No matter who you are or how long it has been since you've had a statistics class,
if you have been told anything about correlation, it is probably this:
Correlation does not equal causation.
Just because two things are related
does not necessarily mean that one is causing the other.
Let's find out why that is.
In order to establish that one variable is causing changes in another variable you have to make sure that there are no other
variables that could be causing the change.
You create an experimental group and a control group that are identical
except that the experimental group gets a drug or a treatment that the control group does not.
If, after the intervention, the experimental group
has changed the only difference between the two groups was the treatment
So, the treatment must be causing the change.
This is an experimental design. In an experimental design the researcher manipulates the x-variable,
who gets the drug,
and measures what happens to the y-variable.
This allows the demonstration of causality.
In a correlational design
you can't establish causality
because the variables are observed as they occur naturally.
No attempt is made to manipulate or control for either one,
however, correlational designs allow us to test for things that we never could using an experimental design.
Imagine you wanted to test a research question about whether caffeine causes jitters.
You could randomly select a group of participants,
randomly divide them into two groups
(experimental and control), and then give the experimental group coffee while the control group gets
decaffeinated coffee
Then you could measure their responses
If the caffeine group was more nervous and twitchy you might conclude that caffeine causes jitters.
What kind of research would this be?
This is an experimental design, and it could be ethically tested
But here's a different experiment. You want to study whether smoking causes cancer.
You randomly select a group of participants, and then you randomly assign some of them to smoke a pack a day,
others to smoke five cigarettes a day, and others to not smoke at all.
Then you follow them for 20 years to see how many developed lung cancer.
Obviously this would not be an ethical experiment, not one you could ever get past an IRB.
On the other hand, you could do
a correlational study.
You could examine rates of lung cancer among people who have already chosen to smoke, and
then compare them to the rates of lung cancer among people who do not smoke.
You did not assign people to be in the smoking group. You simply measured them as you found them.
You found a correlation between smoking and lung cancer, something you would not have been able to do experimentally.
But you could not conclude that smoking causes lung cancer
because you did not control forvariables other than smoking that could possibly explain why someone developed cancer.
For example, we have not considered the direction of causality.
Even if the variables were causally related,
correlation says nothing about which variable is affecting the other.
Perhaps people who have a predisposition to lung cancer are also more likely to become addicted when they first try cigarettes.
Or we know that rates of exercise
correlate with rates of obesity such that when people are more obese they exercise less.
But perhaps it is the obesity that makes it more difficult for them to exercise,
or perhaps it is a circular causation where a lack of
exercise leads to obesity, which then reduces the likelihood to exercise, which then leads to greater obesity.
We know that obesity is correlated with drinking diet soda.
People who are overweight are more likely to drink diet soda.
People who are thin are less likely to drink diet soda. It doesn't mean that the soda is causing people to be overweight.
Perhaps people who are already overweight are more likely to feel the need to cut back on calories by drinking diet soda.
People who are naturally thin don't feel that compulsion. All of this leads us to the warning that
correlation does not imply causation.
When you see a correlation, no matter how strong the relationship is,
do not assume because and effect relationship between the variables.
It is important to add, however, that this does not mean that one variable is not causing the other either.
We just need more information.
There is the possibility of the third variable gremlin.
The correlation between two variables may be caused by another,
possibly unmodeled variable.
Unmodeled means unmeasured.
For example, the ownership of HD television sets correlates with increased deaths from coronary disease.
The third variable may be a sedentary
lifestyle that explains why someone purchases the HD television set, why they spend so much time on the couch watching television,
why they spend so little time exercising, and why they developed coronary disease.
Another well known correlation is that
as the number of bars in a community increases, there is also an increase in the number of churches.
Is that because in a town with all those sinners you need more churches?
Or is that because all those religious people can just drive you to drink?
The answer is the third variable gremlin. Both are driven by
population increase. As the town gets larger, you need more of both churches and bars.
And then there is the phenomenon of the spurious correlation.
There may be no relationship at all between the variables even though they correlate strongly.
The correlation may be just a mathematical artifact.
Tyler Vegan has collected some wonderful examples of spurious correlations on his website and his book Spurious Correlations.
For instance, the age of Miss America contestants correlates with murders by steam and hot objects.
The divorce rate in Maine correlates with the U.S. per capita consumption of margarine.
The number of honey producing bee colonies in the United States
correlates with juvenile arrests for marijuana possession.
None of these relationships are causal,
but if you have enough data in a data set some variables are going to correlate
even though they are not related, and the correlation doesn't mean a thing.
As this exchange from XKCD Comics demonstrates,
inferring causation from correlation can happen very easily.
He says, "I used to think that correlation implied causation. Then I took a statistics class, and now I don't."
And she says, "Sounds like the class helped."
And he says, "Well, maybe."
The correlation between taking the class and his change of mind does not imply causation.
Although it probably was.
You want to be
particularly careful of spurious correlations when they are used to promote an agenda.
For instance,
when the good people of Missouri wanted to help end the abusive puppy mills that flourish in our state.,
an initiative called Prop B was placed on the ballot.
The proposition set minimum standards for the care of dogs
such as requiring adequate food, water, shelter, and not being stacked in wire cages were the dogs below
were getting pooped on by the dog above. Now who could oppose
humane care for animals, right?
Well in response the group of puppy mill owners who opposed the legislation,
because it would cut into profits if they were forced to care for dogs humanely, formed the wildly miss named
Alliance for Truth and
created this flyer. In it they offer some startling spurious correlations. See if you can spot their mistakes.
For example, they noted that Florida passed a law to stop the cruel and inhumane practice of crating pigs
followed by the statement that,
"Florida now has one of the highest unemployment rates in the country."
Are we to believe that Florida's unemployment rate was caused by pig farmers unleashing their pigs?
Next, they cited a law protecting chickens in California that had yet to go into effect and stated,
"California is facing bankruptcy and their foreclosure rate is one of the highest in the country."
This spurious correlation is
particularly pathetic because in addition to try to suggest that home foreclosures were caused by chicken laws,
The Alliance for Truth was utterly ignorant of the basic law of logic that a cause must come before the effect.
They cannot blame existing problems on causes that have not yet happened,
And by the way, neither of those claims about Florida or California were factually correct either.
I spot another correlation here.
"Increased support for puppy mills correlates with an increased use of spurious correlations."
Perhaps both are linked to a third variable something about veracity.
There might also be some kind of correlation that when a group names themselves to insist that they are telling the truth,
they probably are not.
Honest people don't have to tell you that they are honest. You know because they just act honestly.
If you love dogs, please help care for them by adopting from a shelter.
Dogs for sale in pet stores come from puppy mills.
Please, adopt, don't shop.