I am trying to analyze a dataset consisting of counts of amphibian egg masses (3 different species) in nine vernal pools over a four-year period (consecutive years, 2014 to 2017). During each count (one per year), data were also collected on pool area, pool depth, pH, and conductivity. Initially, I did a standard ANOVA to determine whether pool (9 of them), year, area, depth, pH or conductivity were predictors of egg mass numbers in the pools. I was told (by journal manuscript reviewers) that ANOVA was not an appropriate analysis (because of the single value for each combination of factors, which I agree with), and they suggested two alternatives:
- Multiple linear regression or similar model that allows for continuous and categorical variables (new variables could be added, such as percent surrounding forest, distance to nearest pool, any surrounding development, or low/high development pressure), both to be included as opposed to univariate correlations that can mask complex relationships among independent variables.
- Because the same ponds were sampled repeatedly, samples from the same pond in multiple years are not independent replicates. Recommend a repeated measure ANOVA, averaging all the years for each pool and just analyze the data for pool averages.
Please note that sample sizes are small (9 pools, 4 years), so any analysis may not have much statistical power. But even a finding of no effect would have meaning for the study. Any thoughts on appropriate tests/approaches (these suggested ones or others) would be appreciated.
Thanks for the responses. The Bayesian approach is probably the proper one, but I don't think I'm willing to put in the background work to understand/apply it, at least for this project. I'll likely take a crack at the multilevel (mixed?) model, with one IV (independent variable?) for each model, as Peter Flom suggests. I assume that this means running multiple separate models? Some clarification (and maybe appropriate routine/package in R) would be helpful.
The "hypothesis" here is that at least one of the independent variables affects total egg mass counts for a pool. From some preliminary analyses, I already know there is a significant correlation (Spearman) of pool size (area) with counts (the bigger the pool, the more egg masses), so that's one. I'm just looking to verify that with a model (or models, multilevel/hierarchical or otherwise) with which I can also analyze other variables. Perhaps a single model is not appropriate for these data, as mkt points out.
Basic visualization of the data may be all that's needed, but I've found that most journals these days find that insufficient and want hard stats to back it up.