The Punishment Illusion 3: Statistics


The Punishment Illusion 3: Statistics
Are you really assessing what is effective?

In this series on punishment I have talked about the behavioral research on punishment and long term studies on spanking. In this post we discuss the last of three lines of research on punishment: statistics.

Don't worry. You won't have to read eye-glazing percentages about punishment. That is not to say there are not really interesting statistics on punishment (there are). Instead, the science of statistics itself has discovered a phenomenon that can tell us something very important about punishment: regression to the mean.


Stats geeks love regression to the mean because once you really get it, you start seeing it everywhere. It has a lot of explanatory power.

Regression to the mean starts with the idea that there is a mean, or average, around which things cluster. It is often represented by a line down the middle of a bell curve (see example). Things that fall in the middle of the bell curve, near the line, happen more often. Things that happen less often are at the tails (where the little guy is writing).

Let's apply this concept to a specific child behavior. For example, imagine (in a perfect world) that your child remembers to say "please" an average of five times a day. That would make the mean of that behavior five.

However, even though the mean is five, the child doesn't do it exactly five times every day. Usually it is a little higher or a little lower than the mean. Occasionally, at random, it is a lot higher or lower (in the tails of the bell curve). On one day your child may say please ten times and on another day the child may completely forget it.

These kinds of variations in behavior happen all the time regardless of what the parent does. When random variations occur, they usually return to normal (the mean) quickly. That is what "regression to the mean" is: the tendency for exceptionally high or low rates of behavior to go back to normal right away.

So the day after your child remembered to say please ten times, he or she is likely to go back to five. The day after the child totally forgot, he or she is likely to go back to five, at random.

Here is where this can trip you up as a parent. If you are really hyper-focused on a behavior (getting your child to learn to say "please" every time), you are going to have to be very sensitive to every little increase and decrease in pleases, even the random ones. You will try to find reasons why it changed. More than likely, you will find reasons other than "it happened randomly." In other words, you can attribute the behavior change to something you did, even if it had nothing to do with the change.

This is where punishment can seem effective even when it is not. Even stranger, rewards can seem ineffective, even if they are working.

Here is how it works. Lets say you punish your child on the day when he or she forgot to say please, by giving your child a harsh lecture. The very next day, the behavior regresses to the mean, which means it increases. You'll think that the lecturing must have really got through to your child, when it probably didn't.

Conversely, lets say you reward your child on the day he or she says it many times. It will seem ineffective because the next day, he or she will be back to the mean again, which is lower.

You'll start to believe rewards are wishy-washy because your child is now doing worse. You'll think harsh lectures are effective because she always does better. This quirk of statistics can mislead parents, if they are paying especially close day-by-day attention to behavior.

My advice: focus on behavior change over longer periods of time, rather than day to day. Assess change over weeks, not days. Use rewards frequently, punishments rarely.

Here is a wonderful video that explains this concept in detail.

This article was originally published at Reprinted with permission.

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Article contributed by
Advanced Member

Dr. Ronald Crouch


"It's never too late to have a happy childhood."  -Tom Robbins

Location: Kailua, HI
Credentials: PhD
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