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A general problem faced by ecologists and mathematicians alike is how to statistically analyze data from dynamic biological systems observed for limited periods of time. Examination of biological and statistical properties of standardized aquatic microcosms (SAMs) can provide extra insights or artifacts; several examples will be used to support recommendations and cautions on the use of various statistical procedures and interpretation.
Within-experiment statistical analyses of the SAM data include analyses of variance (ANOVAs) on both biological and chemical data. The results of the ANOVAs on each sampling day are expressed as an “interval of nonsignificant difference” (1ND) around the control mean. These IND graphics are essentially results of modified t-tests between the control and treatment means, are easily interpretable, and allow one to quickly view the results of the entire experiment for any response variable. Apparent statistical artifacts can be investigated by examining the replicate data, for example, cases in which the biological and statistical interpretations do not seem to agree. Several other statistical procedures have demonstrated shortcomings, including (1) classical time series, (2) other multivariate methods, and (3) nonparametrie multiple comparisons.
Between-experiment statistical comparisons have proven more difficult. For the interlaboratory copper experiments, we use the days-weighted-by-variable (DWV). With the DWV, we have been able to come to grips with the problem that faces almost any ecological study—many measurements (and thus lots of data) but a limited number of statistical degrees of freedom. The DWV has allowed us to demonstrate where the similarities and differences are between different experiments. For instance, we have been able to state statistically that experiments agreed in the nature and direction of certain effects, but that the exact timing of such effects has differed. Rejected techniques for between-experiment comparisons include the following: (1) day-by-day two-way ANOVA; (2) nonparametric correlations of statistical differences; (3) comparison of fitted regression parameters via ANOVA; (4) differential equation modeling of individual microcosms; (5) integrated distances between microcosm time traces.
toxicity statistics, microcosms, statistics
Associate professor, Center for Quantitative Science, University of Washington, Seattle, WA
Professor, School of Fisheries, WH-10, University of Washington, Seattle, WA