Statisticians: Desired and Feared
John Stufken, TAS Editor
With an ever-increasing demand for statistics, we are desired. But with lingering uneasiness about our methods and concepts, we also are feared. Xiao-Li Meng discusses challenges for our curricula that stem from this new status in the thought-provoking lead article, “Desired and Feared—What Do We Do Now and Over the Next 50 Years?” Naturally, being desired also gives rise to tremendous opportunities for the discipline, and the question is whether we can take advantage of this. By discussing recent developments at Harvard University, Meng rallies the troops with an emphatic “Yes We Can.”
In the General section, Micha Mandel and Yosef Rinott present an interesting study on inference in the presence of selection bias. If, for example, in studying the toxicity of a drug, only successful studies are published, how should we perform inferences about the drug’s toxicity based on only the published results? Does the frequentist paradigm provide a more satisfactory approach than the Bayesian paradigm, or vice versa? In “A Selection Bias Conflict and Frequentist versus Bayesian Viewpoints,” the authors explore these and related questions.
The next two articles in this section focus on paradoxes. Aiyou Chen, Thomas Bengtsson, and Tin Kam Ho revisit the “regression paradox,” where counterintuitive conclusions appear to result from considering a direct and reversed linear regression. They identify sufficient conditions that will lead to this paradox and provide a link to Simpson’s Paradox. On cue, Marios Pavlides and Michael Perlman entertain the question, “How Likely Is Simpson’s Paradox?” Variations of this question are answered, either exactly or through simulation. For example, in a 2 x 2 x 2 contingency table, if the cell probabilities are distributed uniformly over the entire probability simplex, Simpson’s Paradox occurs with probability 1/60.
The article “Uniformly Hyper-Efficient Bayes Inference in a Class of Nonregular Problems,” by Daniel Nordman, Stephen Vardeman, and Melissa Bingham, presents an interesting and unusual class of nonregular continuous statistical models, where ordinary maximum likelihood is not available, but Bayes methods are hyper-efficient and achieve convergence rates far in excess of the usual n-1/2 uniformly across the parameter space.
Arne Bathke, Oliver Schabenberger, Randall Tobias, and Laurence Madden exhibit and explore a relationship between the Greenhouse-Geisser F adjustment and an ANOVA-type statistic in nonparametric inference for factorial designs in their article, “Greenhouse-Geisser Adjustment and the ANOVA-Type Statistic: Cousins or Twins?”
In the final article of this section, Carl Morris and Kari Lock unify the six univariate natural exponential families with quadratic variance functions, exhibiting relationships between these families and with other common distributions.
The Statistical Practice section opens with “A Statistical Problem Concerning the Mar Saba Letter,” by Andrew Solow and Woolcott Smith. This letter was purportedly written by a second-century theologian, but there is evidence that it is a forgery. The authors provide a statistical framework for studying the letter’s authenticity. Per Gösta Andersson follows this with an interesting article that provides a simple method for adjusted confidence intervals when a point estimator and an estimator of its variance are substantially correlated.
In Teacher’s Corner, Amy Froelich, William Duckworth, and Jessica Culhane investigate the randomness of the shuffle feature on the iPod in “Does Your iPod Really Play Favorites?” They provide interesting ideas for classroom use in this article, which was inspired by anecdotal evidence of potential nonrandom behavior of the shuffle feature.
Halvor Mehlum revisits a problem in forensic statistics in “The Island Problem Revisited.” Simplified, the island problem addresses the question of whether a suspect who matches a known rare characteristic that the culprit of a crime is known to possess is guilty of the crime.
Also in the Teacher’s Corner section, Scott Lesch and Daniel Jeske shine a light on lesser-known, but accurate, approximations—all based on the standard normal distribution—of the Poisson and binomial cumulative distribution functions. They also point out how these approximations can be used to highlight relationships between various distributions.
In the final article, “A New Way to Derive Locally Most Powerful Rank Tests,” Anthony Kuk explores a relationship between derivatives of the log-likelihood for observed data (the ranks) and complete data (the underlying continuous variables).