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Analysis of Variance (Anova)
description | simple example | MAIA example | diatom example | how it works | caveats
Description: You provide Anova with a categorical variable to group cases and a dependent variable that is (typically) continuous. Anova tells you if the groups have significantly different values for the dependent variable. This is one-way Anova, but much more complicated designs are also possible.
In addition to testing for significant differences between groups, Anova is a powerful tool for comparing the variability of related types of measures.
Simple example: You want to test whether stream sites in different ecoregions have significantly different substrate sizes, that is, fine sand vs. cobble and gravel. Stream sites are grouped by ecoregion and the dependent variable is defined as average pebble size. Anova tells you whether pebble is significantly different for different ecoregions. This is a simple 1-way Anova.
You might add soil type as an additional independent variable to predict pebble size. If all types of soil are tested for all ecoregions, it is a crossed, or factorial, Anova design. If soil types are tested within each ecoregion, it is a nested design.
MAIA example: Kaufmann, et al. (1999) used Anova to compare the relative precision of different types of stream habitat measures. They estimated the variance associated with differences in stream sites (the "signal") and the variance associated with repeat sampling (the "noise", or error variance) for each habitat measure.
They could have used these variance estimates to test for differences between sites, but instead they wanted to compare habitat measures to each other in order to evaluate their relative precision. Habitat measures with large signal to noise ratios are more precise. Measures with small signal to noise ratios may not be reliable enough to use for assessment.
Figure 1
Figure 1: Signal-to-noise ratios for classes of habitat measures. High signal-to-noise indicates high precision, or repeatability. The precision of several habitat measures are grouped into categories and plotted as box plots. CHMR - channel morphology, HBCL - habitat unit classification, SUB - substrate, FCV - fish cover, HDIS - human disturbance, and RBPH Rapid Bioassessment Protocol habitat values. Physical measures of the channel morphology (e.g., depth, width and slope), were more precise than channel habitat classification measures (e.g., percent riffle, percent glides and percent pools).
Diatom example: Biological metrics and indexes should vary most due to differences in site condition rather than measurement error. Anova was used to estimate the components of variance for the diatom index and its component metrics. Sites with repeat visits during the same year and in subsequent years were used to compare the relative contribution of site differences, annual variability and within-year variability (measurement error) to the overall variability of the biological metrics and index.
Figure 2
In general, the multimetric index was more precise than its component metrics: a greater percentage of its variability was associated with differences in site condition than with time of sampling.
How the method works: Anova compares the variability of the dependent variable within groups to the variability between groups. If groups are more different than are cases within the groups, then the groups are significantly different.
Assumptions/alternatives: Anova is a relatively robust model, it can tolerate a fair amount of departure from normality. Many large outliers or extreme differences in variability among groups, however, are not as easily tolerated.