PSA has been in the news lately as two studies have been completed about the benefits (or lack thereof) of PSA screening (recent articles in NEJM). These studies talk about what happens on average – how many lives are saved (in one study 7 per 10,000). Economic implications come with these results, although with these studies, there were no definitive conclusions.
The problem is an individual is concerned what happens to him (or her for cases other than prostate) much more than what happens on average. So to be told on average some bad thing shouldn’t have happened – it’s a rare event – is not very helpful.
There are similar currents in lab statistics. In GUM (Guide to the expression of Uncertainty in Measurement), one is informed about the location of 95% of the results. But if you have a result that has a large error, then GUM for you is not helpful (large errors are not considered by GUM). Similar arguments apply to six sigma.
Moreover, one could perhaps say the same thing about quality control – and this is in the works with equivalent quality control. The thinking is why run all that quality control when it is rarely out.
What happens on average is important but so are the large deviations that are rare. All results are important – the average and each individual result.