Statistical Graphics Considerations - Office Of Population Research
StatisticalGraphicsConsiderationsDawn KoffmanOffice of Population ResearchPrinceton UniversityJanuary 20151
Statistical Graphics ConsiderationsWhy this topic?“Most of us use a computer to write,but we would never characterize a Nobel prize winning writeras being highly skilled at using a word processing tool.Similarly, advanced skills with graphing languages/packages/toolswon’t necessarily lead to effective communication of numerical data.You must understand the principles of effective graphs in addition to the mechanics.”Jennifer Bryan, Associate Professor Statistics & Michael Smith Labs, Univ. of British Columbia.http://stat545-ubc.github.io/block015 graph-dos-donts.html2
“. quantitative visualization isa core feature of social-scientific practice from start of finish.All aspects of the research process from the initial exploration of data to theeffective presentation of a polished argument can benefit from good graphical habits. the dominant trend is toward a world where the visualization of data and resultsis a routine part of what it means to do social science.”But . for some odd reason“ . the standards for publishable graphical material vary wildy between and even within articles– far more than the standards for data analysis, prose and argument.Variation is to be expected, but the absence of consistency in elements as simple asaxis labeling, gridlines or legends is striking.”Why?Kieran Healy and James Moody, Data Visualization in Sociology, Annu. Rev. Sociol. 2014 40:5.1-5.5.3
maybe this is changing design of statistical graphs was the topic of (at least) 3 articles in academic journals in 2014:Kieran Healy and James Moody,Data Visualization in Sociology,Annu. Rev. Sociol. 2014 40:5.1-5.5.Nicolas P Rougier, Michael Droettboom, and Philip E. Bourne,Ten Simple Rules for Better Figures.PLOS Computational Biology. September 2014.Jonathan A. Schwabish,An Economist’s Guide to Visualizing Data,Journal of Economic Perspectives, Winter 2014.4
What is a statistical graph?“A statistical graph is a visual representation of statistical data.The data are observations and/or functions of one or more variables.The visual representation is a picture on a two-dimensional surfaceusing symbols, lines, areas and text to display possible relations between variables.”David A Burn. Designing Effective Statistical Graphs, Handbook of Statistics, Vol 9. CR Rao, ed. 1993.5
A statistical graph allows us to - see the big pictureGraphs reveal the big picture: an overview of a data set.An overview summarizes the data’s essential characteristics, from which we can discern what’s routine vs. exceptional.- easily and rapidly compare valuesGraphs make it possible to see many values at once and easily and rapidly compare them.- see patterns among valuesGraphs make it easy to patterns formed by sets of values.For example, patterns may describe correlations among values, how values are distributed, or how values change over time.- compare patterns among sets of valuesGraphs let us compare patterns found among different sets of values.From Steven Few, Perceptual Edge: http://www.perceptualedge.com/blog/?p 18976
primary goals of a statistical graph- explore and understand data by accurately representing it- allow viewer to easily see comparisons of interest (including trends)- communicate results in a clear and memorable wayhow to do this is somewhat subjective .- few hard and fast rules- many trade-offs- many guidelines which some may disagree with- iterative process is often helpful. design and “build” multiple version of “same graph”purpose of this workshop is to encourage you to consider- techniques- guidelines- tradeoffsand then to determine what *you* think makes the most sense for your particular case7
One more thing . a disclaimer Let me state clearly . I intend no criticism of graph authors, either individually or as a group.Shortcomings show only that we are all human, and that under the pressure of a large,intellectually demanding task like designing and building a statistical graph it is much tooeasy to do things imperfectly. Additionally, many design considerations involve trade-offs,where there may be, in fact, no “best” solution.Lastly, I have no doubt that some of the “better graphs” I show will provide “bad” examplesfor future viewers – I hope only that they will learn from the experience of studying themcarefully.Inspired by Brian W. Kernighan and P. J. Plauger, Preface to First Edition of The Elements of Programming Style, 1978.8
Workshop OrganizationPreface Why this topic?What is a statistical graph?IIntroductionTables vs graphs (When)Audience and setting (Where)IIRepresenting data accuratelyIIIHighlighting comparisons of interestIVSimplicity and clarityVSummaryVIConclusions(How)9
