Interpretation of Confidence Interval
I admit that it is almost common usage to say that a parameter of interest lies in the confidence interval we construct around a sample statistic, so I won’t count off for that answer. But the most accurate meaning of the confidence interval is that
, for example, 99% of similarly constructed intervals will contain the true value of the parameter. In the graphic, you can see confidence intervals constructed for 20 samples of the population mean. Only one interval does not contain the parameter of interest.
In the strictest sense, we are really talking about the accuracy of our sampling process. These two phraseologies should get you successfully through the quizzes and exams in this course.
Prediction Interval versus Confidence Interval
In reading the many posts in this discussion on confidence intervals, I keep seeing a misuse of confidence intervals, i.e. using them for a forecast of a future value such as forecasting future sales from historical sales data. In reading the references that many of you are using, I’m beginning to think the problem is at least partially due to our use in statistics of the formal definition of “point estimate.” A ‘point estimate’ is an estimate of a population parameter, such as the mean, variance, etc., developed from sample data. Such a point estimate gives us some information about the parameter, but we have learned that an interval estimate, a confidence interval, provides more useful information.
When we want to estimate or forecast/predict a “point” in the future, we should not use a confidence interval; instead we should use a prediction interval. When we are considering the future, we must understand that circumstances might change from that existing when we collected our data and made our ‘point estimate’/CI about the mean GM sales; thus, there may be more uncertainty involved. The formulas we have developed for prediction intervals include this added uncertainty and they produce wider intervals in recognition of this.
Remember there is a difference between a ‘point estimate’ and an estimated/predicted point.