Abstract We improve students’ understanding of the F-test for linear hypotheses in a linear model by explaining elements that affect the power of the test. Including true restrictions in a joint null hypothesis affects test power in a way that is not generally known. Asking a student whether including the true restrictions from the null hypothesis will increase or decrease power, the student is likely

Letter to the Editor: Zhang, J. (2021), “The Mean Relative Entropy: An Invariant Measure of Estimation Error,” The American Statistician, 75, 117-123:comment by Vos and Wu. The American Statistician. Accepted 29 August 2021.

Abstract Rank-based methods are frequently used in the life sciences, and in the empirical sciences in general. Among the best-known examples of nonparametric rank-based tests are the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test. However, recently, potential pitfalls and paradoxical results pertaining to the use of traditional rank-based procedures for more than two samples have been highlighted

Abstract In an observational study, to investigate the treatment effect, one common strategy is to match the control subjects to the treated subjects. The outcomes between the two groups are then compared after the treatment-control match. However, when the outcome is rare, detection of an outcome difference can be challenging. An alternative approach is to compare the treatment or exposure discrepancy

Abstract We propose a single loop diagram and use it to devise a single loop matrix method to computationally solve the Penney-Ante game. This method avoids the nuances of repeated use of conditional probability and Markov chain representations. We remove the limitations of Conway’s trick as applied to a fair coin and generalize the method where the coin is allowed to be biased. A uniform random number

Abstract Motivated by the goal of evaluating real-time forecasts of home team win probabilities in the National Basketball Association, we develop new tools for measuring the quality of continuously updated probabilistic forecasts. This includes introducing calibration surface plots, and simple graphical summaries of them, to evaluate at a glance whether a given continuously updated probability forecasting

(2021). Reviewof Books and Teaching Materials. The American Statistician: Vol. 75, No. 3, pp. 354-354.

Abstract The spread of COVID-19 in the US prompted non-pharmaceutical interventions which caused a reduction in mobility everywhere, although with large disparities between different counties. Using a Bayesian spatial modeling framework, we investigated the association of county-level demographic and socioeconomic factors with changes in workplace mobility at two points in time: during the early stages

Abstract Applications based on machine learning models have now become an indispensable part of the everyday life and the professional world. As a consequence, a critical question has recently arose among the population: Do algorithmic decisions convey any type of discrimination against specific groups of population or minorities? In this paper, we show the importance of understanding how bias can

Abstract The Kaplan–Meier (KM) estimator, which provides a nonparametric estimate of a survival function for time-to-event data, has broad applications in clinical studies, engineering, economics and many other fields. The theoretical properties of the KM estimator including its consistency and asymptotic distribution have been well established. From a new perspective, we reconstruct the KM estimator

Abstract Weighted optimality criteria allow an experimenter to express hierarchical interest across estimable functions through a concise weighting system. We show how such criteria can be implicitly influenced by the estimable functions’ minimum variances, leading to nonintuitive variance properties of the optimal designs. To address this, we propose a new weighted criteria and evaluation approach

Abstract Many statistical methods have been proposed for variable selection in the past century, but few balance inference and prediction tasks well. Here we report on a novel variable selection approach called Penalized regression with Second-Generation P-Values (ProSGPV). It captures the true model at the best rate achieved by current standards, is easy to implement in practice, and often yields

Abstract Spatial confounding, i.e., collinearity between fixed effects and random effects in a spatial generalized linear mixed model, can adversely affect estimates of the fixed effects. Restricted spatial regression methods have been proposed as a remedy for spatial confounding. Such methods replace inference for the fixed effects of the original model with inference for those effects under a model

Abstract If we have an unbiased estimate of some parameter of interest, then its absolute value is positively biased for the absolute value of the parameter. This bias is large when the signal-to-noise ratio (SNR) is small, and it becomes even larger when we condition on statistical significance; the winner’s curse. This is a frequentist motivation for regularization or “shrinkage”. To determine a

(2021). The Model Thinker: What You Need to Know to Make Data Work for You. The American Statistician: Vol. 75, No. 2, pp. 230-231.

(2021). SAS for Mixed Models: Introduction and Basic Applications. The American Statistician: Vol. 75, No. 2, pp. 231-231.

(2021). x + y: A Mathematician's Manifesto for Rethinking Gender. The American Statistician: Vol. 75, No. 2, pp. 232-233.

