The study in which this statistical problem occurred:

In the Journal of American Cardiology (JACC), which is the official journal for the society of board certified cardiologists, there was an article with a major statistical error. This involved a study with the title of “Increased Myocardial Perfusion at Rest and Diminished Perfusion Reserve in Patients With Angiographic Normal Coronary Arteries” (Geltman EM, et al. JACC 1990; 16:586-95). The article illustrates a fundamental flaw in the use of statistics.

An Analogy regarding
this statistical problem

A way to make this fundamental statistical error more understandable is to note the following analogy.  A study examines two groups of people, one group from north of town (northerners) and one group south of town (southerners). The northerners were then divided into the tall northerners and the short northerners on the basis of height. The researchers then inappropriately compared the tall northerner group to the entire undivided southerner group. 

Naturally, the tall northern subgroup who were selected on the basis of being tall would on the average be taller than the undivided total southern group. Similarly, the tall northerner group would also be likely to have a statistically greater value for a foot to waist measurement than the average value for the undivided southerner group. However, one could not say that because of this comparison, that there is a unique subgroup that exists in the northerners of tall people that doesn’t exist in the southerner group. This is fundamental error that the authors of this study made. It was perhaps less obvious because the measurements they used involved PET scanners and cardiac measurements, but that doesn’t make this inappropriate statistical analysis any less wrong than it is for the example given of people divided on the basis of height.