Michael Friendly | York University (original) (raw)

Papers by Michael Friendly

Journal of Computational and Graphical Statistics, 2013

Springer Handbooks Comp.Statistics, 2008

It is common to think of statistical graphics and data visualization as relatively modern develop... more It is common to think of statistical graphics and data visualization as relatively modern developments in statistics. In fact, the graphic representation of quantitative information has deep roots. These roots reach into the histories of the earliest map-making and visual depiction, and later into thematic cartography, statistics and statistical graphics, medicine, and other fields. Along the way, developments in technologies (printing, reproduction) mathematical theory and practice, and empirical observation and recording, enabled the wider use of graphics and new advances in form and content.

Journal of Experimental Psychology: Human Learning & Memory, 1980

In 2 experiments, a total of 13 Ss learned subspan and supraspan lists by sorting list items into... more In 2 experiments, a total of 13 Ss learned subspan and supraspan lists by sorting list items into subsets. An item recognition task followed, and reaction time (RT) was found to be a bilinear function of memory list length. The slope for supraspan lists was more shallow than the slope for subspan lists. The RT data for supraspan lists were

Journal of the history of the behavioral sciences, 2005

Of all the graphic forms used today, the scatterplot is arguably the most versatile, polymorphic,... more Of all the graphic forms used today, the scatterplot is arguably the most versatile, polymorphic, and generally useful invention in the history of statistical graphics. Its use by Galton led to the discovery of correlation and regression, and ultimately to much of present multivariate statistics. So, it is perhaps surprising that there is no one widely credited with the invention of this idea. Even more surprising is that there are few contenders for this title, and this question seems not to have been raised before. This article traces some of the developments in the history of this graphical method, the origin of the term scatterplot, the role it has played in the history of science, and some of its modern descendants. We suggest that the origin of this method can be traced to its unique advantage: the possibility to discover regularity in empirical data by smoothing and other graphic annotations to enhance visual perception.

Hypothesis-error (or "HE") plots, introduced by , permit the visualization of hypothesis tests in... more Hypothesis-error (or "HE") plots, introduced by , permit the visualization of hypothesis tests in multivariate linear models by representing hypothesis and error matrices of sums of squares and cross-products as ellipses. This paper describes the implementation of these methods in R, as well as their extension, for example from two to three dimensions and by scaling hypothesis ellipses and ellipsoids in a natural manner relative to error. The methods, incorporated in the heplots package for R, exploit new facilities in the car package for testing linear hypotheses in multivariate linear models and for constructing MANOVA tables for these models, including models for repeated measures.

The graphic portrayal of quantitative information has deep roots. These roots reach into historie... more The graphic portrayal of quantitative information has deep roots. These roots reach into histories of thematic cartography, statistical graphics, and data visualization, which are intertwined with each other. They also connect with the rise of statistical thinking up through the 19th century, and developments in technology into the 20th century. From above ground, we can see the current fruit; we

Abstract: The graphical displays shown here are implemented in SAS/IMLsoftware whose combination ... more Abstract: The graphical displays shown here are implemented in SAS/IMLsoftware whose combination of matrix operations, built-inStatistical methods for categorical data, such as loglinear models functions for contingency table analysis, and graphics provide aand logistic regression, represent discrete analogs of the analysis of convenient environment for graphical display for multiwayvariance and regression methods for continuous response variables. categorical data (Friendly 1991a; 1992).

Memory & Cognition, 1986

To investigate the properties that make a word easy to recall, we added to existing norms for 925... more To investigate the properties that make a word easy to recall, we added to existing norms for 925 nouns measures of availability, goodness, emotionality, pronunciability, and probability of recall in multiple-trial free recall. Availability, imagery, and emotionality were found to be the best predictors of which words were recalled. This result, which is stable across recall data collected in three separate laboratories, argues for the importance of availability as apredictor of recall and questions the role of the correlated variables of word frequency and meaningfulness. Consistent with earlier work on a smaller sample of words, six factors describe the numerous properties of words studied by psychologists. The six factors are composed of variables based on orthography, imagery and meaning, word frequency, recall, emotionality, and goodness.

This paper first illustrates the use of mosaic displays and other graphical methods for the anal-... more This paper first illustrates the use of mosaic displays and other graphical methods for the anal-ysis of multiway contingency tables. We then introduce several extensions of mosaic displays designed to integrate graphical methods for categorical data with those used for quantitative data. For example, the scatterplot matrix shows all pairwise (marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models. and (b) a generalization of partial residual plots. The conditioning plot, or coplot shows a collection of (conditional) views of several vari...

Computational Statistics & Data Analysis, 2003

This paper outlines a general framework for ordering information in visual displays (tables and g... more This paper outlines a general framework for ordering information in visual displays (tables and graphs) according to the e ects or trends which we desire to see. This idea, termed e ect-ordered data displays, applies principally to the arrangement of unordered factors for quantitative data and frequency data, and to the arrangement of variables and observations in multivariate displays (star plots, parallel coordinate plots, and so forth).

