The Art of Graphical Presentation Types of Variables Guidelines for Good Graphics Charts Common Mistakes in Graphics Pictorial Games Special-Purpose Charts

Types of Variables Qualitative Ordered (e.g., modem, Ethernet, satellite) Unordered (e.g., CS, math, literature) Quantitative Discrete (e.g., number of terminals) Continuous (e.g., time)

Charting Based on Variable Types Qualitative variables usually work best with bar charts or Kiviat graphs If ordered, use bar charts to show order Quantitative variables work well in X-Y graphs Use points if discrete, lines if continuous Bar charts sometimes work well for discrete

Guidelines for Good Graphics Charts Principles of graphical excellence Principles of good graphics Specific hints for specific situations Aesthetics Friendliness

Principles of Graphical Excellence Graphical excellence is the well-designed presentation of interesting data: Substance Statistics Design

Graphical Excellence (2) Complex ideas get communicated with: Clarity Precision Efficiency

Graphical Excellence (3) Viewer gets: Greatest number of ideas In the shortest time With the least ink In the smallest space

Graphical Excellence (4) Is nearly always multivariate Requires telling truth about data

Principles of Good Graphics Above all else show the data Maximize the data-ink ratio Erase non-data ink Erase redundant data ink Revise and edit

Above All Else Show the Data

Above All Else Show the Data

Maximize the Data-Ink Ratio

Maximize the Data-Ink Ratio

Erase Non-Data Ink

Erase Non-Data Ink North East West

Erase Redundant Data Ink North East West

Erase Redundant Data Ink North East West

Revise and Edit

Revise and Edit

Revise and Edit

Revise and Edit

Revise and Edit

Revise and Edit

Specific Things to Do Give information the reader needs Limit complexity and confusion Have a point Show statistics graphically Don’t always use graphics Discuss it in the text

Give Information the Reader Needs Show informative axes Use axes to indicate range Label things fully and intelligently Highlight important points on the graph

Giving Information the Reader Needs

Giving Information the Reader Needs

Limit Complexity and Confusion Not too many curves Single scale for all curves No “extra” curves No pointless decoration (“ducks”)

Limiting Complexity and Confusion

Limiting Complexity and Confusion

Have a Point Graphs should add information not otherwise available to reader Don’t plot data just because you collected it Know what you’re trying to show, and make sure the graph shows it

Having a Point Sales were up 15% this quarter:

Having a Point

Having a Point

Having a Point

Show Statistics Graphically Put bars in a reasonable order Geographical Best to worst Even alphabetic Make bar widths reflect interval widths Hard to do with most graphing software Show confidence intervals on the graph Examples will be shown later

Don’t Always Use Graphics Tables are best for small sets of numbers e.g., 20 or fewer Also best for certain arrangements of data e.g., 10 graphs of 3 points each Sometimes a simple sentence will do Always ask whether the chart is the best way to present the information And whether it brings out your message

Text Would Have Been Better

Discuss It in the Text Figures should be self-explanatory Many people scan papers, just look at graphs Good graphs build interest, “hook” readers But text should highlight and aid figures Tell readers when to look at figures Point out what figure is telling them Expand on what figure has to say

Aesthetics Not everyone is an artist But figures should be visually pleasing Elegance is found in Simplicity of design Complexity of data

Principles of Aesthetics Use appropriate format and design Use words, numbers, drawings together Reflect balance, proportion, relevant scale Keep detail and complexity accessible Have a story about the data (narrative quality) Do a professional job of drawing Avoid decoration and chartjunk

Use Words, Numbers, Drawings Together Put graphics near or in text that discusses them Even if you have to murder your word processor Integrate text into graphics Tufte: “Data graphics are paragraphs about data and should be treated as such”

Reflect Balance, Proportion, Relevant Scale Much of this boils down to “artistic sense” Make sure things are big enough to read Tiny type is OK only for young people! Keep lines thin But use heavier lines to indicate important information Keep horizontal larger than vertical About 50% larger works well

Poor Balance and Proportion Sales in the North and West districts were steady through all quarters East sales varied widely, significantly outperforming the other districts in the third quarter

Better Proportion Sales in the North and West districts were steady through all quarters East sales varied widely, significantly outperforming the other districts in the third quarter

Keep Detail and Complexity Accessible Make your graphics friendly: Avoid abbreviations and encodings Run words left-to-right Explain data with little messages Label graphic, don’t use elaborate shadings and a complex legend Avoid red/green distinctions Use clean, serif fonts in mixed case

An Unfriendly Graph

A Friendly Version

Even Friendlier

Have a Story About the Data (Narrative Quality) May be difficult in technical papers But think about why you are drawing graph Example: Performance is controlled by network speed But it tops out at the high end And that’s because we hit a CPU bottleneck