Tables vs Graphstables: look up individual, precise valuesgraphs: see overall distribution (shape, pattern) of datamake comparisonsperceive trendsoften more useful when working with large sets of data10
A graph trying to also serve as a look-up table .11
A much nicer way to show a graph and table From Stephen Few, Perceptual Edge: http://www.perceptualedge.com/example2.php12
Anscombe’s Quartet4 data sets that havenearly identical summary statisticseach has 11 non-missing pairs of valuesconstructed in 1973 by statisticianFrancis Anscombe to demonstrateimportance of graphing data andeffect of outliersSUMMARY STATISTICSmean value of xmean value of yvariance of xvariance of ycorrelation between x and ylinear regression (best fit) line is:97.5114.10.816y 0.5x 397.5114.10.816y 0.5x 397.5114.10.816y 0.5x 397.5114.10.816y 0.5x 3Anscombe, FJ (1973). "Graphs in Statistical Analysis". American Statistician 27 (1): 17–21.13
hard to see the forest when looking at the trees14
graph allows simple visual examination of effect of outlier on model summary15
US States: percent of population under age 16, iaColoradoConnecticutDelawareDistrict of ka.20002001 2002 2003 2004 2005 2006 2007 2008 2009 2010 .3220.9819.6822.3.3443441333344222233131223242.16
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audience and purpose . differences may lead to different design decisionsyourselfto check data correctnessto examine a variable distribution, outlier values, relationships with other variablesto examine model fitothersto display distributions/relationships of variables that are important to yourresults (“your story”)to most accurately and most clearly present your results- experts vs novice in subject matter? (use acronyms or abbreviations as axis labels?)- experts vs novice at interpreting statistical graphs?18
consider graph’s setting .presentation . limited time . CLARITY, CLARITY, CLARITY. some audience members sitting farther away:larger font size, higher contrast, brighter colors, axis labeling at top, etc.class .limited timeposter session . more time plus possible interaction with author(but usually little text) . graphs need to be able to “stand on their own”print journal article, book, report . possibly more time plus full text ,but may be limited by publication constraints such asgraph size, number, color and resolution may be able to provide more details in an appendixweb (online article, book, report or blog post) . possibly more time plus full textusually less limited by publication constraints usually can provide links to further detail19
II Representing data accurately“The representation of numbers,as physically measured on the surface of the graphic itself,should be directly proportional to the quantities represented.”Edward Tufte“Visual connections should reflect real connections.”Hadley Wickham“Avoid distorting what the data have to say.”Edward TufteTufte, E. The Visual Display of Quantitative Information, Second Ed. Graphics Press, Cheshire CT. 2001.Wickham, H. Stat 405, Effective Visualisation. .pdf20
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line graphs need intervalscales for slopes to bemeaningful .does it make sense to usea line graph whenshowing values for anominal variable?Amazing website by Jennifer 26
do not change scale part way along an axis:1900 1950 1960 1970 19804-5ybefore2-3ybefore1ybefore1st childbornBirth Age 1 Age 3 Age 5 Age 91-2yafter3-4yafter5-9yafter10-18yafter27
consider when to use two (dual) scales for the same axis .two scales measuring the same data with different labels:FahrenheitCelsius28
two scales showing two variables on the same graph ?is the slope of one curve relative to the slope of the other curve meaningful?is the intersection point meaningful?29
a possible alternative?30
in 2012,is Chinesewagegrowthhigher orlower thanUS wagegrowth?31
stackoverflow.com response by Hadley Wickham:Q: How can ggplot2 be used to make plot with 2 axes, one on left, another on right?A: “It's not possible in ggplot2 because I believe plots with separate y scales (not y scales thatare transformations of each other) are fundamentally flawed.- They are not invertible: given a point on the plot space, you can not uniquely map it backto a point in the data space.- They are relatively hard to read correctly compared to other options.- They are easily manipulated to mislead: there is no unique way to specify the relativescales of the axes, leaving them open to manipulation.- They are arbitrary: why have only 2 scales, not 3, 4 or ten?You also might want to read Stephen Few's lengthy discussion on the topic Dual-ScaledAxes in Graphs Are They Ever the Best Solution? “32
consider scale when displaying odds ratios .Odds ratio for menlog scale33Kristin Bietsch, Program in Population Studies PhD candidate, OPR Notestein seminar, November 2014
