Confidence intervals are the most valuable statistical tools available to decision makers, and according a recent Six Sigma IQ article written by Dr. Andrew Sleeper of Successful Statistics, they are not being used as frequently as they should. Sleeper’s article Have Confidence in Your Statistical Analysis!: Learning How to Use Confidence Intervals does an excellent job illustrating why point estimates are useless for making decisions, and how to determine what is the best confidence interval to use. Is it 90%, 95%, or some other value?
The article does not discuss how to calculate confidence intervals, since widely available software (for example, Palisade’s @RISK and StatTools) automates this task. Formulas and calculation methods are well documented in many books.
One example that Dr. Sleeper uses to illustrate his point: Suppose the CEO has decreed that we need CPK to exceed 1.50 for all critical characteristics. If I measure a sample of parts and announce “CPK is 1.63,” this sounds like good news. But then you ask a really good question: “How large is the sample size?” If you discover the sample size was only three, should you be worried? What if you discover the sample size was 300?
We have to make a decision about the capability of the population, but once again, the point estimate is not enough information by itself to make this decision. It is another useless number.
Instead, suppose I said “I am 95 percent confident that CPK is at least 1.52.” Or I could say “I am 97 percent confident that CPK is at least 1.50.” Either of these would be a true statement. And since sample size is used to make these calculations, they provide all information necessary to make the business decision.
These one-sided confidence intervals are often called lower confidence bounds, because the upper limit of each confidence interval is infinity. In the case of CPK, we usually don’t care how large it is, so a lower confidence bound is more appropriate than a two-sided confidence interval.
Because they are single numbers, point estimates are almost always above or below the parameters they are supposed to estimate. Without additional information, point estimates are useless for making decisions. But confidence interval estimates are very likely to be true, and the confidence level specifies and controls the probability that the interval estimates are true. Since properly applied confidence intervals incorporate sample size and other tested assumptions, these are reliable tools to make business decisions.
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