The inverse coefficient of variation (ICV) has gained significant attention as a preferred measure in fields such as economics, healthcare, and clinical trials. This makes it desirable for researchers to determine appropriate sample sizes when using sample-based estimators to estimate the population ICV. In this paper, we derive both the moment and Bayes estimators of the ICV under a skew-normal distribution, and use them to develop equations for sample size determination based on the A Priori Procedure (APP). The multivariate skew-normal model introduces a flexible dependence structure through its shape parameters, allowing correlation patterns that cannot be captured by the standard multivariate normal model. This dependence directly affects the behavior of the ICV estimators and plays an important role in determining the required sample sizes, highlighting the benefits of jointly modeling skewness and dependence. We further construct confidence intervals and evaluate their coverage probabilities via Monte Carlo simulations. Finally, a real-world dataset is analyzed to illustrate the practical applicability of the proposed methodology.

Gain-Probability (G-P) analysis quantifies the probability that a randomly selected individual from one group scores higher or lower than an individual from another group, by varying magnitudes. While G-P methods have been developed under normality and various skewed distributions, symmetric heavy-tailed settings remain largely unexplored, despite their prevalence in finance, environmental science, and other applied domains. We extend the G-P framework to the broad family of scale mixtures of normal (SMN) distributions, including the Student's t, slash, variance gamma (VG), and Pearson Type VII distributions. Analytical expressions for G-P under SMN are derived for both independent and matched data, and parameter estimation is performed using the expectation maximisation (EM) algorithm. Simulation studies show that the proposed estimators are accurate, robust to heavy tails, and improve with sample size, with performance most sensitive to group separation and noise level. An application to daily returns of US and Chinese equity indices demonstrates how G-P analysis captures distributional tail effects that are overlooked by traditional tests. The results support G-P analysis under SMN as a practical, interpretable alternative to significance testing, enabling robust inference for symmetric heavy-tailed data in diverse applied settings.

According to Shiffrin et al. (2026), scientists incompletely understand the phenomena they study. I agree and expand on Shiffrin et al. with a focus on the necessity to make auxiliary assumptions as an additional reason for incomplete understanding.

Researchers using a hierarchical regression paradigm enter different variables at different steps in the analysis, each time determining ΔR². Although ΔR² is traditional for both zero-order correlation coefficients and multiple correlation coefficients, it is not the only possibility. It is also possible to use binomial effect size displays and gain-probability analyses to interpret zero-order correlation coefficients. However, nobody has explored the possibility of extending these latter advances from zero-order correlation coefficients to the multiple correlation coefficients obtained in successive steps of hierarchical regression analyses. The present exposition and tutorial show that binomial effect size display and gain-probability interpretations can imply different conclusions both from each other and from ΔR². The message is not that a single interpretation should dominate but that multiple interpretations provide researchers with a more thorough and comprehensive understanding of the implications of the data. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Researchers and philosophers interested in findings pertaining to social behaviour, or theory of social behaviour, are necessarily concerned with generalising findings, theory or both. There are statistical issues that are ignored at one's peril, pertaining to generalising from a sample to the population from which that sample was drawn. However, if the goal is to generalise to other populations, more conceptual issues come into play. Moreover, if the goal is to test a theory's ability to generalise or be useful for an applied goal, yet more conceptual issues come into play. The present aim is to clarify some of these issues, including relevant questions, so researchers and philosophers can better understand that although certain statistical issues are always relevant, there are many conceptual issues that are sometimes relevant and sometimes not. Those who are interested in social behaviour must necessarily be interested in generalising something, and so the issues discussed are ubiquitously germane.

The interpretation of correlation coefficients has invoked considerable discussion over many decades. One interpretive procedure is to use the coefficient of determination-the squared correlation coefficient-to index variance accounted for in one variable by variance in the other variable. A second interpretive procedure is to construct binomial effect size displays that involve dichotomizing continuous dependent variables. The present goal is to present a third interpretive procedure, with tutorial, to estimate probabilistic (dis)advantages implied by correlation coefficients and construct gain-probability diagrams. The proposed procedure does not involve dichotomizing continuous dependent variables, thereby losing information. In addition, the proposed procedure extends well to comparing correlation coefficients and facilitates subtle and nuanced implications that can enhance theoretical specificity. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

