The 'improved' brown and forsythe test for mean equality: some things can't be fixed

Mehrotra (1997) presented an ‘;improved’ Brown and Forsythe (1974) statistic which is designed to provide a valid test of mean equality in independent groups designs when variances are heterogeneous. In particular, the usual Brown and Fosythe procedure was modified by using a Satterthwaite approximation for numerator degrees of freedom instead of the usual value of number of groups minus one. Mehrotra then, through Monte Carlo methods, demonstrated that the ‘improved’ method resulted in a robust test of significance in cases where the usual Brown and Forsythe method did not. Accordingly, this ‘improved’ procedure was recommended. We show that under conditions likely to be encountered in applied settings, that is, conditions involving heterogeneous variances as well as nonnormal data, the ‘improved’ Brown and Forsythe procedure results in depressed or inflated rates of Type I error in unbalanced designs. Previous findings indicate, however, that one can obtain a robust test by adopting a heteroscedastic statistic with the robust estimators, rather than the usual least squares estimators, and further improvement can be expected when critical significance values are obtained through bootstrapping methods.     

Bayesian palaeoclimate reconstruction

Summary.  We consider the problem of reconstructing prehistoric climates by using fossil data that have been extracted from lake sediment cores. Such reconstructions promise to provide one of the few ways to validate modern models of climate change. A hierarchical Bayesian modelling approach is presented and its use, inversely, is demonstrated in a relatively small but statistically challenging exercise: the reconstruction of prehistoric climate at Glendalough in Ireland from fossil pollen. This computationally intensive method extends current approaches by explicitly modelling uncertainty and reconstructing entire climate histories. The statistical issues that are raised relate to the use of compositional data (pollen) with covariates (climate) which are available at many modern sites but are missing for the fossil data. The compositional data arise as mixtures and the missing covariates have a temporal structure. Novel aspects of the analysis include a spatial process model for compositional data, local modelling of lattice data, the use, as a prior, of a random walk with long-tailed increments, a two-stage implementation of the Markov chain Monte Carlo approach and a fast approximate procedure for cross-validation in inverse problems. We present some details, contrasting its reconstructions with those which have been generated by a method in use in the palaeoclimatology literature. We suggest that the method provides a basis for resolving important challenging issues in palaeoclimate research. We draw attention to several challenging statistical issues that need to be overcome.     

The outcomes of a longitudinal study of non‐organic failure‐to‐thrive

Individuals who had failed‐to‐thrive for non‐organic reasons received psychosocial intervention which was tailor‐made to their particular needs during childhood. Their progress was followed up over 20 years later, including their physical growth and social and cognitive functioning. Not all clients showed the same outcomes. The quality of the parental relationship and the reason for the growth‐faltering were found to be related to the outcomes at 20 years. Unless they experienced a positive and sustained change in their life or circumstances, individuals who had experienced abuse showed poorer outcomes than those whose growth‐faltering had been thought due to neglect, lack of parenting or feeding dif?culties. Abuse tended to be a contributing factor to growth‐faltering more frequently in families where the parents were observed to have a poor relationship with each other. However, a signi?cant change in the quality of care given to the child and the emotional environment experienced by them resulted in positive outcomes 20 years later despite experiencing abuse during childhood. Copyright © 2003 John Wiley & Sons, Ltd.     

Comparing robust generalized variances and comments on efficiency

Numerous papers have considered the problem of comparing univariate measures of dispersion corresponding to two independent groups. This paper considers a multivariate generalization of this problem where the goal is to compare robust generalized variances. For reasons given in the paper, attention is focused on a particular W-estimator where multivariate outliers are downweighted via a projection-type outlier detection method. Included are results on the small-sample efficiency of several estimators plus comments on using the usual generalized variance.     

The age of exploration and exploitation: Younger-looking leaders endorsed for change and older-looking leaders endorsed for stability

The current contribution extends theorizing on leadership and the exploration–exploitation dilemma using an evolutionary perspective. A theoretical connection is made between the exploration–exploitation dilemma and age-biased leadership preferences for exploratory change versus stable exploitation. For the majority of human evolution our species was semi- or entirely nomadic and the trade-off between exploration versus exploitation had substantial physical- and experience-based requirements which align with leadership opportunities as moderated by age. Thus, given the consistency and importance of correctly assigning leadership for the exploration–exploitation dilemma, human evolution has likely selected for age-biased leadership endorsement. Across three experiments we find that younger-looking leaders are endorsed for times of exploratory change and older-looking leaders for stable exploitation. Further, our results indicated that older leaders are endorsed for leading conservative exploitation of nonrenewable resources and younger leaders for exploration of renewable alternatives (i.e., green leadership). The results introduce an age-biased leadership endorsement hypothesis.     

A remark on a social choice problem

If preferences are continuous monotone complete preorders, then there is a continuous social choice aggregation rule which respects unanimity and is anonymous. The simple proof of this result involves a straightforward application of well-known properties of the closed convergence topology.     

Design and analysis of variable fidelity experimentation applied to engine valve heat treatment process design

Summary.  When experimentation on a real system is expensive, data are often collected by using cheaper, lower fidelity surrogate systems. The paper concerns response surface methods in the context of variable fidelity experimentation. We propose the use of generalized least squares to generate the predictions. We also present perhaps the first optimal designs for variable fidelity experimentation, using an extension of the expected integrated mean-squared error criterion. Numerical tests are used to compare the performance of the method with alternatives and to investigate the robustness to incorporated assumptions. The method is applied to automotive engine valve heat treatment process design in which real world data were mixed with data from two types of computer simulation.