Critical Thinking About Statistics

Recently one of us noted a newspaper account saying that 70% of the depressed people in the United States were undiagnosed. That figure sounds very troubling until we step back and say, “Wait a minute! If they are undiagnosed, how do we know they exist?” The very number 70% sounds alarming, and it is probably meant to be by the writer of the article. But the fact remains that the number means nothing because it presupposes a given number of depressed people in the U.S., a number that may be wrong. Suppose I tell you that 30 students came into a college counseling center because they were depressed. Suppose I also tell you, “The bad thing is that there’s another 70 students who are depressed but who are walking around undiagnosed.” You would probably be ready to dispense anti-depressants to the entire student body! But note that the 70 figure means I believe there are a total of 100 depressed students on campus. How do I know that? In fact, all I know for sure is that there are 30. But if I want you to believe that depression is rampant on the campus, I will tell you 70 of our students remain undiagnosed.

Clearly, we need to be critical about how we interpret and react to information from sources we are not confident about trusting. As is sometimes said, “statistics can lie.” However, statistics and data are not the problem; the way data are presented is the problem.

I read the other day that 20% (1 in 5) of Americans suffer some type of mental illness. You could find a number like that upsetting, especially if you are struggling with anxiety issues over some personal crisis, but don’t feel you are “mentally ill.” There are about 250 million adult Americans. If 20% are mentally ill to some degree, that’s 50 million people. The 1 in 5 figure has been around for many years, and it may be close to accurate depending on how “mental illness” is defined, the sample on which the number is based (is it representative of the population?), and what sort of protocol was followed to arrive at the number. Before you passively accept such statistics, however, you owe it to yourself to devote some critical thinking to where it came from. Obviously, 250 million people were not assessed, so who decided on the 1 in 5?

The piece I read also claimed that of the 1 in 5 who were mentally ill, 1 in 5 of them were not seeking help for their illness. Now here’s my problem with that comment: if 20% of those who are mentally ill are not seeking help, how can we possibly know they exist? Think about these figures and the assumptions being made. Suppose we have 1,000 people. If 1 in 5 (20%) are mentally ill, that’s 200 people. Now, of those 200 people, we’re told that 1 in 5 of them (20%) don’t seek help for their mental illness. That means 40 people (20% of 200) are mentally ill but walking around untreated. Says who? Did someone go around asking those original 1,000 people (1) “Are you mentally ill?” and (2) “Are you seeking help?” I doubt it, but how else would we know how many are mentally ill and not seeking treatment?

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