... manuscript. John Fox suggested the use of the Duncan data, shared some of his unpublished wor... more ... manuscript. John Fox suggested the use of the Duncan data, shared some of his unpublished work, and reviewed several chapters. Georges Monette, Dick Goranson, and Herve Abdi also reviewed portions of the manuscript. Grateful ...

This paper describes graphical methods for multiple-response data within the framework of the mul... more This paper describes graphical methods for multiple-response data within the framework of the multivariate linear model (MLM), aimed at understanding what is being tested in a multivariate test, and how factor/predictor effects are expressed across multiple response measures. In particular, we describe and illustrate a collection of SAS macro programs for: (a) Data ellipses and low-rank biplots for multivariate data, (b) HE plots, showing the hypothesis and error covariance matrices for a given pair of responses, and a given effect, (c) HE plot matrices, showing all pairwise HE plots, and (d) low-rank analogs of HE plots, showing all observations, group means, and their relations to the response variables.

In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising... more In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising theories through the gener- ation and evaluation of precise predictions (e.g., Meehl, 1978). The study of personality structure through the five-factor model (FFM; McCrae & John, 1992) is an important area of research where one encounters many precise predictions. Extant methods of assessing such predictions, however, do not allow researchers to examine the outcome of the predictions in great detail. That is, it may be difficult to determine how estimates fail to match predicted values. As Meehl argued, one must examine how a theory fails to predict in order to refine and improve the theory. To promote better theory appraisal in FFM research, we present a powerful new tool, called a tableplot (Kwan, 2008a), that can summarize and clarify factor-analytic results. Specifically, we illustrate how the tableplot enables detailed appraisal of precise predictions in the FFM.

Zeitschrift für Psychologie / Journal of Psychology, 2009

In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising... more In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising theories through the generation and evaluation of precise predictions (e.g., Meehl, 1978). The study of personality structure through the five-factor model (FFM; McCrae & John, 1992) is an important area of research where one encounters many precise predictions. Extant methods of assessing such predictions, however, do not

Psychometrika, 1992

The purpose of this announcement is to describe a collection of general macro programs for statis... more The purpose of this announcement is to describe a collection of general macro programs for statistical graphics for use with the SAS System that have been made available in conjunction with the book, SAS system for statistical graphics, first edition (Friendly, 1991). The primary goals of the book are to survey the kinds of graphic displays that are useful for different questions and data, and to show how can these displays be done with the SAS System. It emphasizes displays that reveal aspects of data not easily captured in numerical summaries or tabular formats and diagnostic displays that help determine if assumptions of an analysis are met.

Journal of Computational and Graphical Statistics, 2013

Springer Handbooks Comp.Statistics, 2008

It is common to think of statistical graphics and data visualization as relatively modern develop... more It is common to think of statistical graphics and data visualization as relatively modern developments in statistics. In fact, the graphic representation of quantitative information has deep roots. These roots reach into the histories of the earliest map-making and visual depiction, and later into thematic cartography, statistics and statistical graphics, medicine, and other fields. Along the way, developments in technologies (printing, reproduction) mathematical theory and practice, and empirical observation and recording, enabled the wider use of graphics and new advances in form and content.

Journal of Experimental Psychology: Human Learning & Memory, 1980

In 2 experiments, a total of 13 Ss learned subspan and supraspan lists by sorting list items into... more In 2 experiments, a total of 13 Ss learned subspan and supraspan lists by sorting list items into subsets. An item recognition task followed, and reaction time (RT) was found to be a bilinear function of memory list length. The slope for supraspan lists was more shallow than the slope for subspan lists. The RT data for supraspan lists were

Journal of the history of the behavioral sciences, 2005

Of all the graphic forms used today, the scatterplot is arguably the most versatile, polymorphic,... more Of all the graphic forms used today, the scatterplot is arguably the most versatile, polymorphic, and generally useful invention in the history of statistical graphics. Its use by Galton led to the discovery of correlation and regression, and ultimately to much of present multivariate statistics. So, it is perhaps surprising that there is no one widely credited with the invention of this idea. Even more surprising is that there are few contenders for this title, and this question seems not to have been raised before. This article traces some of the developments in the history of this graphical method, the origin of the term scatterplot, the role it has played in the history of science, and some of its modern descendants. We suggest that the origin of this method can be traced to its unique advantage: the possibility to discover regularity in empirical data by smoothing and other graphic annotations to enhance visual perception.

Hypothesis-error (or "HE") plots, introduced by , permit the visualization of hypothesis tests in... more Hypothesis-error (or "HE") plots, introduced by , permit the visualization of hypothesis tests in multivariate linear models by representing hypothesis and error matrices of sums of squares and cross-products as ellipses. This paper describes the implementation of these methods in R, as well as their extension, for example from two to three dimensions and by scaling hypothesis ellipses and ellipsoids in a natural manner relative to error. The methods, incorporated in the heplots package for R, exploit new facilities in the car package for testing linear hypotheses in multivariate linear models and for constructing MANOVA tables for these models, including models for repeated measures.

