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In statistical modeling, we strive to specify models that resemble data collected in studies or observed from processes. Consequently, distributional specification and parameter estimation are central to parametric models. Graphical procedures, such as the quantile-quantile (Q-Q) plot, are arguably the most widely used method of distributional assessment, though critics find their interpretation to be overly subjective. Formal goodness of fit tests are available and are quite powerful, but only indicate whether there is a lack of fit, not why there is lack of fit. In this article, we explore the use of the lineup protocol to inject rigor into graphical distributional assessment and compare its power to that of formal distributional tests. We find that lineup tests are considerably more powerful than traditional tests of normality. A further investigation into the design of Q-Q plots shows that de-trended Q-Q plots are more powerful than the standard approach as long as the plot preserves distances in x and y to be the same. While we focus on diagnosing nonnormality, our approach is general and can be directly extended to the assessment of other distributions.

Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian data analysis, like all data analysis, is an iterative process of model building, inference, model checking and evaluation, and model expansion. Visualization is helpful in each of these stages of the Bayesian workflow and it is indispensable when drawing inferences from the types of modern, high dimensional models that are used by applied researchers.

Data from complex surveys are being used increasingly to build the same sort of explanatory and predictive models used in the rest of statistics. Although the assumptions underlying standard statistical methods are not even approximately valid for most survey data, analogues of most of the features of standard regression packages are now available for use with survey data. We review recent developments in the field and illustrate their use on data from NHANES.

Boxplots are useful displays that convey rough information about the distribution of a variable. Boxplots were designed to be drawn by hand and work best for small datasets, where detailed estimates of tail behavior beyond the quartiles may not be trustworthy. Larger datasets afford more precise estimates of tail behavior, but boxplots do not take advantage of this precision, instead presenting large numbers of extreme, though not unexpected, observations. Letter-value plots address this problem by including more detailed information about the tails using \"letter values,\" an order statistic defined by Tukey. Boxplots display the first two letter values (the median and quartiles); letter-value plots display further letter values so far as they are reliable estimates of their corresponding quantiles. We illustrate letter-value plots with real data that demonstrate their usefulness for large datasets. All graphics are created using the R package lvplot , and code and data are available in the supplementary materials.

Abstract Statistical graphics, and data visualization, play an essential but under-utilized, role for data analysis in animal science, and also to visually illustrate the concepts, ideas, or outputs of research and in curricula. The recent rise in web technologies and ubiquitous availability of web browsers enables easier sharing of interactive and dynamic graphics. Interactivity and dynamic feedback enhance human–computer interaction and data exploration. Web applications such as decision support systems coupled with multimedia tools synergize with interactive and dynamic graphics. However, the importance of graphics for effectively communicating data, understanding data uncertainty, and the state of the field of interactive and dynamic graphics is underappreciated in animal science. To address this gap, we describe the current state of graphical methodology and technology that might be more broadly adopted. This includes an explanation of a conceptual framework for effective graphics construction. The ideas and technology are illustrated using publicly available animal datasets. We foresee that many new types of big and complex data being generated in precision livestock farming create exciting opportunities for applying interactive and dynamic graphics to improve data analysis and make data-supported decisions.

A grammar of graphics is a tool that enables us to concisely describe the components of a graphic. Such a grammar allows us to move beyond named graphics (e.g., the \"scatterplot\") and gain insight into the deep structure that underlies statistical graphics. This article builds on Wilkinson, Anand, and Grossman (2005), describing extensions and refinements developed while building an open source implementation of the grammar of graphics for R, ggplot2 . The topics in this article include an introduction to the grammar by working through the process of creating a plot, and discussing the components that we need. The grammar is then presented formally and compared to Wilkinson's grammar, highlighting the hierarchy of defaults, and the implications of embedding a graphical grammar into a programming language. The power of the grammar is illustrated with a selection of examples that explore different components and their interactions, in more detail. The article concludes by discussing some perceptual issues, and thinking about how we can build on the grammar to learn how to create graphical \"poems.\" Supplemental materials are available online.

The aim of the article is to introduce an effective structural and functional model for the socialization and development of these children through group work, implemented in out-of-school education institutions (SFM). The study presents a comprehensive model comprising target, substantive, organizational, procedural, result-oriented, and analytical components. It outlines content and methodological support for socialization and development in various areas, such as naturalistic, tourist, local history, artistic, and aesthetic domains. It also highlights the essential spatial-subject, psycho-didactic, and social conditions required for an inclusive educational environment.

We propose to furnish visual statistical methods with an inferential framework and protocol, modelled on confirmatory statistical testing. In this framework, plots take on the role of test statistics, and human cognition the role of statistical tests. Statistical significance of 'discoveries' is measured by having the human viewer compare the plot of the real dataset with collections of plots of simulated datasets. A simple but rigorous protocol that provides inferential validity is modelled after the 'lineup' popular from criminal legal procedures. Another protocol modelled after the 'Rorschach' inkblot test, well known from (pop-)psychology, will help analysts acclimatize to random variability before being exposed to the plot of the real data. The proposed protocols will be useful for exploratory data analysis, with reference datasets simulated by using a null assumption that structure is absent. The framework is also useful for model diagnostics in which case reference datasets are simulated from the model in question. This latter point follows up on previous proposals. Adopting the protocols will mean an adjustment in working procedures for data analysts, adding more rigour, and teachers might find that incorporating these protocols into the curriculum improves their students' statistical thinking.

This article discusses how to make statistical graphics a more prominent element of the undergraduate statistics curricula. The focus is on several different types of assignments that exemplify how to incorporate graphics into a course in a pedagogically meaningful way. These assignments include having students deconstruct and reconstruct plots, copy masterful graphs, create one-minute visual revelations, convert tables into \"pictures,\" and develop interactive visualizations, for example, with the virtual earth as a plotting canvas. In addition to describing the goals and details of each assignment, we also discuss the broader topic of graphics and key concepts that we think warrant inclusion in the statistics curricula. We advocate that more attention needs to be paid to this fundamental field of statistics at all levels, from introductory undergraduate through graduate level courses. With the rapid rise of tools to visualize data, for example, Google trends, GapMinder, ManyEyes, and Tableau, and the increased use of graphics in the media, understanding the principles of good statistical graphics, and having the ability to create informative visualizations is an ever more important aspect of statistics education. Supplementary materials containing code and data for the assignments are available online.

The complexity of linear mixed-effects (LME) models means that traditional diagnostics are rendered less effective. This is due to a breakdown of asymptotic results, boundary issues, and visible patterns in residual plots that are introduced by the model fitting process. Some of these issues are well known and adjustments have been proposed. Working with LME models typically requires that the analyst keeps track of all the special circumstances that may arise. In this article, we illustrate a simpler but generally applicable approach to diagnosing LME models. We explain how to use new visual inference methods for these purposes. The approach provides a unified framework for diagnosing LME fits and for model selection. We illustrate the use of this approach on several commonly available datasets. A large-scale Amazon Turk study was used to validate the methods. R code is provided for the analyses. Supplementary materials for this article are available online.