Jason W. Osborne

Correlation and, more generally, association is a basic staple of inferential statistics, often easily computed with handheld calculators, simple spreadsheet software, and even by hand. Most modern researchers compute correlations and other indices of relatedness without thinking deeply about their choices. Despite being basic in the current pantheon of analytic options, measures of association are important, almost ubiquitous, and can easily produce errors of inference if not utilized thoughtfully and with attention to detail.

Those individuals who visit doctors are more likely to die than those who do not—a significant and replicable correlation in the literature. Do we have an epidemic of homicidal doctors rampaging through our society? Or is it, perhaps, an artifact of another variable? Perhaps people who are more ill, and therefore more likely to die, are those most likely to visit doctors. Or perhaps there is a curvilinear effect, such that those most likely to visit doctors are either very health conscious or very ill, and the former group are much less likely to die and the latter group much more likely to die. Regardless of what is truly going on, we cannot begin to ...

In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least as fast as iterates of the {\it minimum} modulus, and obtain new results related to Eremenko's conjecture and Baker's conjecture, and the rate of escape in Baker domains. To do this we prove a result of wider interest concerning the existence of points that escape to infinity under the iteration of a positive continuous function.

Neuroendocrine data are typically positively skewed and rarely conform to the expectations of a Gaussian distribution. This can be a problem when attempting to analyse results within the framework of the general linear model, which relies on assumptions that residuals in the data are normally distributed. One frequently used method for handling violations of this assumption is to transform variables to bring residuals into closer alignment with assumptions (as residuals are not directly manipulated). This is often attempted through ad hoc traditional transformations such as square root, log and inverse. However, Box and Cox (Box & Cox, 1964 ) observed that these are all special cases of power transformations and proposed a more flexible method of transformation for researchers to optimise alignment with assumptions. The goal of this paper is to demonstrate the benefits of the infinitely flexible Box–Cox transformation on neuroendocrine data using syntax in spss. When applied to positively skewed data typical of neuroendocrine data, the majority (~2/3) of cases were brought into strict alignment with Gaussian distribution (i.e. a non-significant Shapiro–Wilks test). Those unable to meet this challenge showed substantial improvement in distributional properties. The biggest challenge was distributions with a high ratio of kurtosis to skewness. We discuss how these cases might be handled, and we highlight some of the broader issues associated with transformation. Copyright © 2016 John Wiley & Sons, Ltd.

Purpose The neck disability index (NDI) as a 10-item patient reported outcome (PRO) measure is the most commonly used whiplash associated disorders (WAD) assessment tool. However, statistical rigor and factor structure are not definitive. To date, confirmatory factor analysis (CFA) has not examined whether the factor structure generalizes across different groups (e.g., WAD versus non-WAD). This study aimed to determine the psychometric properties of the NDI in these population groups. Methods This study used CFA to analyze NDI baseline-data for WAD (n = 804; 69 % females) and non-WAD (n = 963; 67 % females), each for the full sample and separate genders. Invariance analyses examined the NDI structure across the four groups. Results Across both populations and gender subgroups the one-factor solutions consistently showed better model fit over two-factor solutions. The NDI was best characterized as one-dimensional and invariant across multiple sub-groups. Conclusion The NDI remains a valid PRO in WAD populations that provides acceptable measurement of neck status that is appropriate for basic functional assessment across genders. However, it is recommended that both clinicians and researchers initiate the transition toward more rigorous and less ambiguous PRO measurement tools for WAD patients and research. This future graduated movement toward other PROs should consider both regional PROs and computerized decision support systems, initially measured concurrently with the NDI to establish ways to convert existing scored data prior to their singular use.