consider scale when displaying odds ratios .Odds ratio of ever having had an HIV test for womenwho had watched any TV during the last yearLinear scaleWestoff CF, DA Koffman and C Moreau. 2011. The Impact of Television and Radio on ReproductiveBehavior and HIV/AIDS Knowledge and Behavior. DHS Analytical Studies No. 24.34
should odds ratios be graphed using a log scale?somewhat controversial .From American Journal of Epidemiology, Jun 29, 2011Letter to the editor by Kenneth Rothman, Lauren Wise and Elizabeth Hatch“The conventional answer to this question seems to be yes, even to the extent thatsome have called on the International Committee of Medical Journal Editors to bangraphs of ratio measures that do no employ a log scale. The policy of the AmericanJournal of Epidemiology nearly achieved this ban; .”“So can there be a compelling reason for an arithmetic [linear] scale? . One couldargue that rate differences have primacy over ratio measures . Plotting ratio measureson a logarithmic scale, however, does not scale effects according to rate differences,whereas the arithmetic scale does .”References.1. Gladen BC, Rogan WJ. On graphing rate ratios. Am J Epidemiol. 1983;118(6):905-908.2. Levine MA, El-Nahas AI, Asa B. Relative risk and odds ratio data are still portrayed withinappropriate scales in the medical literature. J Clin Epidemiol. 2010;63(9):1045-1047.3. Kelsey JL, ThompsonWD, Evans AS. Methods in Observational Epidemiology. NewYork, NY: Oxford University Press; 1986:39.35
From The Lancet: Graphical presentation of relative measures of association,By Ahmad Resa Hosseinpoor and Carla AbouZahr. Volume 375, Issue 9722, p1254, April 2010.Relative measures of association, such as hazard ratio, odds ratio, and risk ratio, are often used to convey comparativeinformation in medicine and public health. Graphical presentation of such ratios is common practice in technical papers.However, there are two crucial features that must be taken into account when presenting ratios in graphical format:(1) the baseline value for a ratio is 1; and (2) ratios are expressed on a logarithmic rather than arithmetic scale.Szklo and Nieto have nicely summarised these two conditions using three examples of ratios with values of 0·5 and 2·0(figure). Part A uses a baseline of zero and an arithmetic scale. The visual impression given is that the risk ratio of 2·0 isfour times larger than the ratio of 0·5. Part B is correct in using a baseline of 1 but wrong in using an arithmetic scale,which gives the impression that the ratio of 2·0 is twice that of the ratio 0·5. In reality, risk ratios of 2·0 and 0·5 areidentical in magnitude but work in opposite directions. Part C shows the correct presentation, using a baseline of 1 and alogarithmic scale.36
pop2012 value mapped to radius of bubble .doubling value results in quadrupling area!pop2012 value mapped to area of bubble .Canada 35, US 314 (about 9 times more)37
over-plotting hides data pointstechniques to accuratelydisplay data density include:adjust point sizeadjust point filladjust point shapeadjust point transparencyuse data stratificationuse point jittering38
adjust point size39
adjust point fill40
adjust point size and fill41
adjust point shape42
adjust point transparency43
use data stratification44
use point jittering – moving overlapping points a bit– trade-off: sacrifice positional precision for more accurate display of data densitySee Ellis & Dix, A Taxonomy of Clutter Reduction for Information Visualisation, IEEE Transactions onVisualization & Computer Graphics, 2007.45
III Highlighting comparisons of interest“At the heart of quantitative reasoning is a single question:Compared to what? ”- Edward TufteTufte, E. Envisioning Information. Graphics Press. Cheshire, CT. 1990.46
Highlight comparisons1. Determine true quantity (or quantities) of interest, for example .- magnitude of A and magnitude of B?or- difference between magnitude of A and magnitude of B?or- ratio of magnitude of A to magnitude of B?2. Make sure the data is easily seen- size, contrast, not hidden by other data markers (points, lines, areas), labels,legends, tick marks, or gridlines3. Show the data, not just summary measures, when possible4. Involve perceptual tasks high on Cleveland’s list of performing accurate judgements- position along a common scale- position along identical, non-aligned scales- length- angle, slope- area- color5. Consider proximity, alignment and ordering47
determine true quantity of interestTo show the difference between A and B, graph the difference between A and B.You may want to graph A and B on their own too, but don’t stop there.show imports and exports to and from Englandto show balance of trade, imports - exports,graph that alsoR graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog48
sometimes surprisingly difficult to calculate the difference between curves:49
