Page 766 - The Toxicology of Fishes

746 The Toxicology of Fishes

Univariate Methods

Univariate techniques, particularly ANOVA, using parametric or log(x + 1) transformed data, are
commonly used in testing fish population endpoints, with either Dunnett’s or the Student–Newman–
Keuls (SNK) method serving as common post hoc tests (Graney et al., 1994). Linear regression and
correlation have also been used, but with less frequency (Liber et al., 1992). When assumptions of
parametric tests, normality, and homogeneity are not met, nonparametric tests such as Spearman’s
coefficient of rank, the Wilcoxon rank sum statistic, or the Kruskal–Wallis test should be used. Whereas
univariate methods of hypothesis testing may be appropriate for single-species endpoints (e.g., bass
reproduction over the season), univariate statistics are inappropriate for multispecies toxicity tests. Often,
in regulatory tests, univariate endpoints are an attempt to understand multivariate systems by looking
at univariate projections, attempting to find statistically significant differences in a key endpoint of
interest. In a regression ANOVA approach, an effective concentration can be determined and used, with
caution. The tests are quite site and situation conditional. Calculated no-observable-effect levels (NOELs)
or lowest-observable-effect levels (LOELs) depend on the statistical power and concentrations chosen
(Graney et al., 1994). Such limits are functions of the experimental design rather than components of
the intrinsic hazard of the chemical being studied. When data are analyzed by ANOVA, Knauer et al.
(2005) suggested that it might be possible to use different significance levels for abundant and for less
abundant species.

Multivariate Methods
Large variances are common in aquatic mesocosm studies. In such situations, the statistical power
required to detect effects can be sufficiently low such that the usefulness of the analysis is questionable.
Even if effects exist, they may not be detected (Peterman, 1989); however, even if univariate procedures
are performed with satisfactory power, interactions among species, populations, or communities are
usually not considered (Kennedy et al., 1999). Multivariate techniques offer potential solutions to these
analytical and interpretational problems (Sparks et al., 1999). Analyzing ecotoxicological field studies
with multivariate techniques has some clear advantages. Whereas fish population dynamics may be an
appropriate endpoint, community-level approaches have more ecological relevance than do studies of
individual populations isolated from their environment. Multivariate statistics analyze all available data

and are more likely to discriminate among treatments; consequently, such approaches may help to
determine the ecological significance of chemical exposure and may reach conclusions based on eco-
logical significance, a fundamental responsibility in field studies (Crossland and La Point, 1992; Van
den Brink and Ter Braak, 1999). Multivariate techniques are also ideal for handling large amounts of
data and endpoints more effectively. Kedwards et al. (1999b) showed how multivariate techniques aid
in the interpretation of biological monitoring studies which otherwise present difficulties related to the
sometimes semiquantitative nature of the data and the unavailability of true control sites, replication,
and experimental manipulation.
Several books detail the methods of multivariate analysis: Ludwig and Reynolds (1988) provided
an introduction to the assumptions, derivations, and use of several multivariate techniques commonly
used for the analysis of ecological communities. Van Wijngaarden et al. (1995) compared detrended
correspondence analysis (DCA), principal components analysis (PCA), and redundancy analysis (RDA)
and their usage in mesocosm research in more detail. Van den Brink et al. (1996) proposed a multivariate
method based on RDA, and Clarke (1999) demonstrated the use of nonmetric multivariate analysis in
community-level ecotoxicology, which does not require the restrictive assumptions of parametric
techniques. Multivariate techniques have become more accessible and user friendly with the availability

of software such as the principle response curves method (Van den Brink and Ter Braak, 1999) and
routines in other software packages. Major steps have also been taken to produce outputs readily
interpretable by both ecologists and environmental managers and regulators. Multivariate techniques
now provide the ecotoxicologists with powerful tools to visualize and present impacts at the community
and ecosystem level.