Will the ASA's Efforts to Improve Statistical Practice be Successful? Some Evidence to the Contrary

ABSTRACT

Recent efforts by the American Statistical Association to improve statistical practice, especially in countering the misuse and abuse of null hypothesis significance testing (NHST) and p-values, are to be welcomed. But will they be successful? The present study offers compelling evidence that this will be an extraordinarily difficult task. Dramatic citation-count data on 25 articles and books severely critical of NHST's negative impact on good science, underlining that this issue was/is well known, did nothing to stem its usage over the period 1960–2007. On the contrary, employment of NHST increased during this time. To be successful in this endeavor, as well as restoring the relevance of the statistics profession to the scientific community in the 21st century, the ASA must be prepared to dispense detailed advice. This includes specifying those situations, if they can be identified, in which the p-value plays a clearly valuable role in data analysis and interpretation. The ASA might also consider a statement that recommends abandoning the use of p-values.     

Saddlepoint Approximations to the Limiting Distribution of the Modified Anderson–Darling Test Statistic

The approximation for the distribution function of test statistic is extremely important in statistics. The standard and higher-order saddlepoint approximations are considered in tails of the limiting distribution for the modified Anderson–Darling test. The saddlepoint approximations are compared with the approximation of Sinclair et al. (1990 Sinclair , C. D. , Spurr , B. D. , Ahmad , M. I. ( 1990 ). Modified Anderson Darling test . Communication Statistics—Theory and Methods 19 : 3677 – 3686 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) for upper tail area. An empirical function is derived to estimate the critical values of a saddlepoint approximation.     

Three Approximate Solutions to the Multivariate Behrens–Fisher Problem

ABSTRACT

This article provides three approximate solutions to the multivariate Behrens–Fisher problem: the F statistic, the Bartlett, as well as the modified Bartlett corrected statistics. Empirical results indicate that the F statistic outperforms the other two and five existing procedures. The modified Bartlett corrected statistic is also very competitive.     

Analytic approach to coset–leader decoding leads to extension of the Welch–Berlekamp theorem

This paper provides a complete proof of the Welch–Berlekamp theorem on which the Welch–Berlekamp algorithm was founded. By introducing an analytic approach to coset–leader decoders for Reed–Solomon codes, the Welch–Berlekamp key-equation of error corrections is enlarged and a complete proof of the Welch–Berlekamp theorem is derived in a natural way, and the theorem is extended such that the BCH-bound constraint is moved.     

Is there an alternative to the european farm typology?

The 1978 European Community Typology for Agricultural Holdings is described in this paper and contrasted with a data based, polythetic-multivariate classification based on cluster analysis.

The requirement to reduce the size of the variable set employed in an optimisation-partition method of clustering suggested the value of principal components and factor analysis for the identification of major ‘source’ dimensions against which to measure farm differences and similarities.

The Euclidean cluster analysis incorporating the reduced dimensions quickly converged to a stable solution and was little influenced by the initial number or nature of ‘seeding’ partitions of the data.

The assignment of non-sampled observations from the population to cluster classes was completed using classification functions.

The final scheme, based on a sample of over 2,000 observations, was found to be both capable of interpretation and meaningful in terms of agricultural structure and practice and much superior in its explanatory power when compared with a version of the principal activity typology.     

On the use of between–within models to adjust for confounding due to unmeasured cluster-level covariates

Between–within models are generalized linear mixed models (GLMMs) for clustered data that incorporate a random intercept together with fixed effects for within-cluster and between-cluster covariates; the between-cluster covariates represent the cluster means of the within-cluster covariates. One popular use of these models is to adjust for confounding of the effect of within-cluster covariates due to unmeasured between-cluster covariates. Previous research has shown via simulations that using this approach can yield inconsistent estimators. We present theory and simulations as evidence that a primary cause of the inconsistency is heteroscedasticity of the linearized version of the GLMM used for estimation.     

On the maximization of likelihoods belonging to the exponential family using a Levenberg–Marquardt approach

The Levenberg–Marquardt algorithm is a flexible iterative procedure used to solve non-linear least-squares problems. In this work, we study how a class of possible adaptations of this procedure can be used to solve maximum-likelihood problems when the underlying distributions are in the exponential family. We formally demonstrate a local convergence property and discuss a possible implementation of the penalization involved in this class of algorithms. Applications to real and simulated compositional data show the stability and efficiency of this approach.     

Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

We explore criteria that data must meet in order for the Kruskal–Wallis test to reject the null hypothesis by computing the number of unique ranked datasets in the balanced case where each of the m alternatives has n observations. We show that the Kruskal–Wallis test tends to be conservative in rejecting the null hypothesis, and we offer a correction that improves its performance. We then compute the number of possible datasets producing unique rank-sums. The most commonly occurring data lead to an uncommonly small set of possible rank-sums. We extend prior findings about row- and column-ordered data structures.     

On the pade tablé and its relationship to the r and sarrays and arm a modeling

The Box-Jenkins method is a popular and important technique for modeling and forecasting of time series. Unfortunately the problem of determining the appropriate ARMA forecasting model (or indeed if an ARMA model holds) is a major drawback to the use of the Box-Jenkins methodology. Gray et al. (1978) and Woodward and Gray (1979) have proposed methods of estimating p and qin ARMA modeling based on the R and Sarrays that circumvent some of these modeling difficulties.

In this paper we generalize the R and S arrays by showing a relationship to Padé approximunts and then show that these arrays have a much wider application than in just determining model order. Particular non-ARMA models can be identified as well. This includes certain processes that consist of deterministic functions plus ARMA noise, indeed we believe that the combined R and S arrays are the best overall tool so fur developed for the identification of general 2nd order (not just stationary) time scries models.     

Constrained Maximization of the Shapiro–Wilk W Statistic to Estimate Parameters of the Johnson S B Distribution

This article presents a constrained maximization of the Shapiro Wilk W statistic for estimating parameters of the Johnson S _B distribution. The gradient of the W statistic with respect to the minimum and range parameters is used within a quasi-Newton framework to achieve a fit for all four parameters. The method is evaluated with measures of bias and precision using pseudo-random samples from three different S _B populations. The population means were estimated with an average relative bias of less than 0.1% and the population standard deviations with less than 4.0% relative bias. The methodology appears promising as a tool for fitting this sometimes difficult distribution.     

An Alternative to Efron's Redistribution-of-Mass Construction of the Kaplan—Meier Estimator

Kaplan and Meier (1958) derived the nonparametric maximum likelihood estimator of the survival function for the case in which some survival times are right-censored. Efron (1967) proposed a redistribution-of-mass construction of the Kaplan—Meier estimator that emphasized and illustrated the contribution of the censored observations. This article presents an alternative construction that, unlike Efron's method, redistributes the mass initially associated with each censored observation directly to the uncensored observations. The proposed construction avoids distributing a given mass more than once and provides additional insight into the nature of the Kaplan—Meier estimator.