There have been many studies published since the seminal work of cognitive psychologists Tversky and Kahneman , which showed that both lay people and trained health care professionals who are familiar with statistics use minimal heuristics to simplify situations. People often dichotomize actions, behaviours and treatments into polar extremes, such as 'safe/dangerous' or 'good/bad'. Thus, vitamins may be seen as good things, although we know that overdosing can kill. Likewise, many people, not just idealistic vegans and vegetarians, see meat as bad despite its nutritional benefits. Another important aspect of irrational or faulty risk appraisal is that judgements are made independent of dose, so for example oxygen is seen as good, despite the fact that 100% can be extremely harmful in some respiratory conditions or when given to premature babies. Lay populations also tend to put too much emphasis on anecdotal but familiar experiences, such as the apocryphal friend or relative who smoked 60 cigarettes a day and drank every night but still lived until their 90s without a day off work.
Communication about probabilities is made even more complicated by the fact that people prefer absolutes, for example 'without an operation death is certain' or 'this treatment is completely safe' .
Some of the common errors seen include a general failure to understand that probabilities in a set must include all possibilities; in other words, for a high-risk woman contemplating mammographic screening, the percentage chance of finding a cancer and the chance of a cancer being absent must add up to 100%. Few appreciate that probabilities of independent events must be multiplied not added. Conditional probability reasoning is another common confusion; the conditional probability of event X given event Y is not necessarily equal to the probability of event Y given X. The probability of breast cancer in a patient with BRCA1 or BRCA2 gene mutation is around 70%, but the probability that a woman with breast cancer also has the gene mutation is substantially lower.
Observations of lay populations' use of figures show that a term such as 50% may be used in rather non-numeric terms, indicating just general uncertainty, a lack of precision, something that may or may not happen.
Probabilities are often just too abstract for understanding and/or decisions. Few of us could say what 1:100,000, for example, means in relation to other common risk behaviours. In fact the risk for being murdered is 1:100,000, death playing soccer 1:50,000, and dying in a road accident over a 50-year period of driving 1:85. The 'risk' for getting three balls in the UK National Lottery is 1:11 , which is rather similar to the lifetime risk of getting breast cancer.
Although we have an understanding of all of these events and the ability to quote the statistics given, perceptions of personal vulnerability to them differ widely and may be complicated further by framing effects.