The importance of preregistration has gained recent traction in psychology. To reduce questionable research practices and improve the credibility of research findings, researchers preregister important details before commencing with data collection. However, current preregistration practices miss an important issue when it comes to evaluating predictions. That is because predictions depend not only on theoretical terms but also auxiliary assumptions. Auxiliary assumptions traverse the distance from nonobservational theoretical terms to observational terms at the level of the empirical hypotheses. Because the credibility of study findings depends on the appraisal of auxiliary assumptions, these assumptions should, at least, be considered in preregistration practices. In this paper we outline the need to consider auxiliary assumptions during preregistration, the benefits of doing so, and how current practices can be amended to accommodate them. If the need for researchers to preregister continues to increase and the belief is that doing so will increase the credibility of psychological research, we believe auxiliary assumptions should become part of these practices.

Researchers on terror-management theory (TMT) often obtain effects on dependent variables, such as worldview assertion, after a delay following mortality salience (contemplating death) but not immediately. As justification, TMT researchers invoked a post hoc assumption: Death thoughts are immediately suppressed following mortality salience but rebound after a delay. In contradiction, Trafimow and Hughes and Rife et al. found that death thoughts are more accessible immediately following mortality salience than after a delay. The contradiction is so problematic that ignoring it trends toward degenerative science. TMT research might exemplify a larger problem in psychology.

There have been significant advances in the science of meaning in life (MIL). Researchers have made empirical predictions about the antecedents and consequences of meaning and the best ways it can be enhanced. Yet, it is important that researchers in this area consider the auxiliary assumptions associated with their predictions. Auxiliary assumptions, which traverse the distance from nonobservational theoretical terms to observational terms at the level of the empirical hypotheses, have important implications for the appraisal of empirical victories and defeats. In this paper, we outline the importance of auxiliary assumptions in MIL research. To ensure the validity of findings associated with MIL, we hope this paper encourages researchers to pay close attention to the auxiliary assumptions associated with their predictions.

Most basic researchers who collect data do so with the goal of testing theories. However, there is disagreement among realists versus pragmatists about whether theories are best characterized in terms of truth or verisimilitude, or in terms of problem-solving ability. Nonetheless, authorities in both philosophical camps agree that empirical hypotheses can be true or false. Consequently, tests of empirical hypotheses are straightforward. In contrast, the present thesis is that even tests of empirical hypotheses may be less straightforward than researchers appreciate. Gain-probability thinking can clarify crucial caveats and qualifications.

Despite being only a few years old, there is already a reasonably large literature on the a priori procedure, designed to aid researchers in determining sample sizes needed to ensure that sample statistics to be obtained provide good estimates of corresponding population parameters. One of the directions this literature has taken has been to expand the typical assumption of normally distributed data to include skew normally distributed data. In turn, the expansion allows the use of locations, or differences in locations; as opposed merely to means, or differences in means. Another direction the expansion has taken is to consider correlation coefficients. However, there is considerable mathematics associated with both expansions that might not be accessible to most substantive researchers. Therefore, the present goal is to provide links to free and user-friendly programs so that even mathematically unsophisticated substantive researchers can perform the calculations.

Based on previous research featuring generalized distributions, we propose an extension to both generalized skew normal distributions introduced [14] and skew flexible normal distributions proposed by Gómez et al. [9]. The properties of this family of distributions are explored, and the parameters are estimated using the maximum likelihood method. Two simulation studies are conducted, along with two real data examples, to demonstrate the primary findings.

Because they sometimes conflate basic and applied research goals, social scientists rely on problematic null hypothesis statistical testing (NHST) to decide their empirical studies' theoretical and practical implications. For basic social science research, population predictions based on single studies provide insufficient evidence for deciding a tested theory's truthfulness and usefulness. Whether or not such studies can contribute to practical decision-making, their predictions must meaningfully augment that theory's support. In contrast, applied social science research for public policymakers and regulators must present predictions in a way that improves practical decision-making. As a result, gain-probability (G-P) analyses rather than NHST and effect size calculations can better inform theoretical and practical decisions regardless of research type. Furthermore, the theoretical and practical issues addressed by adopting G-P analysis can be considered within a larger philosophical context.

