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EnvStats pp 113–148Cite as

Prediction and Tolerance Intervals

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Abstract

Any activity that requires constant monitoring over time and the comparison of new values to “background” or “standard” values creates a decision problem: if the new values greatly exceed the background values, has a change really occurred, or have the true underlying concentrations stayed the same and this is just a “chance” event? Statistical tests are used as objective tools to decide whether a change has occurred (although the choice of Type I error level and acceptable power are subjective decisions). For a monitoring program that involves numerous tests over time, figuring out how to balance the overall Type I error with the power of detecting a change is not a trivial problem, but it is also a problem that has been dealt with for a long time in the statistical literature under the heading of “multiple comparisons.” Prediction intervals and tolerance intervals are two tools that you can use to attempt to solve the multiple comparisons problem. This chapter discusses the functions available in EnvStats for constructing prediction and tolerance intervals. See Millard et al. (2014) for a more in-depth discussion of this topic.

Keywords

  • Confidence Level
  • Lognormal Distribution
  • Gamma Distribution
  • Prediction Interval
  • Sampling Occasion

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 6.1

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Authors and Affiliations

  1. Probability, Statistics and Information, Seattle, Washington, USA

    Steven P. Millard

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  1. Steven P. Millard
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Millard, S.P. (2013). Prediction and Tolerance Intervals. In: EnvStats. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8456-1_6

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