# The normal distribution, multiple comparisons and risks of false alarm

I often think to myself that if we could effectively teach one single concept to all citizens, get them to really understand it and apply it to life we would all be better off. It has relevance for so many facets of our public and private decision making; ofttimes ignorance of this concept makes for a dismal political or personal outcome.
Brazillion Thoughts has an English-language translation of a post originally written by Karl at Ecce Medicus.

Many times, in my practice, I am required to explain some statistical concepts to my patients in order to make them avoid some frequent pitfalls. The most common concept I explain is what is "normal" in lab exams. Let's suppose someone invents a new lab test to measure the glucose in the blood. How would we determine what are the normal values for this test?

• David says:

an interesting post, but - wow !! - did the writer ever pick the wrong example. Way too complex for the lesson at hand.
Blood glucose is both skewed and kurtotic. There are far more asymptomatic people walking around with glucose +3 SD above the mean (undiagnosed diabetics) than there are -3 SD (which is a glucose level that would render you nearly comatose). In the case of blood glucose, "normal" is defined not by the statistical parameters of the population but by a cutoff value that "best separates" healthy from diabetic. I'm using the term "best separates" in the Receiver-Operator sense of providing the most clinically appropriate prediction that further testing is required.

• Funky Fresh says:

UUUUUUUUUUUUUUUUUUUUUGH...not the maths, Monkey. They make my brain hurt.

• becca says:

Wait, you mean doctors don't do corrections for multiple tests?
Damn. Shoulda gone to med schoool. Such an easier way to make a living.

• Hope says:

His logic only works if all of the tests are statistically independent. Are there really a “brazillion” independent tests that you can do for a given disease based on a blood sample?

• becca says:

Hope- only if the "disease" is pregnancy

• Isabel says: