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Departments: SPC for the Real World

Davis Balestracci

Degrees of Freedom

Dare I say, “Who cares?”



As I’ve said many times in this column, even as a degreed statistician, I cringe at the legalized torture that passes for statistical training. (Yes, training. What would you rather your children or grandchildren have: sex “education” or sex “training”?) Many people who write to me need to make sure that I know--as if this gives their statistical pronouncements more credence--that he or she is a Shainin Red X Master and/or certified Black Belt (or Master Black Belt) and/or has such-and-such ASQ certification and/or is even an ASQ Fellow.

Oh do these folks love to teach statistics. Which brings me to the concept of “degrees of freedom.”

I once saw an article, a “simplified” explanation of degrees of freedom (DOF) written, the author explained, because people seem to have trouble grasping the concept. (They do.) The author used a Deming quote that made my palms sweat:

“Degrees of freedom is a term denoting the proper divisor (example, n-1 ) required under a 2d* moment of a sample drawn without replacement to give an unbiased estimate of a variance…. The number of degrees of freedom, as has been explained, is the divisor required under the 2d moment ( ns 2 ) to get an unbiased estimate of s 2 . Thus ns 2 /( n-1 ) is an unbiased estimate of s 2 , and n-1 is the number of degrees of freedom in the estimate.” (W. Edwards Deming, Some Theory of Sampling, Dover Publications, 1950, pages 352 and 541)

Well, now… that certainly “simplifies” it!

Yes, the concept is difficult, and at least statisticians should understand it. (It occasionally comes in handy.) But, really: Why does a practitioner need to clog his or her brain with this for everyday work?

As a well-respected statistical colleague recently wrote me:

“I get this question all the time (ANOVA tables in particular seem to terrorize people)... but I wish people were asking better questions about the problem they’re trying to understand/solve, the quality of the data they’re collecting/crunching, and what on earth they’re actually going to do with the results and their conclusions. In a well-meaning attempt not to turn away any statistical questions, my own painful attempts to explain DOF have only served to distract the people who are asking from what they really should be thinking about.”

From an algebraic standpoint, at one time it was useful to know how DOF are calculated: You needed that number and a table of t- or F-values to manually turn the crank on statistical tests. But in the age of computers, no one has to do that anymore.


Is there a thing called DOF? Yes.

Is it important? People think it’s important, but in the big scheme of things, there are far more important issues in data collection and interpretation.

Is it hard to understand? Absolutely. Over the years, I’ve explained it a zillion different ways to people, and 99.9 percent of them still don’t really understand.

Is it important to understand it? I’d rather people understood that the quality of their data is far more important than the quantity of it.


Here’s an odd segue that gives me a chance to make a point, celebrate the opening of baseball season (as I write this on March 5), give statisticians and our ilk a good ribbing, and offer those of you who are really mad at me a chance to get your sense of humor back. Politicians have long been guilty of creating self-serving jargon--and to this I would add statistical “trainers,” which can sometimes border on Stengelese. Let me explain.

In 1958, Casey Stengel, the New York Yankees’ manager at the time, was in Washington, D.C. to testify before a special House subcommittee, which was studying monopoly power regarding baseball’s antitrust exemption. Asked if his team would keep on winning, he said:

“Well, I will tell you I got a little concerned yesterday in the first three innings when I saw the three players I had gotten rid of, and I said when I lost nine what am I going to do and when I had a couple of my players I thought so great of that did not do so good up to the sixth inning I was more confused but I finally had to go and call on a young man in Baltimore that we don’t own and the Yankees don’t own him, and he is doing pretty good, and I would actually have to tell you that I think we are more like a Greta Garbo-type now from success.”

That’s one sentence, 121 words, and just a fraction of Stengel’s 45-minute discourse ( www.baseball-almanac.com/quotes/casey_stengel_senate_testimony.shtml). It’s an absolute hoot, and Mickey Mantle’s one-sentence testimony at the end is priceless.

So how about we stop the “training” and do a little more “education”?

About the author
Davis Balestracci is a member of the American Society for Quality and past chair of its statistics division. He would love to wake up your conferences with his dynamic style and unique, entertaining insights into the places where process, statistics, and quality meet. Visit his web site at www.dbharmony.com.