don’t ask viewers to do extra workPew Research Center Fact Tank. December 12, 2014.Wealth inequality has widened along racial, ethnic lines since end of Great 4/12/12/racial-wealth-gaps-great-recession/50
don’t ask viewers to do extra workR graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog51
R graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog52
R graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog53
show the data - make sure itcan be easily seen.consider:- size- contrast- overplotting- hidden by tick marks,legends, labels, gridlines,reference lines,text annotationsR graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog54
show the data, not just summary measures, when possible55
show the data - display and compare distributions of continuous variables.how?- box plot- violin plot- histogram- density diagramwhy?look for shape of distribution: normal, uniform, bi-modal, skewed, etc.also look for outliers, data errors, missing dataunderstand data before modeling56
box plot:box showingmedian, iqr andcontiguous valuesup to 1.5 timesupper and lowerquartilesviolin plot:symmetric shapeshowing density ofdata values57
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histogram:frequency showsnumber of valueswithin each binof continuousvalueshistogram mayshow proportionof values withineach bin, ratherthan frequency59
density curve:similar tohistogram, but issmooth andcontinuousviolin plot:symmetric shapeshowing density ofdata values60
Density curve:similar tohistogram, but issmooth andcontinuousViolin plot:symmetric shapeshowing density ofdata values61
1. Position along a common scale2. Position along identical, nonaligned scales3. Length4. Angle-slopeInvolve perceptual tasks high onWilliam Cleveland’s list of performingaccurate judgements.5. Area“Order is based on the theory of visualperception, on experiments in graphicalperception, and on informalexperimentation.”6. Color hue and color intensity- William S. Cleveland, The Elementsof Graphing Data, 1985.via Data Design, 62
Pie charts may be the most criticized graph form, but are surprisingly common.They encode values in angles and areas, which are hard for humans to judge.It is easier to judge position along a common scale,which is why many think dot plots are more effective than pie charts.angle/areaposition along a common scaleR graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog63
R graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog64
“A table is nearly always better than a dumb pie chart; the only worse design than a piechart is several of them for then the viewer is asked to compare quantities located inspatial disarray both within and between pies . Given their low data-density and failureto order numbers along a visual dimension, pie charts should never be used.”- Tufte, The Visual Display of Quantitative Information,1983, page 178.“Pie charts have severe perceptual problems. Experiments in graphical perception haveshown that compared with dot charts, they convey information far less reliably. But if youwant to display some data , and perceiving the information is not so important, then a piechart is fine.”- Becker and Cleveland, S-Plus Trellis Graphics User’s Manual. 1996.65
Common misunderstandingPie charts are bad! Die pie chart, DIEPie charts are bad when you want toaccurately compare two numbersBut:As good as bars for estimatingpercentage of whole.Better than bars for comparingcompound proportions (A B vs C D)I. Spence. No Humble Pie: the Origins and Usage of aStatistical Chart. Journal of Educational and BehavioralStatistics, 30:353-368, 2005.Hadley Wickham, Creating Effective Visualisations, slide presentation June 2012:http://courses.had.co.nz/12-effective-vis/66
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perceptual tasks – using length vs position along a common scaletrends for categories on left and right are easy to see,but trends for categories in middle are hard to judgestacked bar charts: difficult to decode because they lack a common baseline for judging lengthR graph Catalog by Jennifer Bryan http://shinyapps.stat.ubc.ca/r-graph-catalog68
Humans are fairly good at comparing differences in length, but only when things share acommon reference point. (Cleveland, William S. and Robert McGill. “GraphicalPerception and Graphical Methods for Analyzing Scientific Data.” Science 229.4716(1985): 828-833.via Data Design, 69
when to use, or not use, stacked bar charts? importance of a common baseline for comparisons.Solomon Messing 11/when-to-use-stacked-barcharts/70
Men in 2000Amanda Cox, New York Times. Online Dec 11, 2014. The Upshot: The Rise of Men Who Don’t Work and71What They Do Instead. Source Data: Current Population Survey (through Oct of each year.)
Men in 2014Amanda Cox, New York Times. Online Dec 11, 2014. The Upshot: The Rise of Men Who Don’t Work and72What They Do Instead. Source Data: Current Population Survey (through Oct of each year.)