Showing a Story About the Data

Do a Professional Job of Drawing This is easy with modern tools But take the time to do it right Align things carefully Check the final version in the format you will use I.e., print the Postscript one last time before submission Or look at your slides on the projection screen

Avoid Decoration and Chartjunk Powerpoint, etc. make chartjunk easy Avoid clip art, automatic backgrounds, etc. Remember: the data is the story Statistics aren’t boring Uninterested readers aren’t drawn by cartoons Interested readers are distracted Does removing it change the message? If not, leave it out

Examples of Chartjunk Gridlines! In or out? Filled Labels Borders and Fills Galore Pointless Fake 3-D Effects Gridlines! Vibration Filled “Walls” Unintentional Heavy or Double Lines Filled “Floor” Clip Art

Common Mistakes in Graphics Excess information Multiple scales Using symbols in place of text Poor scales Using lines incorrectly

Excess Information Sneaky trick to meet length limits Rules of thumb: 6 curves on line chart 10 bars on bar chart 8 slices on pie chart Extract essence, don’t cram things in

Way Too Much Information

What’s Important About That Chart? Times for cp and rcp rise with number of replicas Most other benchmarks are near constant Exactly constant for rm

The Right Amount of Information

Multiple Scales Another way to meet length limits Basically, two graphs overlaid on each other Confuses reader (which line goes with which scale?) Misstates relationships Implies equality of magnitude that doesn’t exist

Some Especially Bad Multiple Scales

Using Symbols in Place of Text Graphics should be self-explanatory Remember that the graphs often draw the reader in So use explanatory text, not symbols This means no Greek letters! Unless your conference is in Athens...

It’s All Greek To Me...

Explanation is Easy

Poor Scales Plotting programs love non-zero origins But people are used to zero Fiddle with axis ranges (and logarithms) to get your message across But don’t lie or cheat Sometimes trimming off high ends makes things clearer Brings out low-end detail

Nonzero Origins (Chosen by Microsoft)

Proper Origins

A Poor Axis Range

A Logarithmic Range

A Truncated Range

Using Lines Incorrectly Don’t connect points unless interpolation is meaningful Don’t smooth lines that are based on samples Exception: fitted non-linear curves

Incorrect Line Usage

Pictorial Games Non-zero origins and broken scales Double-whammy graphs Omitting confidence intervals Scaling by height, not area Poor histogram cell size

Non-Zero Origins and Broken Scales People expect (0,0) origins Subconsciously So non-zero origins are a great way to lie More common than not in popular press Also very common to cheat by omitting part of scale “Really, Your Honor, I included (0,0)”

Non-Zero Origins

The Three-Quarters Rule Highest point should be 3/4 of scale or more

Double-Whammy Graphs Put two related measures on same graph One is (almost) function of other Hits reader twice with same information And thus overstates impact

Omitting Confidence Intervals Statistical data is inherently fuzzy But means appear precise Giving confidence intervals can make it clear there’s no real difference So liars and fools leave them out

Graph Without Confidence Intervals

Graph With Confidence Intervals

Confidence Intervals Sample mean value is only an estimate of the true population mean Bounds c1 and c2 such that there is a high probability, 1-a, that the population mean is in the interval (c1,c2): Prob{ c1 < m < c2} =1-a where a is the significance level and 100(1-a) is the confidence level Overlapping confidence intervals is interpreted as “not statistically different”

Graph With Confidence Intervals

Scaling by Height Instead of Area Clip art is popular with illustrators: Women in the Workforce 1980 1960

The Trouble with Height Scaling Previous graph had heights of 2:1 But people perceive areas, not heights So areas should be what’s proportional to data Tufte defines a lie factor: size of effect in graphic divided by size of effect in data Not limited to area scaling But especially insidious there (quadratic effect)

Women in the Workforce Scaling by Area Here’s the same graph with 2:1 area: Women in the Workforce 1980 1960

Poor Histogram Cell Size Picking bucket size is always a problem Prefer 5 or more observations per bucket Choice of bucket size can affect results:

Special-Purpose Charts Histograms Scatter plots Gantt charts Kiviat graphs

Histograms

Scatter Plots Useful in statistical analysis Also excellent for huge quantities of data Can show patterns otherwise invisible

Gantt Charts Shows relative duration of Boolean conditions Arranged to make lines continuous Each level after first follows FTTF pattern

Kiviat Graphs Also called “star charts” or “radar plots” Useful for looking at balance between HB and LB metrics

Useful Reference Works Edward R. Tufte, The Visual Display of Quantitative Information, Graphics Press, Cheshire, Connecticut, 1983. Edward R. Tufte, Envisioning Information, Graphics Press, Cheshire, Connecticut, 1990. Edward R. Tufte, Visual Explanations, Graphics Press, Cheshire, Connecticut, 1997. Darrell Huff, How to Lie With Statistics, W.W. Norton & Co., New York, 1954