Interval Analysis: getting to the heart of what confidence, prediction, and tolerances intervals are

The differences and uses of the three most common intervals used in statistics are not well known. While not surprising in the general populace, it is also the case for many statisticians. Traditional statistical education focuses on confidence intervals. While confidence intervals are important, it is not uncommon for misunderstanding of what they entail. Where do prediction and tolerance intervals fit in? This study performs an in-depth Monte Carlo study comparing the interval types to known populations. Graphical and tabular assessments allow the correct application and understanding of confidence, prediction, and tolerance intervals to be seen. This quantifies their differences and illustrates what can be expected and when to use a given approach. In addition to a generic detailed analysis of interval types, applications to oil & gas pipelines are provided with specific guidance on when to use confidence, prediction, and tolerance intervals to address the application needs.