Abstract Sample size derivation is a crucial element of planning any confirmatory trial. The required sample size is typically derived based on constraints on the maximal acceptable type I error rate and minimal desired power. Power depends on the unknown true effect and tends to be calculated either for the smallest relevant effect or a likely point alternative. The former might be problematic if

Abstract For students of probability and statistics, the Cantor distribution provides a useful example of a continuous probability distribution on the real line which cannot be obtained by integrating its derivative or indeed any density function. While usually treated as an advanced topic, we show that the basic facts about the Cantor distribution can be rigorously derived from a sequence of uniform

Abstract This manuscript is a statistical investigation into the 2017 Major League Baseball scandal involving the Houston Astros, the World Series championship winner that same year. The Astros were alleged to have stolen their opponents’ pitching signs in order to provide their batters with a potentially unfair advantage. This work finds compelling evidence that the Astros on-field performance was

Abstract A two-tailed test comparing the means of two independent populations is perhaps the most commonly used hypothesis test in quantitative research, featured centrally in medical research, A/B testing, and throughout the sciences. When data are skewed, the standard two-tailed t test is not appropriate and the permutation test comparing the two means (or medians) has been a widely recommended alternative

Abstract Agent-based models (ABMs) are popular in many research communities, but few statisticians have contributed to their theoretical development. They are models like any other models we study, but in general, we are still learning how to fit ABMs to data and how to make quantified statements of uncertainty about the outputs of an ABM. ABM validation is also an underdeveloped area that is ripe

Abstract The difference between two binomial proportions is commonly used in applied research. Since many studies encounter incomplete data, proper methods to analyze such data are needed. Here, we present a proper multiple imputation procedure for constructing confidence interval for difference between binomial proportions using Newcombe’s method, which is known to have a better coverage probability

When investigators seek to estimate causal effects, they often assume that selection into treatment is based only on observed covariates. Under this identification strategy, analysts must adjust for observed confounders. While basic regression models have long been the dominant method of statistical adjustment, more robust methods based on matching or weighting have become more common. Of late, even

Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian computation. In comparison with the traditional Metropolis-Hastings algorithm, HMC offers greater computational efficiency, especially in higher dimensional or more complex modeling situations. To most statisticians, however, the idea of HMC comes from a less familiar origin, one that is based on the theory of classical mechanics. Its implementation

Abstract The Wilcoxon rank sum test for two independent samples and the Kruskal–Wallis rank test for the one-way model with k independent samples are very competitive robust alternatives to the two-sample t-test and k-sample F-test when the underlying data have tails longer than the normal distribution. However, these positives for rank methods do not extend as readily to methods for making all pairwise

(2021). Data Visualization: Charts, Maps, and Interactive Graphics. Robert Grant. The American Statistician: Vol. 75, No. 1, pp. 113-113.

(2021). Fundamentals of Probability with Stochastic Processes, 4th ed. Saeed Ghahramani. The American Statistician: Vol. 75, No. 1, pp. 113-114.

(2021). Spatio-Temporal Statistics With R. The American Statistician: Vol. 75, No. 1, pp. 114-114.

(2021). McCann and Habiger (2020), “The Detection of Nonnegligible Directional Effects With Associated Measures of Statistical Significance,”. The American Statistician: Vol. 75, No. 1, pp. 115-115.

(2021). Response to the Letter to the Editor on “The Detection of Nonnegligible Directional Effects With Associated Measures of Statistical Significance,” The American Statistician, 74:3, 213–217: Comment by Roger Berger. The American Statistician: Vol. 75, No. 1, pp. 116-116.

Abstract This paper focuses on the minimum Bayes factor compatible with a p-value, considering a set of priors with restricted strength. The resulting minimum Bayes factor depends on both the strength of the set of priors and the sample size. The results can be used to interpret the evidence for/against the hypothesis provided by a p-value in a way that accounts for the strength of the priors and the

Abstract Understanding the concept of randomness is fundamental for students in introductory statistics courses, but the notion of randomness is deceivingly complex, so it is often emphasized less than the mechanics of probability and inference. The most commonly used classroom tools to assess students’ production or perception of randomness are binary choices, such as coin tosses, and number sequences

Abstract The jackknife is a reliable tool for reducing the bias of a wide range of estimators. This note demonstrates that even such versatile tools have regularity conditions that can be violated even in relatively simple cases, and that caution needs to be exercised in their use. In particular, we show that the jackknife does not provide the expected reliability for bias-reduction for the sample

Abstract The problem considered is that of making inferences about the value of a parameter vector θ based on the value of an observable random vector y that is subject to selection of the form y ​ ∈ ​ S (for a known subset S). According to conventional wisdom, a Bayesian approach (unlike a frequentist approach) requires no adjustment for selection, which is generally regarded as counterintuitive and

Abstract A variety of random graph models have been proposed in the literature to model the associations within an interconnected system and to realistically account for various structures and attributes of such systems. In particular, much research has been devoted to modeling the interaction of humans within social networks. However, such networks in real-life tend to be extremely sparse and existing

In current curricula, authentic statistical practice generally only occurs in capstone projects undertaken by advanced undergraduate and Master’s students. We argue that deferring practice is a mis...

