer the relationship between other variables. In a sense, we find ourselves in a task of intuitive statistics dealing with causal reasoning and structural equation modeling and path analysis (Campbell & Stanley, 1966; Byrne, 1994).
In other literatures on reasoning, such as syllogistic logic (e.g; Revlin & Mayer, 1978; Wilkins, 1928), there is a prescriptive truth. If all A are B and all B are C, then it is true that all A are C. But in the relationships among three variables, there is no such prescriptive truth. Inferences may depend on the weight of linguistic tendencies such as with atmosphere theory (Woodworth & Sells, 1935; Chapman & Chapman, 1959) or with the ability to generate instances (e.g., Revlis, 1975). Moreover, with sets of the variables, the instances will depend on the context and its implication on the structure of the system. One would expect different systems of inference to apply for sets of variables in mathematical systems (e.g., A = B + C), physical systems (e.g., A = velocity, B = mass, C = force), economic systems (e.g., A = net profit, B = advertising cost, C = market penetration), ecological systems (e.g., A = population of Species 1, B = population of Species 2, C = population of Species 3), and social and personality systems (e.g., A = self esteem, B = personal income, C = number of friends).
In this pilot study, we initiate a line of research
on inference about pairwise relationships in systems of variables. We present a new task and experimental
design in which we present two relationships and then ask the participant to
infer a third relationship. Each
task is of the form:
As A increases, B
increases.
As C decreases, B
increases.
Then as B increases,
what happens to A?
- increases
- decreases
- no change
Each letter (A, B, C) is
replaced in the problem by the name of some chemical.
Experiment
Participants.
Twenty-four undergraduates participated in the study
as partial fulfillment of a course requirement. Seven were female and 16 were male (one did not indicate
gender on the demographics questionnaire ). Their ages ranged from 17 to 24 with a mean of 19.75. When asked to give a self rating of use
of overall use of computers (1=no experience, 10=very experienced) the mean was
7.13 (s.d. = 1.68). When asked to
give a self rating on the World Wide Web on the same scale, the mean was 7.39
(s.d. = 1.37).
Task Materials
Seventy-two judgment problems were generated by
varying the relationship between the first two variables and second two
variables and permuting the order of the variables. The problems are listed in Table 1. Sets of chemical names were randomly
selected from a pool and substituted for the letters A, B, and C for each
participant such that no two names in one problem began with the same
letter. The order of the 72
problems was supposed to have been randomized for each of the participant; but
due to an error in the database, they were randomized once, and presented in
the same order for all of the participants.
All problems were presented in a browser window and
displayed on a 15 inch flat panel monitor. The task was administered on Apple Macintosh computers
running MacOS X 10.2 and the Safari web browser. Responses were indicated by clicking on one of three radio
buttons for the inferred relationship.
Figure 1 shows a screen shot of one of the problems. After the participant clicked on a
relationship and clicked on the ÒContinueÓ button, the browser paged to the
next problem.
Figure 1. Screen shot of the one of the 72 relationship inference problems.
Procedure
The participants agreed to the conditions of the
informed consent and their questions were answered. The participants filled in a pre-test questionnaire for age,
gender, and self-report of computer knowledge and use of the World Wide
Web. The judgment task was then
described to the participants.
They were told that they were to help a geologist make inferences about
the relationships among chemicals in rocks. They would be told two relationships and then had to infer
the third. When they were finished
they were asked to take a test of spatial visualization ability called the VZ2
(Ekstrom, French, & Harmon, 1976).
This took six minutes and was administered in the browser window. After the test, they were debriefed and
asked if they had any questions.