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264 Biases in probability assessment
would conclude that there was. Yet if we calculate the conditional
probabilities we find:
p(Illness present|symptom present) = 12/18 = 2/3
p(Illness present|symptom absent) = 6/9 = 2/3
which shows that the presence or absence of the symptom has no effect
on the probability of having the illness. This study, and others (e.g.
Smedslund 17 ), suggested that people only consider the frequency of
cases where both symptom and disease are present. In other words, they
only consider the number in the top left-hand corner cell of the above
table. The large value in this cell creates the illusion of a relationship.
Data in the other cells is ignored even though it is crucial to any accurate
assessment of the strength of the relationship.
Test your judgment: answer to question 15
Q15. There is no evidence that the cost of the computers is associated
with their chances of needing repair in the first year.
The probability that the cheap brand will require repair in the
first year is 120/144 = 5/6 while the probability for the expensive
brand is 40/48 which also equals 5/6.
While people often see non-existent association between variables, they
can also miss associations that do exist, even when these associations are
strong. This is often because they have no prior expectation that the two
variables will be related. 18
Is human probability judgment really so poor?
The above discussion may give the impression that human judgments
about probability are fundamentally flawed, but is this really the case?
Over the last decade much of the work on heuristics and biases has been
questioned. Most criticisms have centered on the fact that the research has
largely been based on inexperienced decision makers carrying out artificial
tasks in psychological laboratories, rather than real-world decision
makers making real decisions. We review these arguments next.