Probably positive

Understanding the stats

Diagram showing results of cancer screening

‘Big Picture: Number Crunching’ (2013)

Q: My doctor has told me that if I get a ‘positive’ result in a medical test, it doesn’t definitely mean that I have the disease. Why not?

A: No test is 100 per cent accurate. Not all positive test results mean that someone has a particular condition; not all negative results mean that a disease is absent. Positive and negative test results can be described as true or false, depending on whether they classify correctly the person tested.

The diagram shows the outcome of breast screening by an X-ray technique called mammography. For every 1,000 women screened, 41 have a positive result and are called back for more tests. Of these, 8 women will be found to have cancer, and 33 will be found not to. So, an initial positive result means just a 20 per cent chance of cancer. Overall, 966.8 (8 + 958.8) women per 1,000 screened will get a ‘true’ result, making this technique 97 per cent accurate.

Further reading

About this resource

This resource was first published in ‘Number Crunching’ in June 2013.

Statistics and maths, Medicine, Health, infection and disease
Number Crunching
Education levels:
16–19, Continuing professional development