The Normal Curve
Gregory K. Moffatt, Ph.D.
Mark Twain once said there are three kinds of lies, "Lies, damn lies, and statistics." In a way he was right. You can manipulate numbers to say about anything you want to say. For example, in the last presidential election, people in Bush's camp used the victory as "evidence of a conservative move" throughout the country. Kerry used the very same election results to argue that even though he lost, "more people voted for him (the losing candidate) than at any time in history." This, he said, was evidence that people were dissatisfied with Republicans.
Another likely interpretation of these data is that many of the people who voted Republican weren't voting for Bush. They were voting against Kerry. And in regard to Kerry's loss, it doesn't matter how many people voted for him, he lost by a huge margin, losing nearly every single county in the U.S. If it hadn't been for a few major cities, Kerry's loss would have been a landslide.
Even though statistics can be misused by those with personal agendas, statistics still has a place. The statistical tool I most often use is the normal curve. Also called the "bell curve" because of its shape, the normal curve allows researchers to hypothesize about what is normal and what is not. By this point in the article, the seven of you who are still reading are asking yourselves what this has to do with children. In a word - everything!
Everybody knows that no two children are the same. But while parents, psychologists, pediatricians, and teachers recognize this truth, the statistician is able to help them all answer a question they might not even know how to ask. The question is this: "How different can a child be in terms of behavior, development, and so forth, before we call his/her behavior 'abnormal'?" This is what the normal curve allows us to answer.
Let's consider a specific behavior - activity. Think of the normal curve like this - in the very middle are all those children who are normal in their level of activity. They play, run around, and sometimes have to be told more than once to sit still in some environments. They represent what most kids do. Moving to the left on the normal curve we begin to see children who are more active than those whose behavior ranks in the middle and moving to the right from the center on the curve we begin to see children who are less active than those children in the middle. There is a measurable point on the normal curve in both directions where we can mathematically say that the given behavior is beyond normal.
The normal curve is also symmetrical so as you move each direction, there is a mirror point on the other side of the middle. Therefore, any point A on the right of the curve represents exactly the same statistical probability (level of active behavior) as its mirror point B on the other side of the curve.
Now for the two of you still reading, what this means is that a child whose behavior is exceptionally reserved may represent exactly the same "odd-ness of behavior" as a child whose behavior is exceptionally active. However, we tend to notice the active child as "abnormal" because his behavior interrupts what we want to do. Most people won't recognize the quiet child as abnormal because he doesn't cause us any trouble and yet both children represent the same level (probability) of abnormality.
As I evaluate children on any behavior, I have the normal curve for that behavior in my head. I am concerned about both sides of the curve. More often than not, I receive calls from parents or teachers about a child's behavior when it falls only on one side of the curve. Sometimes I can happily report that the child's behavior is "normal" meaning it has not yet past that point on the curve where we call it abnormal, yet his behavior is to the left of what most children do. It is especially hard for parents to understand this if they have another child whose behavior is on the mirror point on the other side of the middle. The disparity between the behaviors of these two children is so great they feel certain something is wrong with the "active" child, yet the behavior of both children is equally normal/abnormal.
This range of normality allows me to distinguish between normal and abnormal and represents a critical distinction that prevents me as a clinician from diagnosing a child with a "mental illness" when in fact his behaviors may simply be different than most, but not clinically abnormal. Keeping this in mind might help you be patient with your normal, but active, child.