When we calculate a statistic for example, a mean, a variance, a
proportion, or a correlation coefficient, there is no reason to expect
that such point estimate would be exactly equal to the true population
value, even with increasing sample sizes. There are always sampling
inaccuracies, or error. In most Six Sigma projects, there are at least
some descriptive statistics calculated from sample data. In truth, it
cannot be said that such data are the same as the population’s true
mean, variance, or proportion value. There are many situations in which
it is preferable instead to express an interval in which we would expect
to find the true population value.
This interval is called an interval
estimate. A confidence interval is an interval, calculated from the
sample data, that is very likely to cover the unknown mean, variance, or
proportion. For example, after a process improvement a sampling has
shown that its yield has improved from 78% to 83%. But, what is the
interval in which the population’s yield lies? If the lower end of the
interval is 78% or less, you cannot say with any statistical certainty
that there has been a significant improvement to the process. There is
an error of estimation, or margin of error, or standard error, between
the sample statistic and the population value of that statistic. The
confidence interval defines that margin of error. The next page shows a
decision tree for selecting which formula to use for each situation. For
example, if you are dealing with a sample mean and you do not know the
population’s true variance (standard deviation squared) or the sample
size is less than 30, than you use the t Distribution confidence
interval. Each of these applications will be shown in turn.
Confidence Intervals in Six Sigma Methodology
