Compatibility Hypothesis

Study 2: Prediction of Academic Performance

Our second test of the compatibility hypothesis involves the prediction of a student’s grade in a course. We asked 258 subjects from the University of Oregon to predict the performance of 10 target students in a history course on the basis of the students’ performance in two other courses: English literature and philosophy. For each of the 10 targets, the subjects were given a letter grade (from A+ to D) in one course and a class rank (from 1 to 100) in the other course. Half the subjects predicted the students’ grade in history, whereas the other half predicted the students’ class rank in history. Each of the four combinations of performance measures (grade/rank) and courses (literature/philosophy) was presented to a different group of subjects.

The compatibility hypothesis implies that a given predictor (e.g., grade in philosophy) will be given more weight when the criterion is expressed on the same scale (e.g., grade in history) than when it is expressed on a different scale (e.g., rank in history). The relative weight of grades to ranks, then, will be higher in the group that predicts grades than in the group that predicts ranks.

As in the previous study, we first correlated the criteria with the predictors. The (zero-order) correlations of g with G and R were .83 and .82, respectively, whereas the correlations of r with G and R were .70 and .91, respectively, in accord with the compatibility hypothesis. We next regressed the mean predictions of grades and ranks onto the two predictors. The letter grades were coded D = 1, C− = 2*, . . .* A+ = 10. (To make the regression weights positive, the ranking order was reversed.) The multiple regression for both grades and ranks fit the average data very well with multiple correlations of .99. Let g**i and r**i denote the mean observed predictions of grade and rank, respectively, for a student with a grade G**i in one course and a rank R**i the other course. There was no significant interaction between the scale (rank/grade) and the course (literature/philosophy); therefore, the data for the two courses were pooled. The multiple-regression equations, then, take the form

g**i = αgG**i + β**g R**i

r**i = α**r G**i + β**r R**i,

when the independent variables are expressed in standardized units. Thus, α g and α**r are the regression weights for the grades (G**i) estimated from the predicted grades and ranks, respectively. Similarly, β**g and β**r are the corresponding weights for the second predictor, class rank. The relative weights for the first predictor in each of the two response modes are

A**g = αg/(α**g + β**g)

A**r = αρ/(α**r + β**r).

These values measure the relative contribution of G**i in the prediction of grade and rank, respectively. Because the grades and ranks are monotonically related, A**g and A**r should be approximately equal if the weighting of the dimensions is independent of the response scale. However, if the match between the predictor and the criterion enhances the weight of the more compatible predictor, then A**g should exceed A**r.

The values estimated from the regression equations were A**g = .51 and A**r = .40, in accord with the compatibility hypothesis. Thus, grade in philosophy was weighted more heavily in the prediction of grade in history than in prediction of rank in history. Similarly, rank in philosophy was weighted more heavily in the prediction of rank in history than in the prediction of grade history.

To obtain an ordinal test of the compatibility hypothesis within the data for each subject, we analyzed the reversals of order induced by the change weights. There were 21 pairs of students (i, j) in which G**i > Gj and Rj > R**i. If G is weighted more heavily than R in the prediction of grades and r is weighted more heavily than G in the prediction of rank, we would expect g**i > g**j and r**j > r**i.

Indeed, subjects who predicted grades favored the student with the higher G 58% of the time, whereas subjects who predicted rank favored the student with the higher G only 42% of the time. (Ties were excluded from this analysis.) This difference is statistically significant (p *< .*001). Recall that subjects did not compare students directly; the ordering was inferred from their predictions.

The compatibility effects observed in the previous two studies may be mediated by a process of anchoring and adjustment. Subjects may use the score on the compatible variable (the attribute that matches the criterion) as an anchor and then adjust this number up or down according to the value of the noncompatible variable. Because adjustments of an anchor are generally insufficient (Slovic & Lichtenstein, 1971; Tversky & Kahneman, 1974), the compatible attribute would be overweighted. An anchoring and adjustment process, therefore, provides a natural mechanism for generating compatibility effects. To test whether compatibility effects occur in the absence of anchoring, we replaced the prediction task described previously with a choice task in which the subject is no longer required to make a numerical prediction that would invoke anchoring. The following study, then, investigates the compatibility hypothesis in a context in which anchoring and adjustment are unlikely to play a significant role.

Seventy-eight Stanford undergraduates were presented with 20 pairs of students taken from the stimuli used in Study 2. In each pair, one student had a higher grade and the other a higher rank. Half the subjects were asked to predict, for each pair, which student would achieve a higher grade in history, whereas the remaining subjects were asked to predict, for each pair, which student would achieve a higher rank in history. Because both groups were asked to predict only which of two students would do better in history and not to make a numeric prediction, their tasks were virtually identical. Nevertheless, the student with the higher grade was selected 56% of the time by the grade group and only 49% of the time by the rank group (p *< .*05), indicating that the compatibility effect is present even in a choice task that does not require a quantitative response and is, therefore, unlikely to involve an adjustment of a numeric anchor. The strategy of anchoring and adjustment, however, probably contributes to the compatibility effect observed in numeric predictions.