Changes between 2000 and 201473
stacked bar charta line graph alternativewhen x axis displays time?(aggregation of time periodsand vehicle types)Solomon Messing 11/when-to-use-stacked-barcharts/74
combine bar chart and dot plot?- hard to read country names- hard to compare men and women (bars and points are far apart)- emphasizes data for womenPercentage of Employed Who are Senior Managers, by Gender,WomenMen2008(Percent)201510The Why Axis Blog: yDenmarkLuxembourgSwedenGermanySlovak NorwayPortugalAustriaSwitzerlandPolandCzech RepublicSloveniaIsraelSpainHungaryOECD reeceBelgiumEstoniaIrelandAustraliaNew ZealandUnited States0United 575
Percentage of Employed Who are SeniorManagers, by Gender, 2008combine bar chart and dot plot?- hard to read country names- hard to compare men and women(bars and points are far apart)- emphasizes data for womenWomenMenUnited StatesNew ZealandUnited celandFranceItalyNetherlandsFinlandOECD averageHungarySpainIsraelSloveniaPolandCzech RepublicSwitzerlandAustriaPortugalNorwaySlovak Korea0The Why Axis Blog: http://thewhyaxis.info/gap-remake/510Percent152076
Percentage of Employed Who are SeniorManagers, by Gender, 2008two bar charts- hard to read country names- hard to compare men and women(bars and points are far apart)- emphasizes data for womenWomenMenUnited StatesNew ZealandUnited celandFranceItalyNetherlandsFinlandOECD averageHungarySpainIsraelSloveniaPolandCzech RepublicSwitzerlandAustriaPortugalNorwaySlovak Korea0The Why Axis Blog: http://thewhyaxis.info/gap-remake/100Percent1077
Percentage of Employed Who are SeniorManagers, by Gender, 2008dot plot- hard to read country names- hard to compare men and women- emphasizes data for womenWomenMenUnited StatesNew ZealandUnited celandFranceItalyNetherlandsFinlandOECD averageHungarySpainIsraelSloveniaPolandCzech RepublicSwitzerlandAustriaPortugalNorwaySlovak Korea0The Why Axis Blog: http://thewhyaxis.info/gap-remake/510Percent152078
dot plot- add ratioPercentage of Employed Who are SeniorManagers, by Gender, 2008WomenMenUnited StatesNew ZealandUnited ndAustriaPortugalNorwaySlovak Korea0The Why Axis Blog: Women/Men 10.540.490.530.490.310.360.730.14152079
bar chart- graph ratio rather thanpercent for women andpercent for men?- sort using ratio rather thanpercent for womenPercentage of Employed Women Who areSenior Managers Relative to Percentage ofEmployed Men Who are Senior Managers, 2008United StatesNew nSloveniaCanadaUnited KingdomIrelandGreeceBelgiumOECD averageIcelandEstoniaIsraelSlovak PortugalSwedenCzech etherlandsFinlandDenmarkTurkeyKorea0.00The Why Axis Blog: 0.450.360.310.140.250.50Ratio0.751.0080
color dimensions: hue, chroma, luminance (hcl)hue: unordered (position along color wheel)chroma (purity): ordered how much gray is added to pure colorluminance(lightness) : ordered how much black orwhite is added topure colorMaureen Stone, Choosing Colors for Data Visualization, choosing colors.pdf81
use color dimensions- to distinguish groups- to highlight particular data- to encode quantitative valuesonly vary color for a reasonvarying color and pattern and lengthFrom Stephen Few, Perceptual Edge:http://www.perceptualedge.com/articles/visual business intelligence/rules for using color.pdf82
hue is unordered and not perceived quantitatively . usually a poor choice for indicating magnitudehow to order these colors from smallest to largest?Two ways to encode quantitative data using color- sequential scale:single hue where color varies from light to darkorsingle hue where color varies from pale to pureHow to order these colorsfrom smallest to largest?- diverging scale: two hues with a neutral color in between,where each hue varies from light to dark or pale to pureFrom Stephen Few, Perceptual Edge:http://www.perceptualedge.com/articles/visual business intelligence/rules for using color.pdf83
use hue to distinguish groupsuse equally spacedhues along color wheel,for example:84
use color to highlightuse soft colors todisplay mostinformation andbright and/or darkcolors for emphasisvia Data Design, osing colors.pdf
use color to encode quantitative informationuse a single huewhere color variesfrom light to darkor pale to l business intelligence/rules for using color.pdf
use color to encode quantitative informationuse two hues with a neutral color in between,where each hue varies from light to dark or pale to pure to create a diverging scaleIssue 1Issue 2Issue 3Issue 4Issue 5StronglyAgreeNoAgree Opinion DisagreeStronglyDisagree87Based on Solomon Messing Blog: en-to-use-stacked-barcharts/
