Regression Toward the Mean

Regression Toward the Mean is one of the most common types of Statistical Bullshit in industry.  And, as the title quotation insinuates, some consultants have made an entire career swindling money from organizations through manipulating this statistical phenomenon.  If you are currently in practice, or ever plan to be, read on to discover whether you are currently being swindled out of thousands – or possibly millions!

Businesses are always on a time-series.  That is, most organizations are not worried about the profit that they turned today, but rather the profit that they will turn tomorrow.  For this reason, many types of statistics and methodologies applied in business are meant to analyze longitudinal trends in order to predict future results.

Let’s take perhaps the simplest time-series design: a single variable measured on multiple occasions.  In this example, let’s say that we are looking at overall company revenue in millions.

Month	Revenue
January	10.5
February	10
March	11
April	12.5
May	10.5
June	10
July	12
August	11
September	11
October	5

It seems that the average company revenue over the month was $11 million, but a severe drop occurred in October.  What would you do if your company revenue looked something like this?

Most anyone would say panic and take extreme measures – and that is what most companies do.  A company may replace the CEO, lay-off a large number of workers, or immediately implement a new corporate strategy.  Let’s say that a company does all three for our example, and the result looks like this:

Success!  The new CEO is a genius!  The lay-offs worked!  And the new corporate strategy is brilliant!  Right?  Well, maybe not.

The Regression Toward the Mean phenonmemon suggests that a time-series dataset will revert back to its average after an extreme value.  In other words, when an extreme high- or low-value occurs, it is much more difficult to get any more extreme than it is to revert back to the average.  So, in this instance, it is fully possible that the company’s actions successfully caused revenue to revert back to more normal values; however, it is perhaps just as likely that the revenue simply regressed back toward the mean naturally.  So, the new changes (and money spent!) may have actually done very little or even nothing at all…but you can always be sure that the new CEO will take credit for it.

Let’s discuss another common example of Regression Toward the Mean in business.  Imagine you are a floor manager at a factory, and your monthly number of dangerous incidents looks something like this.

Week	Incidents
January	5
February	4
March	8
April	6
May	6
June	4
July	2
August	8
September	5
October	20

Wow!  Quite the spike in incidents!  So, what do you do?  Of course, you’d request for your CEO to bring in a safety expert to reduce the number of dangerous incidents, and I can guarantee that the results will look something like this:

Another success!  The safety expert saved lives!  You are brilliant!  As you guessed, however, this may not be the case.

Once again, a Regression Toward the Mean effect may have occurred, and the number of safety incidents naturally reverted back to an average level.  The money spent on the safety expert could have been used for other more fruitful purposes, but you can nevertheless take credit for saving your coworker’s lives.

Despite these two examples (and many many more that could be provided), not all instances of extreme values can be cured by waiting for the values to revert to more typical figures.  Sometimes, an effect is actually occurring, and an intervention is truly needed to fix a problem.  Without it, things could possibly get even worse.

So, what should you do when extreme values occur?  Perform an intervention?  Wait it out?  In academia, the answer is simple.  Most researchers have the luxury of collecting data from a control group that does not receive the intervention, and then comparing the data after a sufficient amount of time has passed.  If the intervention group resulted in better outcomes than the control group, then the intervention was indeed a success.  If the two groups have roughly equal outcomes, then the intervention had no effect.

Businesses do not have such luxuries.  Decisions need to be made quickly and correctly – or else someone could lose their job (or their life!).  For this reason, it is often common practice to go ahead and perform the intervention.  If the values return to normal, then you seem like a genius.  If they do not, then at least you tried.  On the other hand, if you do nothing and the values return to normal, then you seem like a genius again.  If they do not return to normal, however, then it seems like you ignored the severity of the issues.  The table below summarizes this issue:

	Values Remain Extreme	Values Return to Normal
Do Nothing	You Ignored the Issue	You Succeeded!
Do Something	You Tried	You Succeeded!

Long story short, you should probably make an attempt to fix the issue, although it may simply be Statistical Bullshit in the end.

Before concluding, one last question should be answered about Regression Toward the mean: How exactly can people make a career on it?

Well, imagine that you are a safety consultant, and you receive several consulting offers at once.  You look at the companies, and they all seem to have a relatively stable number of incidents; however, you notice one that is going through a period of elevated incidents.   Now that you know about Regression Toward the Mean, you know that you should take this company’s offer.  Not only will they (probably) be willing to spend lots of money, but you (probably) need to do very little to reduce the incident rate.  Even if your safety suggestions are bogus, you can still appear to be a competent safety consultant.  Although it may sound crazy, I think you would be surprised how often this occurs in the real-world.

That is all for Regression Toward the Mean.  Do you have your own Regression Toward the Mean story?  Maybe a question?  Feel free to email me at MHoward@SouthAlabama.edu.  Until next time, watch out for Statistical Bullshit!