The Disastrous Effects of Forgetting that Correlation is not Causation

At Anovisions, we look at relationships in data all the time. One constant concern is how we describe those relationships. The fact that a variable "predicts" an "outcome" variable in a regression reflects only how we set up the regression. We could swap the predictor and the outcome variable in the equation and view the same relationship from the other end, only this time the original "outcome" variable would be the "predictor." The two terms are mathematical in nature and they do not reflect cause and effect.

Cause and effect is extremely hard to prove. All we can do is identify that relationships exist, at least initially. A long way down the road from an initial study, after scientific findings from all sorts of other experiments have validated our efforts, after scientific theory has provided a reasonable model for understanding the relationships in question, after the same findings have been repeated in a large variety of populations—only then can we say, "This causes that." But the smartest among us will continue to keep the question open, assuming nothing.

 For more information about how we can help interpret your results, visit us at our website, www.anovisions.com.

Ode to Those Who Think Sideways

For Dr. William Jefferys

Shall I introduce you to Bayes?

His inferences always amaze.

It's not what you think—

without a stiff drink—

But it will end your frequentist phase.

No, really, it is what you think

—unless to you orange is pink.

For without a good prior

You'll never get hired

And maybe should find a good shrink.

If Bayesian stats make you cuss,

Or your Bayesian book you did toss,

Please don't give up hope:

If you really can't cope,

Just try this new book by Laplace.

I got data! . . . Now what?

So you're a small business, maybe with an online store. You made a beautiful website with Google sites or another hosting service like GoDaddy and tied it to Google Analytics (or Omniture, WebTrends, CoreMetrics, or VisualSciences), because that's what everybody does. Now you have all kinds of charts and graphs and maps and even this thing called a "site overlay." These charts tell you about the behavior and location of the people who come to your website. The charts and numbers might even reveal seasonal trends in certain activities or products on your site—except you have no clue how to interpret the data.


Lets say you are getting thousands of hits on your website but you don't know what that means for sales. Is there a correlation? Is the web traffic causing the sale or is the sale causing the web traffic? If you were to contract us at Anovisions we might look at you data and run a Pearson's (or Spearman's) correlation  analysis followed by a regression analysis that would tell us that web traffic is a driver of sales and it makes sense to invest more in web advertising. Or not. This inexpensive service pays for itself very quickly as you implement the step-by-step plan we provide for you.

Check out www.anovisions.com or email sheila@anovisions.com to learn more.

Lies, damn lies, and statistics

How much can you trust the studies that you hear about in the news every day? If somebody says, "A new study shows that weight gain causes earlier deaths," should you believe it?

Here are a few rules of thumb to follow when deciding what to believe:

1. If the word "cause" is anywhere in the sentence, delete it from your memory. It is very hard to prove cause and effect. As a matter of fact, weight gain does not "cause" earlier death. The study that hit the presses years ago and made us all afraid has been debunked because of some interesting choices in the study design. I won't go into details: This is Practical Stats, after all.
2. If the reporter (or whoever) uses the words "associated" or "correlated," and then goes on to conclude that you should behave differently, scoff and ignore the story. What many people who repeat study findings simply don't know (or acknowledge) is that weight gain and early death, for instance, might both be caused by a third phenomenon, such as exposure to cheap unhealthy food. It may not be the weight gain that is "causing" early death, but rather the chemical processes set off by certain types of diets. That chemical process may (may) cause both weight gain and early death. So don't rush out to go on a diet if you gain a few pounds before you talk to your doctor about it. 
3. Remember that all studies are biased by the cultures in which they are produced. For example, Americans are committed as a nation to early independence for children and to a certain style of education. So when you hear someone say that "enrolling children in day care centers early is linked to better adaptation to school" you might conclude that you need to enroll your children right away in a day care center so they will behave well in school. But let's think this through. First, that little phrase "is linked to" implies that the one (day care) causes the other (better behavior in school). And second, is better behavior in school the end game for your children? Behind the entire "finding" is the hidden implication that behaving well in school is the best possible thing, that behaving well in school predicts that your children will lead happy lives (or do we prefer "successful lives"?). Note that school is nothing like life, where you are exposed to people of various ages and must get along with them every day, where you have the choice of working in a lab or at home with your computer, where you can make money leading mountain climbing expeditions or fixing what's broke, where fewer and fewer of us spend our days in the factories after which the American school system was modeled, and (this is the important bit) where your skills at being in a family matter more than anything else. Ask the question, "Has anybody studied the link between early time at home and happiness in family life in adulthood?" Look for the cultural bias when you hear about a study. Ask yourself what your goals are and then figure out whether the hidden cultural bias in a finding applies to you. Then follow your heart, not the numbers, and do the right thing for yourself and those you love.