With the objective of identifying intrinsic forms of mathematical production in complex analysis (CA), this study presents an analysis of the mathematical activity of five original works that contributed to the development of Cauchy's integral theorem. The analysis of the mathematical activity was carried out through the identification of the…

In narrative synthesis of evidence, it can be the case that the only quantitative measures available concerning the efficacy of an intervention is the direction of the effect, that is, whether it is positive or negative. In such situations, the sign test has been proposed in the literature and in recent Cochrane guidelines as a way to test whether…

Researchers are often inclined to test agreement or discrepancy hypotheses using difference scores. This commentary explains 2 mathematical-statistical principles underlying associations with difference scores and 2 conceptual-interpretation problems that make difference scores inappropriate for testing such hypotheses. The commentary provides…

In linear regression models estimated by ordinary least squares, it is often desirable to use hypothesis tests and confidence intervals that remain valid in the presence of heteroskedastic errors. Wald tests based on heteroskedasticity-consistent covariance matrix estimators (HCCMEs, also known as sandwich estimators or simply "robust"…

The article provides perspectives on p values, null hypothesis testing, and alternative techniques in light of modern robust statistical methods. Null hypothesis testing and "p" values can provide useful information provided they are interpreted in a sound manner, which includes taking into account insights and advances that have…

The ability to generate novel hypotheses is an important problem-solving capacity of humans. This ability is vital for making sense of the complex and unfamiliar world we live in. Often, this capacity is characterized as an inference to the best explanation--selecting the "best" explanation from a given set of candidate hypotheses.…

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects…

In the field of cognitive psychology, the "p"-value hypothesis test has established a stranglehold on statistical reporting. This is unfortunate, as the "p"-value provides at best a rough estimate of the evidence that the data provide for the presence of an experimental effect. An alternative and arguably more appropriate measure of evidence is…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

This paper examines strategies for interpreting and reporting estimates of intervention effects for subgroups of a study sample. Specifically, the paper considers: why and how subgroup findings are important for applied research, the importance of pre-specifying sub- groups before analyses are conducted, the importance of using existing theory and…

Researchers often have expectations that can be expressed in the form of inequality constraints among the parameters of a structural equation model. It is currently not possible to test these so-called informative hypotheses in structural equation modeling software. We offer a solution to this problem using M"plus." The hypotheses are…

In Volume 23(2) of the "Australian Senior Mathematics Journal," Boncek and Harden present an exercise in fitting a Markov chain model to rainfall data for Darwin Airport (Boncek & Harden, 2009). Days are subdivided into those with precipitation and precipitation-free days. The author abbreviates these labels to wet days and dry days.…

This article explores the configural weighted average (CWA) hypothesis suggesting that extension biases, like conjunction and disjunction errors, occur because people estimate compound probabilities by taking a CWA of the constituent probabilities. The hypothesis suggests a process consistent with well-known cognitive constraints, which…

This article extends the Bonett (2003a) approach to testing the equality of alpha coefficients from two independent samples to the case of m [greater than or equal] 2 independent samples. The extended Fisher-Bonett test and its competitor, the Hakstian-Whalen (1976) test, are illustrated with numerical examples of both hypothesis testing and power…

The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to…