Thinking and Deciding

378 QUANTITATIVE JUDGMENT
Kahneman and Tversky’s subjects), the worse the predictor is. In the extreme, if the
subject were in the ninetieth percentile on shoe size, that would probably have no
relation at all to grades, and your best guess would be that the student would have a
GPA at the class mean of 2.5. Sense of humor is probably as useless as shoe size in its
power to predict college GPA, so your best guess might be a little over 50% (or a little
under, if you think that humor gets in the way of good grades). Mental concentration
is probably a better predictor than sense of humor but not as good a predictor as the
percentile rank in GPA itself, so the best prediction should be somewhere between
2.5 and 3.5.
To see why we should regress toward the mean, let us suppose a student scores
at the ninetieth percentile on the mental concentration test, and let us ask whether
we would expect the student to obtain a GPA of 3.5 (which, let us assume, is the
ninetieth percentile for GPA), or higher, or lower. Mental concentration is not a perfect
predictor of grades, so some of the students who score in the ninetieth percentile
on the mental concentration test will do better than a GPA of 3.5, and some will do
worse. More students will do worse than will do better, however, because there are
more students with a GPA below 3.5 than there are with a GPA above it. There are,
for example, more students with a GPA of 3.4 than with a GPA of 3.6, because 3.4 is
closer to the mean GPA. It is therefore more likely that a randomly selected student
will have a GPA of 3.4 and a mental concentration score at the ninetieth percentile
than a GPA of 3.6 and a mental concentration score at the ninetieth percentile. The
same argument applies to GPAs of 3.3 and 3.7, 3.2 and 3.8, and so on. If we predict
that students in the ninetieth percentile in mental concentration will have a GPA of
3.5, we are, in effect, ignoring the prior probability of their GPAs being above or
below 3.5 (as discussed in Chapter 6). We can think of the mental concentration
score as a datum, from which we must infer the probability of various hypotheses
about the student’s GPA. The hypotheses below 3.5 are more likely at the outset, so
they remain more likely after the datum is obtained. Nonregressiveness may be
overcome by thinking about missing data. Ganzach and Krantz (1991) gave subjects
experience at predicting the college grade-point average (COL) from descriptions
that included ACH and SAT (as described earlier in this chapter). When subjects
then made predictions on the basis of single predictor (SAT or ACH), they regressed
these predictions toward the mean, unlike other subjects who did not have the experience
of using more than one predictor. It seems that these experienced subjects
thought about the missing predictors and assumed moderate values for them. This
heuristic will not always work, however, because it is not always possible to know
what are the missing predictors.
Another example of nonregressiveness, failure to regress enough toward the mean,
is prediction of completion times (Buehler, Griffin, and Ross, 1994). Projects of all
sorts, from massive works of construction to students’ papers to professors’ textbooks,
are rarely completed in the amount of time originally estimated. Cost overruns
are much more common than underruns (to the point where my spelling checker
thinks that only the former is an English word). In 1957, for example, the Sydney
(Australia) Opera House was predicted to cost $17 million and to be completed in