EXAMPLE 6.25 Cell Phones and Brain Cancer
Might the radiation from cell phones be harmful to users? Many studies have found little or no connection between using cell phones and various illnesses. Here is part of a news account of one study:
A hospital study that compared brain cancer patients and a similar group without brain cancer found no statistically signifcant association between cell phone use and a group of brain cancers known as gliomas. But when 20 types of glioma were considered separately, an association was found between phone use and one rare form. Puzzlingly, however, this risk appeared to decrease rather than increase with greater mobile phone use.21
Think for a moment: Suppose that the 20 null hypotheses for these 20 sig-nifcance tests are all true. Then each test has a 5% chance of being signifcant at the 5% level. That’s what means—results this extreme occur only 5% of the time just by chance when the null hypothesis is true. Because 5% is 1/20, we expect about one of 20 tests to give a signifcant result just by chance. Running one test and reaching the level is reasonably good evidence that you have found something; running 20 tests and reaching that level only once is not.