proximity - grouped bar charts are difficult because it’s hard to make comparisons betweenvalues that aren’t near each other . try to put values to be compared near each other- hard to compare data for each group (males, both, females) across countries,because other bars get in the way- non-zero baseline (again)Life expectancy at birth, top 10 OECD countriesDarkhorse Analytics Blog: 8
Darkhorse Analytics Blog: 9
Grouped Bar Graph vs Line Graph90
ease comparisons - align things vertically91
ease comparisons – use common axes92
ordering – don’t sort alphabetically93
relationships among subsetsconsider having two continuous variables, plus a third categorical variable.how to compare the relationships both within and between categories ?- distinguish between categories using characteristics such as color, shape, fillR graph Catalog by Jennifer Bryan: http://shinyapps.stat.ubc.ca/r-graph-catalog94
a graph showing small multiples (sometimes called a trellis, lattice, grid, panel or facet graph)shows a series of small graphs displaying the same relationships for different subsets of data.“Small multiple designs, multivariate and data bountiful, answer directly by visually enforcingcomparisons of changes, of the differences among objects, of the scope of alternatives.For a wide range of problems in data presentation, small multiples are the best design solution.”- Edward Tufte, Envisioning Information, p. 67.R graph Catalog by Jennifer Bryan: http://shinyapps.stat.ubc.ca/r-graph-catalog95
small multiples: “a series of graphics, showing the same combination of variables,indexed by changes in another variable.”- Edward TufteTufte, E. Envisioning Information. Graphics Press. Cheshire, CT. 1990.96
R graph Catalog by Jennifer Bryan: http://shinyapps.stat.ubc.ca/r-graph-catalog97
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small multiples- countries ordered bymost recent data pointrather than alphabetically- scale labels on outer edgesonly, rather than one set perpanel- only used three labels forthe 11 years on the plot- did not overdo the verticalscale eithe
What is a statistical graph? "A statistical graph is a visual representation of statistical data. The data are observations and/or functions of one or more variables. The visual representation is a picture on a two-dimensional surface using symbols, lines, areas and text to display possible relations between variables." David A Burn.
In addition to the many applications of statistical graphics, there is also a large and rapidly growing research literature on statistical methods that use graphics. Recent years have seen statistical graphics discussed in complete books (for example, Chambers et al. 1983; Cleveland 1985,1991) and in collections of papers (Tukey 1988; Cleveland
Graphics API and Graphics Pipeline Efficient Rendering and Data transfer Event Driven Programming Graphics Hardware: Goal Very fast frame rate on scenes with lots of interesting visual complexity Pioneered by Silicon Graphics, picked up by graphics chips companies (Nvidia, 3dfx, S3, ATI,.). OpenGL library was designed for this .
Evolution of ODS Graphics Early Development of SAS Graphics In the beginning SAS had a less than stellar reputation regarding graphics output. PROC PLOT produced crude raster graphics using a line printer. Then there was SAS/GRAPH and visuals became better. Vector graphics used to produce quality output. Lots of options but too many to learn well (difficult to use “on the fly”).
An Introduction to R Graphics 3 This example is basic R graphics in a nutshell. In order to produce graphical output, the user calls a series of graphics functions, each of which produces either a complete plot, or adds some output to an existing plot. R graphics follows a\painters model,"which means that graphics output occurs in steps,
Interactive graphics rggobi (GGobi) Link iplots Link Open GL (rgl) Link Graphics and Data Visualization in R Overview Slide 5/121. . Graphics and Data Visualization in R Graphics Environments Base Graphics Slide 16/121. Line Plot: Single Data Set plot(y[,1], type "l", lwd 2, col "blue") 2 4 6 8 10 0.2 0.4 0.6 0.8 Index
SAS Output Delivery System (ODS) Graphics started appearing in SAS 9.2. Collectively these new tools were referred to as "ODS Graphics," "SG Graphics" and "Statistical Graphics". When first starting to use these tools, the traditional SAS/GRAPH software user might come upon some very significant
animation to standard data graphics require careful study. In this paper, we investigate the design of animated transitions between statistical data graphics backed by a shared data table. We extend theoretical treatments of data graphics to include transitions and introduce a taxonomy of transition types. We then posit design
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