There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Researchers often conduct mediation analysis in order to indirectly assess the effect of a proposed cause on some outcome through a proposed mediator. The utility of mediation analysis stems from its ability to go beyond the merely descriptive to a more functional understanding of the relationships among variables. A necessary component of mediation is a statistically and practically significant indirect effect. Although mediation hypotheses are frequently explored in psychological research, formal significance tests of indirect effects are rarely conducted. After a brief overview of mediation, we argue the importance of directly testing the significance of indirect effects and provide SPSS and SAS macros that facilitate estimation of the indirect effect with a normal theory approach and a bootstrap approach to obtaining confidence intervals, as well as the traditional approach advocated by Baron and Kenny (1986). We hope that this discussion and the macros will enhance the frequency of formal mediation tests in the psychology literature. Electronic copies of these macros may be downloaded from the Psychonomic Society's Web archive at www.psychonomic.org/archive/.

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SPSS and SAS procedures for estimating indirect effects in simple mediation models.

Background The analysis of microbial communities through DNA sequencing brings many challenges: the integration of different types of data with methods from ecology, genetics, phylogenetics, multivariate statistics, visualization and testing. With the increased breadth of experimental designs now being pursued, project-specific statistical analyses are often needed, and these analyses are often difficult (or impossible) for peer researchers to independently reproduce. The vast majority of the requisite tools for performing these analyses reproducibly are already implemented in R and its extensions (packages), but with limited support for high throughput microbiome census data. Results Here we describe a software project, phyloseq, dedicated to the object-oriented representation and analysis of microbiome census data in R. It supports importing data from a variety of common formats, as well as many analysis techniques. These include calibration, filtering, subsetting, agglomeration, multi-table comparisons, diversity analysis, parallelized Fast UniFrac, ordination methods, and production of publication-quality graphics; all in a manner that is easy to document, share, and modify. We show how to apply functions from other R packages to phyloseq-represented data, illustrating the availability of a large number of open source analysis techniques. We discuss the use of phyloseq with tools for reproducible research, a practice common in other fields but still rare in the analysis of highly parallel microbiome census data. We have made available all of the materials necessary to completely reproduce the analysis and figures included in this article, an example of best practices for reproducible research. Conclusions The phyloseq project for R is a new open-source software package, freely available on the web from both GitHub and Bioconductor.

/pdf/phyloseq-an-r-package-for-reproducible-interactive-analysis-1ez1xx3dlr.pdf

phyloseq: an R package for reproducible interactive analysis and graphics of microbiome census data.

This article provides researchers with a guide to properly construe and conduct analyses of conditional indirect effects, commonly known as moderated mediation effects. We disentangle conflicting definitions of moderated mediation and describe approaches for estimating and testing a variety of hypotheses involving conditional indirect effects. We introduce standard errors for hypothesis testing and construction of confidence intervals in large samples but advocate that researchers use bootstrapping whenever possible. We also describe methods for probing significant conditional indirect effects by employing direct extensions of the simple slopes method and Johnson-Neyman technique for probing significant interactions. Finally, we provide an SPSS macro to facilitate the implementation of the recommended asymptotic and bootstrapping methods. We illustrate the application of these methods with an example drawn from the Michigan Study of Adolescent Life Transitions, showing that the indirect effect of intrinsic student interest on mathematics performance through teacher perceptions of talent is moderated by student math self-concept.

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Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions.

Hadley Wickham1, Mara Averick1, Jennifer Bryan1, Winston Chang1, Lucy D’Agostino McGowan8, Romain François1, Garrett Grolemund1, Alex Hayes12, Lionel Henry1, Jim Hester1, Max Kuhn1, Thomas Lin Pedersen1, Evan Miller13, Stephan Milton Bache3, Kirill Müller2, Jeroen Ooms14, David Robinson5, Dana Paige Seidel10, Vitalie Spinu4, Kohske Takahashi9, Davis Vaughan1, Claus Wilke6, Kara Woo7, and Hiroaki Yutani11

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Welcome to the Tidyverse

In the light of continuing debate over the applications of significance testing in psychology journals and following the publication of Cohen's (1994) article, the Board of Scientific Affairs (BSA) of the American Psychological Association (APA) convened a committee called the Task Force on Statistical Inference (TFSI) whose charge was "to elucidate some of the controversial issues surrounding applications of statistics including significance testing and its alternatives; alternative underlying models and data transformation; and newer methods made possible by powerful computers" (BSA, personal communication, February 28, 1996). Robert Rosenthal, Robert Abelson, and Jacob Cohen (cochairs) met initially and agreed on the desirability of having several types of specialists on the task force: statisticians, teachers of statistics, journal editors, authors of statistics books, computer experts, and wise elders. Nineindividuals were subsequently invited to join and all agreed. These were Leona Aiken, Mark Appelbaum, Gwyneth Boodoo, David A. Kenny, Helena Kraemer, Donald Rubin, Bruce Thompson, Howard Wainer, and Leland Wilkinson. In addition, Lee Cronbach, Paul Meehl, Frederick Mosteller and John Tukey served as Senior Advisors to the Task Force and commented on written materials.

/pdf/statistical-methods-in-psychology-journals-guidelines-and-2dxv2y8x6m.pdf

Statistical Methods in Psychology Journals: Guidelines and Explanations

The cluster heat map is an ingenious display that simultaneously reveals row and column hierarchical cluster structure in a data matrix. It consists of a rectangular tiling, with each tile shaded on a color scale to represent the value of the corresponding element of the data matrix. The rows (columns) of the tiling are ordered such that similar rows (columns) are near each other. On the vertical and horizontal margins of the tiling are hierarchical cluster trees. This cluster heat map is a synthesis of several different graphic displays developed by statisticians over more than a century. We locate the earliest sources of this display in late 19th century publications, and trace a diverse 20th century statistical literature that provided a foundation for this most widely used of all bioinformatics displays.

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The History of the Cluster Heat Map

The Grammar of Graphics, or GOG, denotes a system with seven orthogonal components. By orthogonal, we mean there are seven graphical component sets whose elements are aspects of the general system and that every combination of aspects in the product of all these sets is meaningful. This sense of the word orthogonality, a term used by computer designers to describe a combinatoric system of components or building blocks, is in some sense similar to the orthogonal factorial analysis of variance (ANOVA), where factors have levels and all possible combinations of levels exist in the ANOVA design. If we interpret each combination of features in a GOG system as a point in a network, then the world described by GOG is represented in a seven-dimensional rectangular lattice.

The Grammar of Graphics

The psychophysicist S.S. Stevens developed a measurement scale typology that has dominated social statistics methodology for almost 50 years. During this period, it has generated considerable controversy among statisticians. Recently, there has been a renaissance in the use of Stevens's scale typology for guiding the design of statistical computer packages. The current use of Stevens's terminology fails to deal with the classical criticisms at the time it was proposed and ignores important developments in data analysis over the last several decades.

https://www.cs.uic.edu/~wilkinson/Publications/stevens.pdf

Nominal, Ordinal, Interval, and Ratio Typologies are Misleading

We introduce Tukey and Tukey scagnostics and develop graph-theoretic methods for implementing their procedure on large datasets.

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Leland Wilkinson

Papers

Statistical Methods in Psychology Journals: Guidelines and Explanations

The History of the Cluster Heat Map

The Grammar of Graphics

Nominal, Ordinal, Interval, and Ratio Typologies are Misleading

Graph-theoretic scagnostics