Concerns regarding a call for pluralism of information theory and hypothesis testing
Paul M. Lukacs, Colorado Division of Wildlife, 317 W. Prospect Road, Fort Collins, CO 80526, USA (e-mail Paul.Lukacs@state.co.us).
- 1Stephens et al. (2005) argue for ‘pluralism’ in statistical analysis, combining null hypothesis testing and information-theoretic (I-T) methods. We show that I-T methods are more informative even in single variable problems and we provide an ecological example.
- 2I-T methods allow inferences to be made from multiple models simultaneously. We believe multimodel inference is the future of data analysis, which cannot be achieved with null hypothesis-testing approaches.
- 3We argue for a stronger emphasis on critical thinking in science in general and less reliance on exploratory data analysis and data dredging. Deriving alternative hypotheses is central to science; deriving a single interesting science hypothesis and then comparing it to a default null hypothesis (e.g. ‘no difference’) is not an efficient strategy for gaining knowledge. We think this single-hypothesis strategy has been relied upon too often in the past.
- 4We clarify misconceptions presented by Stephens et al. (2005).
- 5We think inference should be made about models, directly linked to scientific hypotheses, and their parameters conditioned on data, Prob(Hj | data). I-T methods provide a basis for this inference. Null hypothesis testing merely provides a probability statement about the data conditioned on a null model, Prob(data | H0).
- 6Synthesis and applications. I-T methods provide a more informative approach to inference. I-T methods provide a direct measure of evidence for or against hypotheses and a means to consider simultaneously multiple hypotheses as a basis for rigorous inference. Progress in our science can be accelerated if modern methods can be used intelligently; this includes various I-T and Bayesian methods.