John Wiley & Sons, Ltd.

Testing against “normal” with environmental data

Normal ranges are some fraction of a reference distribution deemed to represent an expected condition (typically 95%). They are frequently used as the basis for generic criteria for monitoring programs designed to test whether a sample is outside of “normal”, as in reference condition approach studies. Normal ranges are also the basis for criteria for more classic environmental effects monitoring programs designed to detect differences in mean responses between reference and exposure areas. Limits on normal ranges are estimated with error that varies depending largely on sample size. Direct comparison of a sample (or a mean) to estimated limits of a normal range will, with some frequency, lead to incorrect conclusions about whether a sample (or a mean) is in or outside the normal range when the sample (or mean) is near the limit. Those errors can have significant costs and risk implications. This paper describes tests based on non‐central distributions that are appropriate for quantifying the likelihood samples (or means) are outside a normal range. These non‐central tests reverse the burden of evidence (assuming that the sample (or mean) is at or outside normal), and thereby encourage proponents to collect more robust sample sizes that will demonstrate that the sample (or mean) is not at the limits or beyond the normal range. These non‐central equivalence and interval tests can be applied to uni‐ and multivariate responses, and to simple (e.g., upstream vs downstream) or more complex (e.g., before vs after or upstream vs downstream) study designs. Statistical procedures for the various tests are illustrated with benthic invertebrate community data collected as part of the Regional Aquatics Monitoring Program (RAMP) in the vicinity of oil sands operations in northern Alberta. An Excel workbook is provided (in Supplemental Information) with functions and calculations to carry out the various tests. This article is protected by copyright. All rights reserved

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