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

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 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, methods based on matching or weighting have become more common. Of late, methods

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

Abstract 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

Abstract 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 mistake: undergraduate students should achieve experience via repeated practice from their first years onward, to achieve heightened levels of confidence and competence prior to graduation. However

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

(2020). Multiple Imputation in Practice: With Examples Using IVEware. The American Statistician: Vol. 74, No. 4, pp. 417-417.

(2020). Xinjie Hu, Aekyung Jung, and Gengsheng Qin (2020), “Interval Estimation for the Correlation Coefficient,” The American Statistician, 74:1, 29–36: Comment by Krishnamoorthy and Xia. The American Statistician: Vol. 74, No. 4, pp. 418-418.

(2020). A Response to the Letter to the Editor on “Interval Estimation for the Correlation Coefficient,” The American Statistician, 74:1, 29–36: Comment by Krishnamoorthy and Xia. The American Statistician: Vol. 74, No. 4, pp. 419-419.

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

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

Abstract Rank statistics {R1,…,Rn} of actual variates {X1,…,Xn} play an important role in University undergraduate nonparametric statistics courses. This paper derives explicit expressions of the correlation coefficients between Xi and Rj for not only i = j but also i≠j, for i.i.d. continuous variables X1,…,Xn with a distribution function FX(·) of X and n≥2: (a) ρXi,Ri=n−1n+1ρX,FX(X)∈(0,n−1n+1] for

Abstract 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

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 curriculum. This paper outlines how to increase the educational potential of Lorenz curves as an application in both the calculus class and introductory probability classroom. We show how calculus and 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 properties of different computational and statistical methods. Also, some statistical methods, such as Monte-Carlo methods, rely on data simulation. Lunn and Davies (1998) proposed linear time complexity methods

(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). Comment on “Test for Trend With a Multinomial Outcome” by Szabo (2019) The American Statistician: Vol. 74, No. 3, pp. 313-314.

(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 requirement was satisfied, the use of which requires knowledge about the unknown population covariance matrix. In this article, we show that the orthogonal mapping requirement for his theorem is equivalent

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

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

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 article explains why, how to mathematically compute such a number, why they often cannot be obtained in a straightforward way, how to numerically compute them in a robust way and, among other things, what would

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 trials. We use segmentation of pattern events and diagrams of Markov chains to illustrate the recursive structures represented by generating functions. We then relate the results of pattern time to the probability

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 possible publication bias using a truncated normal distribution. We attempt to estimate the mean of the underlying normal sampling distribution using only summary data readily available in most published

Abstract This article is a primer for a decision-theoretic approach to hypothesis testing for students and teachers of basic statistics. Using three examples at an introductory level, this article demonstrates how decision-theoretic hypothesis testing can be taught to the students of basic statistics. It also demonstrates that students and researchers can make more sensible and unambiguous decisions

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

The (bivariate) Poisson distribution is the most common distribution for (bivariate) count random variables. The univariate Poisson distribution is characterized by the famous Stein–Chen identity. We demonstrate that this identity allows to derive even sophisticated moment expressions in such a simple way that the corresponding computations can be presented in an introductory Statistics class. Then

In the Anglo-American legal system, courts rely heavily on experts who perform an essential social function in supplying information to resolve disputes. Experts are the vehicles through which facts of any technical complexity are brought out. The adversarial nature of this legal system places expert witnesses in a quandary. Enjoined to serve the court and their profession with unbiased, independent

(2020). R Markdown: The Definitive Guide. The American Statistician: Vol. 74, No. 2, pp. 209-210.

(2020). Model-Based Clustering and Classification for Data Science: With Applications in R. The American Statistician: Vol. 74, No. 2, pp. 208-209.

(2020). Capture-Recapture Methods for the Social and Medical Sciences. The American Statistician: Vol. 74, No. 2, pp. 207-208.

(2020). The Art of Statistics: How to Learn From Data. The American Statistician: Vol. 74, No. 2, pp. 207-207.

(2020). Benjamin, D. J., and Berger, J. O. (2019), “Three Recommendations for Improving the Use of p-Values”, The American Statistician, 73, 186–191: Comment by Foulley. The American Statistician: Vol. 74, No. 1, pp. 101-102.

Sufficiency, conditionality, and invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to teach modern methods. However, being the philosophical cornerstones of statistical inference, a minimal understanding of these principles should be part of any curriculum

The study of conditions under which a two-dimensional random variable (X, Y) will have the property that X/(X+Y)=dY/(X+Y) was initiated by Bhattacharjee and Dhar. Some additional perhaps unexpected examples related to this phenomenon are provided. Discrete and absolutely continuous cases are discussed in detail. Singular continuous cases are briefly mentioned.

Games can be a powerful tool for learning about statistical methodology. Effective game design involves a fine balance between caricature and realism, to simultaneously illustrate salient concepts in a controlled setting and serve as a testament to real-world applicability. Striking that balance is particularly challenging in response surface and design domains, where real-world scenarios often play

In a test of significance, it is common practice to report the p-value as one way of summarizing the incompatibility between a set of data and a proposed model for the data constructed under a set of assumptions together with a null hypothesis. However, the p-value does have some flaws, one being in general its definition for two-sided tests and a related serious logical one of incoherence, in its

This article explores models for geostatistical data for situations in which the region where the phenomenon of interest varies is partitioned into two disjoint subregions. This is called a binary map. The goals of the article are 3-fold. First, a review is provided of the classes of models that have been proposed so far in the literature for geostatistical binary data as well as a description of their

(2020). Comment on “A Note on Collinearity Diagnostics and Centering” by Velilla (2018) The American Statistician: Vol. 74, No. 1, pp. 68-71.

The article revisits univariate and multivariate linear regression models. It is shown that least-square estimators (LSEs) are minimum risk estimators in general class of linear unbiased estimators under some general divergence loss. This amounts to the loss robustness of LSEs.

Online consumer product ratings data are increasing rapidly. While most of the current graphical displays mainly represent the average ratings, Ho and Quinn proposed an easily interpretable graphical display based on an ordinal item response theory (IRT) model, which successfully accounts for systematic interrater differences. Conventionally, the discrimination parameters in IRT models are constrained