JMP, a business division of SAS, has a short seven page white paper that describes the differences between confidence, prediction, and tolerance intervals using a simple manufacturing example. Formulas are provided along with instructions for using JMP menus to calculate the interval types from a data set.
Statistical intervals help us to quantify the uncertainty surrounding the estimates that we calculate from our data, such as the mean and standard deviation. The three types of intervals presented here—confidence, prediction and tolerance—are particularly relevant for applications found in science and engineering because they allow us to make very practical claims about our sampled data.
|That confidence interval is a random variable
No one understands error bars
It’s not an eye-opening read per se, but it’s nonetheless important to understand the nuances between the different interval types. The table provided at the end, with an interpretation of each interval type for the example provided, is a good summary of the ideas presented.