Analysis of Variance Methods

Analysis of variance (ANOVA) can be conducted using site, test period, and the interaction between site and test period as explanatory factors for Ceriodaphnia survival or reproduction, or fathead minnow survival or growth. ANOVA (SAS-GLM, available for use on personal computers; SAS Institute, 1985) provides an estimate of the amount of variation in survival, reproduction, or growth that is explained (R2) by the three factors together. Duncan's multiple-range test (a SAS-GLM option) or other multiple-comparison tests can be used to identify sites or test periods where the response factor is low. When Duncan's multiple-range test is used to identify differences among sites, sites are sorted according to mean responses. Sites that have an unusually low mean value for any of the four response parameters can be considered as suspect for toxicity. If the study involves a linear array of sites below a discharge, and the effects attributable to date and the interaction of site and test period are small, the procedure could permit the investigator to identify a "no-observed-effect site," analogous to the NOEC of effluent toxicity tests.

If data for a sufficiently large number of test periods are available, and one or two of the test periods have unusually low mean values for a response parameter, the data set can be pruned by eliminating data from the suspect test period(s). This procedure may be justified if the response parameter in question (e.g., fathead minnow growth) is unusually low in water from all sources, including references sites, and the control. The elimination of data for test periods that have suspiciously low values for the response factors should increase R2 for the full model (site, test period, and the interaction between site and test period) and lower the significance of test period. An analysis reported in Boston et al. (1994) showed an increase in the amount of explained variance in Ceriodaphnia survival and reproduction by eliminating suspect dates from the data set. In contrast, neither the results for minnow survival or growth did not benefit much from data pruning. Pruning should be used only when it is thoroughly justified. In such cases, the justification should be explained, and the consequences of the act of pruning should be considered carefully. The objective of pruning is not to increase the R2 of a linear model but to reveal temporal or spatial patterns in biological quality of the water that may otherwise be obscured by excessive variance due to test dates where growth, survival, or reproduction of test organisms was low in control or reference conditions.

When using toxicity test methods to assess ambient water quality, a bioassay should simultaneously meet two key objectives: It should discriminate readily among sites, and it should exhibit little variation from test period to test period, when applied to noncontaminated control water or to water from a noncontaminated reference site. An ANOVA-based analysis of results of 285 site and test-period combinations was used to determine which test organism—Ceriodaphnia or fathead minnow larvae—best fulfilled these objectives (Boston et al., 1994). That analysis



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