When data analysts operate within different statistical frameworks (e.g., frequentist versus Bayesian, emphasis on estimation versus emphasis on testing), how does this impact the qualitative conclusions that are drawn for real data? To study this question empirically we selected from the literature two simple scenarios -involving a comparison of two proportions and a Pearson correlation- and asked four teams of statisticians to provide a concise analysis and a qualitative interpretation of the outcome. The results showed considerable overall agreement; nevertheless, this agreement did not appear to diminish the intensity of the subsequent debate over which statistical framework is more appropriate to address the questions at hand.
Finally, Gelman disagreed with most if what had been said in the discussion thus far. Specifically, he said: “I don’t think ‘alpha’ makes any sense, I don’t think 95% intervals are generally a good idea, I don’t think it’s necessarily true that points in 95% interval are compatible with the data, etc etc.”
Despite the (unfortunately near-universal) ambiguity about the nature of the data, the background knowledge, and the research question, each analysis team added valuable insights and ideas. This reinforces the idea that a careful statistical analysis, even for the simplest of scenarios, requires more than a mechanical application of a set of rules; a careful analysis is a process that involves both skepticism and creativity. Perhaps popular opinion is correct, and statistics is difficult. On the other hand, despite employing widely different approaches, all teams nevertheless arrived at a similar conclusion. This tentatively supports the Fisher-Jeffreys conjecture that, regardless of the statistical framework in which they operate, careful analysts will often come to similar conclusions.
van Dongen, N. N. N., van Doorn, J. B., Gronau, Q. F., van Ravenzwaaij, D., Hoekstra, R., Haucke, M. N., Lakens, D., Hennig, C., Morey, R. D., Homer, S., Gelman, A., Sprenger, J., & Wagenmakers, E.-J. (in press). Multiple perspectives on inference for two simple statistical scenarios. The American Statistician. PsyArXiv Preprint.