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Chapter 4: Problem 101

A doctor is studying cholesterol readings in his patients. After reviewing the cholesterol readings, he calls the patients with the highest cholesterol readings (the top \(5 \%\) of readings in his office) and asks them to come back to discuss cholesterol-lowering methods. When he tests these patients a second time, the average cholesterol readings tend to have gone down somewhat. Explain what statistical phenomenon might have been partly responsible for this lowering of the readings.

Short Answer

Expert verified
The statistical phenomenon responsible for the second reading's average cholesterol being lower is 'Regression to the Mean'. This concept posits that when an extreme value, like a high cholesterol reading, is measured again, it is likely to be closer to the average.

Step by step solution

01

Explaining Regression to the Mean

Regression to the Mean is a statistical concept that suggests if a variable is extreme the first time you measure it, it will be closer to the average the next time you measure it. This phenomenon occurs due to a random variation.
02

Applying the concept to the exercise

In this case, the doctor chose the patients with the highest cholesterol readings - who had extreme values. By inviting these patients for a second test, there is a good chance that their cholesterol readings will regress towards the average, appearing as though their cholesterol levels have decreased.
03

Other factors to consider

Note that it is possible that other factors could have given a real lowering of cholesterol levels between the two readings, like changes made by patients in response to the initial high readings. However, even in the absence of these factors, Regression to the Mean is expected to take place.

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