There is a general belief that science progresses over time and given that the number of scientists is increasing, this is a reasonable first approximation. The use of statistics in ecology has been one of ever increasing improvements of methods of analysis, accompanied by bandwagons. It is one of these bandwagons that I want to discuss here by raising the general question:
Has the introduction of new methods of analysis in biological statistics led to advances in ecological understanding?
This is a very general question and could be discussed at many levels, but I want to concentrate on the top levels of statistical inference by means of old-style frequentist statistics, Bayesian methods, and information theoretic methods. I am prompted to ask this question because of my reviewing of many papers submitted to ecological journals in which the data are so buried by the statistical analysis that the reader is left in a state of confusion whether or not any progress has been made. Being amazed by the methodology is not the same as being impressed by the advance in ecological understanding.
Old style frequentist statistics (read Sokal and Rohlf textbook) has been criticized for concentrating on null hypothesis testing when everyone knows the null hypothesis is not correct. This has led to refinements in methods of inference that rely on effect size and predictive power that is now the standard in new statistical texts. Information-theoretic methods came in to fill the gap by making the data primary (rather than the null hypothesis) and asking the question which of several hypotheses best fit the data (Anderson et al. 2000). The key here was to recognize that one should have prior expectations or several alternative hypotheses in any investigation, as recommended in 1897 by Chamberlin. Bayesian analysis furthered the discussion not only by having several alternative hypotheses but by the ability to use prior information in the analysis (McCarthy and Masters 2006). Implicit in both information theoretic and Bayesian analysis is the recognition that all of the alternative hypotheses might be incorrect, and that the hypothesis selected as ‘best’ might have very low predictive power.
Two problems have arisen as a result of this change of focus in model selection. The first is the problem of testability. There is an implicit disregard for the old idea that models or conclusions from an analysis should be tested with further data, preferably with data obtained independently from the original data used to find the ‘best’ model. The assumption might be made that if we get further data, we should add it to the prior data and update the model so that it somehow begins to approach the ‘perfect’ model. This was the original definition of passive adaptive management, which is now suggested to be a poor model for natural resource management. The second problem is that the model selected as ‘best’ may be of little use for natural resource management because it has little predictability. In management issues for conservation or exploitation of wildlife there may be many variables that affect population changes and it may not be possible to conduct active adaptive management for all of these variables.
The take home message is that we need in the conclusions of our papers to have a measure of progress in ecological insight whatever statistical methods we use. The significance of our research will not be measured by the number of p-values, AIC values, BIC values, or complicated tables. The key question must be: What new ecological insights have been achieved by these methods?
Anderson, D.R., Burnham, K.P., and Thompson, W.L. 2000. Null hypothesis testing: problems, prevalence, and an alternative. Journal of Wildlife Management 64(4): 912-923.
Chamberlin, T.C. 1897. The method of multiple working hypotheses. Journal of Geology 5: 837-848 (reprinted in Science 148: 754-759 in 1965). doi:10.1126/science.148.3671.754.
McCarthy, M.A., and Masters, P.I.P. 2005. Profiting from prior information in Bayesian analyses of ecological data. Journal of Applied Ecology 42(6): 1012-1019. doi:10.1111/j.1365-2664.2005.01101.x.
Walters, C. 1986. Adaptive Management of Renewable Resources. Macmillan, New York.