Rank statistics { R 1 , … , R n } of actual variates { X 1 , … , X n } play an important role in university undergraduate nonparametric statistics courses. This article derives explicit expressions...

Among plausible causes for replicability failure, one that has not received sufficient attention is the environment in which the research is conducted. Consisting of the population, equipment, personnel, and various conditions such as location, time, and weather, the research environment can affect treatments and outcomes, and changes in the research environment that occur when an experiment is redone

(2020). Mathematical and Statistical Skills in the Biopharmaceutical Industry: A Pragmatic Approach. The American Statistician: Vol. 74, No. 4, pp. 416-417.

(2020). Editorial Collaborators. The American Statistician: Vol. 74, No. 4, pp. 420-421.

The Lorenz curve and Gini index have great social relevance due to concerns regarding income inequality. However, their discussion is limited in the undergraduate statistics and mathematics curricu...

Abstract Hypothesis tests are conducted not only to determine whether a null hypothesis (H0) is true but also to determine the direction or sign of an effect. A simple estimate of the posterior probability of a sign error is PSE = (1 – PH0)p/2 + PH0, depending only on a two-sided p-value and PH0, an estimate of the posterior probability of H0. A convenient option for PH0 is the posterior probability

High-dimensional correlated binary data arise in many areas, such as observed genetic variations in biomedical research. Data simulation can help researchers evaluate efficiency and explore propert...

Multiple imputation has become an increasingly popular technique for handling missing data in studies ranging from cross-sectional to longitudinal studies and from randomized clinical trials to com...

Let X1,…,Xn be a sample from a bivariate normal distribution with mean vector μ and the covariance matrix Σ , N2(μ,Σ) . Define X¯=1n∑i=1nXi and S=∑i=1n(Xi−X¯)(Xi−X¯)′. Hu, Jung, and Qin (2020) have...

Thank you very much for writing the letter on our article. We very much appreciate your comments.Krishnamoorthy and Xia (2007) and our article developed the generalized variable (GV) and generalize...

The Savage-Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrestricted prior. A generalization was proposed by Verdinelli

(2020). The 9 Pitfalls of Data Science. The American Statistician: Vol. 74, No. 3, pp. 307-307.

(2020). Feature Engineering and Selection: A Practical Approach for Predictive Models. The American Statistician: Vol. 74, No. 3, pp. 308-309.

(2020). Modern Statistics for Modern Biology. The American Statistician: Vol. 74, No. 3, pp. 309-311.

(2020). Surprises in Probability: Seventeen Short Stories. The American Statistician: Vol. 74, No. 3, pp. 311-311.

(2020). Time Series: A Data Analysis Approach Using R. The American Statistician: Vol. 74, No. 3, pp. 312-312.

(2020). Micha Mandel (2020), “The Scaled Uniform Model Revisited,” The American Statistician, 74:1, 98–100: Comment. The American Statistician: Vol. 74, No. 3, pp. 315-315.

Follmann developed a multivariate test, when X ∼ MVN(μ,Σ), to test H0 versus H1 − H0 where H0: μ=0 and H1:μ≥0. Follmann provided strict lower bounds on the power function when an orthogonal mapping...

It seems surprising that when applying widely used random number generators to generate one million random numbers on modern architectures, one obtains, on average, about 116 collisions. This artic...

We present a method of generating functions to compute the distributions of the first-arrival and inter-arrival times of random patterns in independent Bernoulli trials and first-order Markov trial...

Abstract Binge-watching behavior is modeled for a single season of an original program from a streaming service to understand and make predictions about how individuals watch newly released content. Viewers make two choices in binge watching. First, the onset when individuals begin viewing the program is modeled using a change point between epidemic viewing with a nonconstant hazard rate and endemic

Publication bias can occur for many reasons, including the perceived need to present statistically significant results. We propose and compare methods for adjusting a single published estimate for ...

We explore the arguments for maximizing the `evidence' as an algorithm for model selection. We show, using a new definition of model complexity which we term `flexibility', that maximizing the evidence should appeal to both Bayesian and Frequentist statisticians. This is due to flexibility's unique position in the exact decomposition of log-evidence into log-fit minus flexibility. In the Gaussian linear