APPLICABILITY OF THE t‐TEST FOR DETECTING TRENDS IN WATER QUALITY VARIABLES1

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Abstract
A major concern in managing water resources is whether or not water quality variables have changed over time or space. The two‐sample Student's t‐test is probably the most commonly used statistical test for this purpose. Given that the underlying assumptions of the test may often be violated by water quality variables, a major concern regarding applicability of the test arises. This paper reviews and synthesizes available information in order to examine the effects of non‐normality, unequal variances, serial dependence, and seasonality on the performance of the two‐sample t‐test. The results suggest the t‐test is robust for non‐normal distributions if the distributions have the same shape (either symmetric or skewed) and sample sizes are equal. The t‐test is also robust for unequal variances if the sample sizes are equal. The t‐test appears not to be robust when: 1) samples come from two distributions of different shape, 2) samples have unequal variances and unequal sample sizes, 3) serial dependence in observations is present, or 4) seasonal changes, in concentration are present and not removed.

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