A persuasive bias leading people to neglect or underestimate the effect of known underlying population probabilities – the background information to judgemental situations – emphasizing instead specific information about the individual case of interest when deciding the likelihoods of outcomes.

For example, a night time hit-and-run traffic incident involves a taxi cab. Two taxi companies operate there: Green cabs and Blue cabs. The following information is at hand:

r	Of the cabs in the city 85%are Green and 15% are blue;
r	The incident was seen by one independent witness who identified the taxi as a Blue cab (testimony from the victim not available);
r	Assessment of court-ordered testing of witness reliability for vehicle colour identification under similar night time conditions concluded that correct identification occurred 80% of the time with failures 20%.

The prior probability is .15 because 15% of cabs in the city are Blue. The issue is whether in this individual case the cab involved was Blue.

What is the probability that the vehicle involved was Blue rather than Green?

The rate of correct identifications is .80 and the false identifications .20. The probability that the cab involved was Blue is .41. When asked to estimate such probabilities most people grossly overestimate the likelihood in the individual case and neglect the effect of the base rate.

Example two:

A person in her late thirties visits her doctor with concerns that a small lump she has discovered in her body may be cancerous.

Of people with the ‘profile’ of this patient – her age, family and medical history, and so forth – let’s say the base rate probability of cancer is known to be .01 (either malignant or benign). Of such category of patients who have cancer a cancer-screening test indicates cancer 80% of the time (sensitivity*). In such patients who do not have cancer this imaging device produces a false result 20% of the time (specificity†). The doctor orders the screening procedure and a positive result is returned, that is, the test indicates cancer.

For every 1000 cases of this sort let’s suppose that: 

r	approximately 10 have cancer and 990 do not;
r	of the latter group the screening procedure will give a cancer reading for approximately 198 and a “clean bill of health” for approximately 792;
r	of the 10 with cancer the test will indicate 8 have the condition but that 2 do not.

The prior probability is .01 because 1% of patients with this ‘profile’ have cancer. The issue is whether in this individual case the patient has cancer – should the patient be referred for a biopsy.

What is the probability that the patient has cancer rather than not?

The probability that this person has cancer is .039. Most people would judge the chance that the patient has cancer to be much higher than around 4 per cent. The base rate in this example is extreme at just one per cent such that the accuracy of the test is too low to overcome the low probability that cancer is present: the strength of the evidence is insufficient to substantially shift this very low base rate much.