[From the working paper, “Multiple Perspectives on Inference for Two Simple Statistical Scenarios” by van Dongen et al., posted at PsyArXiv Preprints]
“When analyzing a specific data set, statisticians usually operate within the confines of their preferred inferential paradigm. For instance, frequentist statisticians interested in hypothesis testing may report p-values, whereas those interested in estimation may seek to draw conclusions from confidence intervals. In the Bayesian realm, those who wish to test hypotheses may use Bayes factors and those who wish to estimate parameters may report credible intervals. And then there are likelihoodists, information-theorists, and machine-learners — there exists a diverse collection of statistical approaches, many of which are philosophically incompatible.”
“… We invited four groups of statisticians to analyze two real data sets, report and interpret their results in about 300 words, and discuss these results and interpretations in a round-table discussion.”
“… Despite substantial variation in the statistical approaches employed, all teams agreed that it would be premature to draw strong conclusions from either of the data sets.”
“… 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.”
“… 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.