Tim Harford:

The practical implications of misplaced confidence when dealing with statistical evidence are obvious and worrying
A little two-part test for you. Imagine you’re a doctor, considering whether to recommend a particular kind of cancer screening, “A”. You discover that this form of screening improves five-year survival rates from 68 per cent to 99 per cent. (The five-year survival rate is the proportion of patients alive five years after the cancer was discovered.) The question is: does the screening test “A” save lives?
Part two: now you consider an alternative screening test, “B”. You discover that test “B” reduces cancer deaths from two per 1,000 people to 1.6 per 1,000 people. So: does screening test “B” save lives?