On the mathematics of the Jeffreys–Lindley paradox

This paper is concerned with the well known Jeffreys–Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior for the null hypothesis tends to one when the uncertainty, i.e., the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.     

Stress-strength reliability of exponentiated Fréchet distributions based on Type-II censored data

In this paper, we consider inference of the stress-strength parameter, R, based on two independent Type-II censored samples from exponentiated Fréchet populations with different index parameters. The maximum likelihood and uniformly minimum variance unbiased estimators, exact and asymptotic confidence intervals and hypotheses testing for R are obtained. We conduct a Monte Carlo simulation study to evaluate the performance of these estimators and confidence intervals. Finally, two real data sets are analysed for illustrative purposes.     

Asian children’s verbal development: A comparison of the United States and Australia

Using longitudinal cohort studies from Australia and the United States, we assess the pervasiveness of the Asian academic advantage by documenting White-Asian differences in verbal development from early to middle childhood. In the United States, Asian children begin school with higher verbal scores than Whites, but their advantage erodes over time. The initial verbal advantage of Asian American children is partly due to their parent’s socioeconomic advantage and would have been larger had it not been for their mother’s English deficiency. In Australia, Asian children have lower verbal scores than Whites at age 4, but their scores grow a faster rate and converge towards those of Whites by age 8. The initial verbal disadvantage of Asian Australian children is partly due to their mother’s English deficiency and would have been larger had it not been for their Asian parent’s educational advantage. Asian Australian children’s verbal scores grow at a faster pace, in part, because of their parent’s educational advantage.     

Assessment of individual bioequivalence using sufficient bootstrap procedure

This paper proposes a sufficient bootstrap method, which uses only the unique observations in the resamples, to assess the individual bioequivalence under 2 × 4 randomized crossover design. The finite sample performance of the proposed method is illustrated by extensive Monte Carlo simulations as well as a real‐experimental data set, and the results are compared with those obtained by the traditional bootstrap technique. Our records reveal that the proposed method is a good competitor or even better than the classical percentile bootstrap confidence limits.     

Improved bonferroni procedures for testing overall and pairwise homogeneity hypotheses

Simes' (1986) improved Bonferroni test is verified by simulations ^?to control the α-level when testing the overall homogeneity hypothesis with all pairwise t statistics in a balanced parallel group design. Similarly, this result was found to hold (for practical purposes) in various underlying distributions other than the normal and in some unbalanced designs. To allow the use of step-up procedures based on pairwise t statistics, simulations were used to verify that Simes' test, when applied to testing multiple subset homogeneity hypotheses with pairwise t statistics also keeps the level ? α. Some robustness as above was found here too. Tables of the simulation results are provided and an example of a step-up Hommel-Shaffer type procedure with pairwise comparisons is given.     

Charisma as signal: An evolutionary perspective on charismatic leadership

We present an evolutionary perspective on charismatic leadership, arguing that charisma has evolved as a credible signal of a person's ability to solve a coordination challenge requiring urgent collective action from group members. We suggest that a better understanding of charisma's evolutionary and biological origins and functions can provide a broader perspective in which to situate current debates surrounding the utility and validity of charismatic leadership as a construct in the social sciences. We outline several key challenges which have shaped our followership psychology, and argue that the benefits of successful coordination in ancestral environments has led to the evolution of context-dependent psychological mechanisms which are especially attuned to cues and signals of outstanding personal leadership qualities. We elaborate on several implications of this signaling hypothesis of charismatic leadership, including opportunities for deception (dishonest signaling) and for large-scale coordination.     

Impact of a Homonegativity Awareness Workshop on Attitudes Toward Homosexuality

The current study evaluated the effects of a homonegativity awareness workshop on attitudes toward homosexuality and examined individual difference variables associated with attitude change. Participants included 71 female and 43 male students (approximate mean age?=?23). Compared to a control group of introductory psychology students, participants were less homonegative and erotophobic (F(1, 359)?=?62.47 and 15.92, ps?<?.001) after the workshop. Implications for contact with gay and lesbian persons through structured intervention programs on attitudes toward homosexuality are discussed in terms of both the practice and theory of reducing prejudice and discrimination.     

A general class of test statistics for Van Valen's Red Queen hypothesis

Van Valen's Red Queen hypothesis states that within a homogeneous taxonomic group the age is statistically independent of the rate of extinction. The case of the Red Queen hypothesis being addressed here is when the homogeneous taxonomic group is a group of similar species. Since Van Valen's work, various statistical approaches have been used to address the relationship between taxon age and the rate of extinction. We propose a general class of test statistics that can be used to test for the effect of age on the rate of extinction. These test statistics allow for a varying background rate of extinction and attempt to remove the effects of other covariates when assessing the effect of age on extinction. No model is assumed for the covariate effects. Instead we control for covariate effects by pairing or grouping together similar species. Simulations are used to compare the power of the statistics. We apply the test statistics to data on Foram extinctions and find that age has a positive effect on the rate of extinction. A derivation of the null distribution of one of the test statistics is provided in the supplementary material.     

Bootstrap methods for multivariate hypothesis testing

The nonparametric and parametric bootstrap methods for multivariate hypothesis testing are developed. They are used to approximate the null distribution of the test statistics proposed by Duchesne and Francq (2015 Duchesne, P., Francq, C. (2015). Multivariate hypothesis testing using generalized and {2}-inverses—with applications. Statistics 49:475–496.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), resulting in bootstrap testing procedures. In the problem of testing for the mean vector of a multivariate distribution, the asymptotic validity of the bootstrap methods is proved. The finite sample performance of the new solutions is demonstrated by means of Monte Carlo simulation studies. They indicate that for small-sample size, the bootstrap tests provide a better finite sample properties than the asymptotic tests considered by Duchesne and Francq (2015 Duchesne, P., Francq, C. (2015). Multivariate hypothesis testing using generalized and {2}-inverses—with applications. Statistics 49:475–496.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).     

Improving Weight of Evidence Approaches to Chemical Evaluations

Federal and other regulatory agencies often use or claim to use a weight of evidence (WoE) approach in chemical evaluation. Their approaches to the use of WoE, however, differ significantly, rely heavily on subjective professional judgment, and merit improvement. We review uses of WoE approaches in key articles in the peer‐reviewed scientific literature, and find significant variations. We find that a hypothesis‐based WoE approach, developed by Lorenz Rhomberg et al., can provide a stronger scientific basis for chemical assessment while improving transparency and preserving the appropriate scope of professional judgment. Their approach, while still evolving, relies on the explicit specification of the hypothesized basis for using the information at hand to infer the ability of an agent to cause human health impacts or, more broadly, affect other endpoints of concern. We describe and endorse such a hypothesis‐based WoE approach to chemical evaluation.