The graphic portrayal of quantitative information has deep roots. These roots reach into historie... more The graphic portrayal of quantitative information has deep roots. These roots reach into histories of thematic cartography, statistical graphics, and data visualization, which are intertwined with each other. They also connect with the rise of statistical thinking up through the 19th century, and developments in technology into the 20th century. From above ground, we can see the current fruit; we

Abstract: The graphical displays shown here are implemented in SAS/IMLsoftware whose combination ... more Abstract: The graphical displays shown here are implemented in SAS/IMLsoftware whose combination of matrix operations, built-inStatistical methods for categorical data, such as loglinear models functions for contingency table analysis, and graphics provide aand logistic regression, represent discrete analogs of the analysis of convenient environment for graphical display for multiwayvariance and regression methods for continuous response variables. categorical data (Friendly 1991a; 1992).

Memory & Cognition, 1986

To investigate the properties that make a word easy to recall, we added to existing norms for 925... more To investigate the properties that make a word easy to recall, we added to existing norms for 925 nouns measures of availability, goodness, emotionality, pronunciability, and probability of recall in multiple-trial free recall. Availability, imagery, and emotionality were found to be the best predictors of which words were recalled. This result, which is stable across recall data collected in three separate laboratories, argues for the importance of availability as apredictor of recall and questions the role of the correlated variables of word frequency and meaningfulness. Consistent with earlier work on a smaller sample of words, six factors describe the numerous properties of words studied by psychologists. The six factors are composed of variables based on orthography, imagery and meaning, word frequency, recall, emotionality, and goodness.

This paper first illustrates the use of mosaic displays and other graphical methods for the anal-... more This paper first illustrates the use of mosaic displays and other graphical methods for the anal-ysis of multiway contingency tables. We then introduce several extensions of mosaic displays designed to integrate graphical methods for categorical data with those used for quantitative data. For example, the scatterplot matrix shows all pairwise (marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models. and (b) a generalization of partial residual plots. The conditioning plot, or coplot shows a collection of (conditional) views of several vari...

Computational Statistics & Data Analysis, 2003

This paper outlines a general framework for ordering information in visual displays (tables and g... more This paper outlines a general framework for ordering information in visual displays (tables and graphs) according to the e ects or trends which we desire to see. This idea, termed e ect-ordered data displays, applies principally to the arrangement of unordered factors for quantitative data and frequency data, and to the arrangement of variables and observations in multivariate displays (star plots, parallel coordinate plots, and so forth).

... manuscript. John Fox suggested the use of the Duncan data, shared some of his unpublished wor... more ... manuscript. John Fox suggested the use of the Duncan data, shared some of his unpublished work, and reviewed several chapters. Georges Monette, Dick Goranson, and Herve Abdi also reviewed portions of the manuscript. Grateful ...

This paper describes graphical methods for multiple-response data within the framework of the mul... more This paper describes graphical methods for multiple-response data within the framework of the multivariate linear model (MLM), aimed at understanding what is being tested in a multivariate test, and how factor/predictor effects are expressed across multiple response measures. In particular, we describe and illustrate a collection of SAS macro programs for: (a) Data ellipses and low-rank biplots for multivariate data, (b) HE plots, showing the hypothesis and error covariance matrices for a given pair of responses, and a given effect, (c) HE plot matrices, showing all pairwise HE plots, and (d) low-rank analogs of HE plots, showing all observations, group means, and their relations to the response variables.

In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising... more In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising theories through the gener- ation and evaluation of precise predictions (e.g., Meehl, 1978). The study of personality structure through the five-factor model (FFM; McCrae & John, 1992) is an important area of research where one encounters many precise predictions. Extant methods of assessing such predictions, however, do not allow researchers to examine the outcome of the predictions in great detail. That is, it may be difficult to determine how estimates fail to match predicted values. As Meehl argued, one must examine how a theory fails to predict in order to refine and improve the theory. To promote better theory appraisal in FFM research, we present a powerful new tool, called a tableplot (Kwan, 2008a), that can summarize and clarify factor-analytic results. Specifically, we illustrate how the tableplot enables detailed appraisal of precise predictions in the FFM.

Zeitschrift für Psychologie / Journal of Psychology, 2009

In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising... more In the debate over null hypothesis significance testing, Paul Meehl strongly advocated appraising theories through the generation and evaluation of precise predictions (e.g., Meehl, 1978). The study of personality structure through the five-factor model (FFM; McCrae & John, 1992) is an important area of research where one encounters many precise predictions. Extant methods of assessing such predictions, however, do not

Psychometrika, 1992

The purpose of this announcement is to describe a collection of general macro programs for statis... more The purpose of this announcement is to describe a collection of general macro programs for statistical graphics for use with the SAS System that have been made available in conjunction with the book, SAS system for statistical graphics, first edition (Friendly, 1991). The primary goals of the book are to survey the kinds of graphic displays that are useful for different questions and data, and to show how can these displays be done with the SAS System. It emphasizes displays that reveal aspects of data not easily captured in numerical summaries or tabular formats and diagnostic displays that help determine if assumptions of an analysis are met.