“Applicability of the t-Test for Detecting Trends in Water Quality Variables,” by Robert H. Montgomery and Jim C. Loftis2

Montgomery and Loftis (1987) have listed several situations for which the t-test does not accurately reproduce Type I errors, and should therefore be avoided. Characteristics common to water quality data (skewness or other non-normality, presence of outliers and less-thans) also reduce the power of the t-test, in relation to nonparametric alternatives. Thus if one is interested in reaching correct decisions when trends or differences exist, and not just when they do not, the t-test should not be considered “robust” (in the sense of being generally applicable) when its assumptions are violated. Further, t-tests assume that differences in means are relevant (the mean is a good measure of central tendency), and that data groups differ by some additive amount. When all of these assumptions are recognized, and in light of the availability of truly robust and comparatively powerful non-parametric alternatives, we believe there is little applicability of the t-test for detecting trends or differences in water quality variables.