5.3 Tolerance Limits

Tolerance intervals are statistical ranges typically constructed from on-site backgroundNatural or baseline groundwater quality at a site that can be characterized by upgradient, historical, or sometimes cross-gradient water quality (Unified Guidance). data. Tolerance limits define the rangeThe difference between the largest value and smallest value in a dataset (NIST/SEMATECH 2012). of data that fall within a specified percentage with a specified level of confidence. The upper tolerance limit has been commonly used to establish a background threshold value, however, prediction limitsIntervals constructed to contain the next few sample values or statistics within a known probability (Unified Guidance). are often favored for establishing a background threshold value in groundwater because they account for repeated measures. An upper tolerance limit (UTL) is designed to contain, but not exceed, a large fraction (that is, 95%, 99%) of the possible background concentrations, thus providing a reasonable upper limit on what is likely to be observed in background. Similarly, the lower tolerance limit (LTL) is designed to contain at most a certain percentage of the possible background concentrations, thus providing a reasonable lower limit on what is likely to be observed in background. The fraction to be contained or ‘covered’ by the limit is the coverage parameter, and must be specified along with a desired confidence levelDegree of confidence associated with a statistical estimate or test, denoted as (1 – alpha) (Unified Guidance).. Tolerance limits explicitly account for the degree of variation in the background population and the size of the sample of measurements used to construct the limit. Table F-2 includes information about checking assumptions for Tolerance limits. Tolerance limits and confidence limits (see Section 5.2) are distinct, even though in some cases the one-sided upper limits for both methods are equivalent.


Publication Date: December 2013

Permission is granted to refer to or quote from this publication with the customary acknowledgment of the source (see suggested citation and disclaimer).


This web site is owned by ITRC.

1250 H Street, NW • Suite 850 • Washington, DC 20005

(202) 266-4933 • Email: [email protected]

Terms of Service, Privacy Policy, and Usage Policy


ITRC is sponsored by the Environmental Council of the States.