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COMMON MISTEAKS MISTAKES IN USING STATISTICS: Spotting and Avoiding Them

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Misunderstandings arising from lack of clarity about the reference category

Gigerenzer et al1 give the following example:

A physician may tell a patient that if he takes a certain antidepressant, his chance of developing a sexual problem is 30% to 50%. The patient may interpret that as saying that in 30% to 50% of the occasions on which he wishes to have sex, he will have a problem. But the physician means that 30 to 50% of his patients who take the medication develop a sexual problem.

The physician has intended one reference category (patients who take the medication) for the percent, but the patient has heard another (occasions on which he wishes to have sex). The physician's phrasing has in fact "led" the patient to this interpretation, by stating the risk in terms of the individual patient ("his chance"), rather than in terms of the category of all patients who take the medication. 

Notes:

1.  Gerd Gigerenzer, Wolfgang Gaissmaier, Elke Kurz-Milcke, Lisa M. Schwartz, Steven Woloshin (2007), "Helping Doctors and Patients Make Sense of Health Statistics," 
Psychological Science in the Public Interest, vo. 8, No. 2, pp. 53 - 96. Download from http://www.psychologicalscience.org/journals/index.cfm?journal=pspi&content=pspi/8_2