Six Sigma Tutorial -> Confidence Intervals

Six Sigma Confidence Intervals

Confidence intervals are very important to Six Sigma methodology.

To understand Confidence Intervals better, consider this scenario:

Acme Nelson, a leading market research firm conducts a survey among voters in USA asking them whom would they vote if elections were to be held today. The answer was a big surprise! In addition to Democrats and Republicans, there is this surprise independent candidate, John Doe who is expected to secure 22% of the vote.

We asked Acme, how sure are you? In other words how accurate is this prediction?

Their answer: "Well, we are 95% confident that John Doe will get 22% (plus or minus 2%) vote"

In the statistical world, they are saying that John Doe will get a vote between 20% to 24% (also known as Confidence Range) with a probability of 95% (Confidence Level).

Definition of Confidence Interval

According to University of Glasgow Department of Statistics, Confidence Interval is defined as:

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data. If independent samples are taken repeatedly from the same population, and a confidence interval calculated for each sample, then a certain percentage (confidence level) of the intervals will include the unknown population parameter. Confidence intervals are usually calculated so that this percentage is 95%, but we can produce 90%, 99%, 99.9% (or whatever) confidence intervals for the unknown parameter.

In our Acme Nelson survey example

• The confidence interval is the range 20 to 24
• The confidence level is 95%
• The confidence limits are 20 (lower limit) and 24 (upper limit)
• The unknown population parameter is the  'percentage of the total vote' John Doe is expected to Get