ABSTRACTTo a naïve falsificationist, one theory‐refuting finding falsifies a theory. In contrast, sophisticated science philosophers have emphasised larger research systems that include theories and auxiliary assumptions. Theory‐refuting findings can be accommodated by blaming poor auxiliary assumptions, refining theories, improving auxiliary assumptions, or pronouncing that the benefits of the research system render theory‐refuting findings unimportant. Popper, Kuhn, Lakatos, and Laudan have proposed research systems, with many disagreements between them. The present thesis is that each proposal is subject to two caveats. None of these philosophers sufficiently considered the opportunity costs associated with ignoring theory‐refuting findings. Secondly, it is not clear that previous pronouncements about how research systems work in the hard sciences necessarily apply well to modern psychological science. The interaction of these issues suggests that theory‐refuting findings may have more potential for mattering in modern psychology than would seem apparent from sophisticated research system perspectives.

Archer advised psychology researchers to reject replication and experimentalism. The present comment counters Archer’s recommendations. Researchers should be more, not less, concerned with methodology to improve the quality of replication attempts and more convincingly test theories.

There is a trepidation, anxiety, or intuition, which has persisted for more than a century, that psychology theories are less anchored in fundamental laws than physics theories. Rather than attempt to refute the concern, the present work accepts it and tries out candidate explanations. These pertain to empirical laws, parsimony, scope, reductionism, falsifiability, mathematical operations (multiplication vs. addition), internal coherence, ceteris paribus stipulations, and purposeful omission of relevant factors (idealization). The conceptions underlying these explanations are not strictly independent, but they point to different distinctive features that might account for the unequal status of physics and psychological science and to different means of improving contemporary psychology. Although the available evidence for or against these candidate explanations is scarce and relies mainly on a few telling examples, we conclude that the last of our candidate explanations-reliance on idealized universes-works best and leads to the most insights about what psychology might learn from physics and what research strategies might foster the ideal of theory-driven psychological science in the future. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

The focus of the present article is not on failures to replicate but on the more optimistically framed and more fruitful question: What stable findings can be reproduced reliably and can be trusted by decision makers, managers, health agents, or politicians? We propagate the working hypothesis that a twofold key to stable and replicable findings lies in the existence of theoretical constraints and, no less important, in researchers' sensitivity to metatheoretical, auxiliary assumptions. We introduce a hierarchy of four levels of theoretical constraints-a priori principles, psychophysical, empirical, and modelling constraints-combined with the TASI taxonomy of theoretical, auxiliary, statistical, and inferential assumptions Trafimow, Journal for the Theory of Social Behaviour, 52, 37-48, (2022). Although theoretical constraints clearly facilitate stable and replicable research findings, TASI reminds us of various reasons why even perfectly valid hypotheses need not always be borne out. The presented framework should help researchers to operationalize conditions under which theoretical constraints render empirical findings most predictable.

Psychologists have a traditional concern with participant samples from narrow populations and deleterious effects on researchers' ability to generalize findings. Recently, both individuals and authoritative organizations, such as the American Psychological Association, have merged this external validity concern with diversity and inclusion concerns. The American Psychological Association directive for researchers to include diverse samples seems obviously well-taken as it purports to mitigate these problems at once; it simultaneously increases external validity and promotes diversity and inclusion. However, we show that there are complications. These include problems with internal and external validity conceptualizations; that sometimes generalization failures can support, rather than detract from, external validity; the crucial role auxiliary assumptions play in impacting internal and external validity; Lakatosian degenerative science and its problematic application; and distinguishing between merely including diverse groups in research samples versus analyzing for group differences. These complications imply a nuanced perspective of whether samples from narrow populations are undesirable. That a sample is from a narrow population might, or might not, preclude strong support or disconfirmation for the theory, including its ability to generalize. Our nuanced perspective militates against the current trend of journal directives to require diverse samples. Sample suitability for particular researcher goals should be judged on a case-by-case basis that takes into account that sometimes samples from narrow populations can nevertheless engender impressive scientific progress and sometimes not.

The a priori procedure (APP) is concerned with determining appropriate sample sizes to ensure that sample statistics to be obtained are likely to be good estimates of corresponding population parameters. Previous APP work pertaining to proportions has used the normal approximation to the binomial distribution, but this is problematic when the population proportion is near zero or one. The present contribution addresses the issue in four ways. First, we add a skew normal approximation that does a better job than the normal approximation. Second, we add a Bayesian component making use of a prior beta distribution that is conjugate to the binomial distribution. Third, we provide simulations and real data examples, one of them is a set of Covid-19 data. Finally, we include free and user-friendly computer programs to aid researchers in making the calculations.