Data Display Techniques

Data Display TechniquesChristine R. Curran, PhD, RN, CNAOctober, 2001

(c) Chris Curran, 2001

Data Versus InformationHow does one determine which display format to use: Text, Table, Graph, Other?How does display content / ink affect the amount of information obtained?rounding of numbers Labels: when and where use of white spaceHow does color affect our ability to see information?


Human Cognitive ProcessesHumans want to organize dataThe human mind operates by associationHumans process data through data reduction strategiesChunking of dataPattern recognition & exceptions to patterns are used to make judgmentsAnalogy & metaphor are often used in learning & recall of information

Data Displays Should FacilitatePerception of salient featuresComprehension of informationRecall of the information


Data Versus InformationMethods used to glean information from the volumes of data available to us:tools (calculators, computers)decision support systemsdata presentation


The data and the type of task drive the choice of display format How to Choose a Display Format


Types of Data DisplaysWordsHeadingsTextNumbersDigitalNumericTableAnalogPictureGraphIconVideo


WordsAvoid all capital lettersUse labels or symbols rather than a keyUse Serif font for textUse San-serif font for headings


Text: SamplesTITLE Text should be displayed in Serif font. One should avoid all capital letters.

Title Text should be displayed in Serif font. One should avoid all capital letters.


Properties of Numerical Data Displays Digitaltask: symbolicdata: discrete, quantitativefocus:specificprocess: analysisdisplay: table

Analogtask: spatialdata: continuous, qualitativefocus:holisticprocess: perceptiondisplay: graph, icon


Principles of Numerical Data DisplaysArrange data to convey meaningproximity of datause of white spacenavigationMake patterns and exceptions within the data obvious at a glance (seeing the data)roundinglabeling & spacingdisplay format


Digital Display: TablesUse in small data sets (20 numbers to be displayed or less)Used to display numbers


Rules for Table Displays Ehrenberg, 1977Round to 2 significant or effective digitseliminate leading 0 trailing 0 does not matterPut figures to be compared in columns rather than in rowsAdd row & column averages (make the main effects explicit)Order rows & columns by sizeShow larger numbers above smaller numbers


Rules for Table Displays Ehrenberg, 1977Spacing & layoutWhite space is your friendUse white space to signal the chunks of dataSingle spacing guides the eye down the columnUse gaps (white space) between groups (columns or rows) to guide the eye across the data & to cluster dataData meant to be compared should be close together


Data RoundingAnyone who cannot learn to cope with rounding errors will probably not get much out of statistical data Ehrenberg, 1977, pg. 282


PrincipleThe Data should drive the order of the presentation. Displays should not be configured by the structure of the data collection methodology or analysis.


Table: Example


Table: Revised Example


Correlation Matrix: Example


Correlation Matrix: Revised Example


Graphical Data Display: A Form of Decision SupportGoalsfind relevant data in a dynamic environmentvisualize the semantics of the domainreconceptualize the nature of the problem

(Bennett, Toms & Woods, 1993)


The Power of a GraphEnables one to take in quantitative information in a qualitative way, organize it, and see patterns and structure not readily revealed by other means.


Graphical Perception The process of visual decoding of quantitative and categorical data from a graph. Cleveland, 1984


Analog Display: GraphsUsed to display large datasetsTypes of Graphs:

Universal - Literal Continuum


Universal Graph: Example


Literal Graph


Graphical Design Concepts & PrinciplesSemantic Mapping (Roscoe, 1968; Kosslyn, 1989)Configural Displays (Garner, 1970)Chunking (Newell & Simon, 1973)Theory of Graph Comprehension (Pinker, 1981)8 Visual Variables (Bertin, 1981)Emergent Features (Pomerantz, 1981)Data-Ink Ratio & Small Multiple (Tufte, 1983,1990, 1997)Elementary Perceptual Tasks (Cleveland & McGill, 1984)Proximity Compatibility (Wickens, 1986)Metaphor Graphics (Cole, 1988)Cognitive Fit (Vessey, 1991)


Design Principles for Computer Displays (Cole, 1994)

Design for the analog mind and both hemispheresDesign for correct encoding of information (represent the users model)Provide a clear context


Graphic Design


Visual Decoding of Graphs Requires Pattern PerceptionPattern perception requires:detectionvisual grouping of a patternestimation


Elementary Perceptual Tasks(ordered from most to least accurate)Position along a common scalePositions along nonaligned scalesLength, Direction, AngleAreaVolume, CurvatureShading, Color Saturation Cleveland & McGill, 1984


Position Along a Common Scale


Position Along Non-Aligned Scales


Length


Direction


Angle


Area


Volume


Curvature


Shading


Color Saturation


Elementary Perceptual TasksCleveland & McGill, 1984


Common Graphs by Elementary Perceptual Task


Recommendations: Based on Graphical PerceptionParts of a Wholedot chartgrouped dot chartbar charts (instead of divided bars or pie charts)Framed Rectangle Charts(instead of Shaded Statistical Maps

Cleveland & McGill, 1984


Dot Chart


Grouped Dot Chart


Bar Charts


Grouped Bar Chart


Divided Bar Chart


Pie Chart


Framed Rectangle


Research Findings: Graphical PerceptionPerception of ChangeLine GraphsGrouped Bar GraphsPerception of ProportionPie ChartsDivided Bar Graphs(differs from Cleveland & McGill)

Hollands & Spence, 1992


Cognitive Fit Vessey, 1991


Proximity Compatibility PrincipleTo the extent that multiple aspects of data or information must be mentally integrated, they should be physically integrated or proximate in the display. Wickens, 1986


Emergent FeaturesA property of the configuration of multiple dimensions of an object that does not exist when the dimensions are specified independently. Pomerantz, 1981


Innovative New DesignsMetaphor Graphics


Clinical Data DisplayCole, 1988


Bugs

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Cole DB Single

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Patient Died

Each Patient = one icon

Metastases

Thick deep extremity primary tumor

Thin deep axial primary tumor

Lymph nodes removed

Cole DB Screen

High

Integrality

Low

LowHigh

Meaningfulness

Male

Female

&A

Page &P

The higher on the vertical scale and the more to the right, the better the graph Cole, 1995

Tufte EMR Single

-1yradmission datetoday's date

result type, medication, etc.most recent value

critically elevated+Note: initials, credentials: date

elevated+Note: initials, credentials: date

normal rangeNote: initials, credentials: date

reduced-

critically reduced-

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Page &P

LastName, FirstName, MI Admission Date Today's Date Patient Location

Problem List: Diagnosis 1, diagnosis 2, Diagnosis 3, etc.

More than 1 year prior to admission

One year prior to admission

First week of admission

Today's value

Tufte EMR Screen

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Vessey

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Problem Representation

Problem Solving Task

Mental Representation

Problem Solution

Table Demo

[From Nursing Research (1996), 45(6), pg.354]

Revised Table

Table 1.Summary Statistics of the Independent VariablesTable 1.Summary Statistics of the Independent Variables

VariableMSDMinimumMaximumVariableMSDMinimumMaximum

Total Sample

Weight179.2840.14104300Total Sample

Systolic Blood Pressure130.6816.3993182Cholesterol Level19430107339

Diastolic Blood Pressure77.1111.0152111Weight17940104300

Cholesterol Level194.4430.11107339Systolic Blood Pressure1311693182

Coping Score0.230.45-0.781.41Diastolic Blood Pressure771152111

Type ACoping Score0.20.5-0.81.4

Weight188.5139.16112298

Systolic Blood Pressure138.1616.98107182Type A

Diastolic Blood Pressure79.8311.0454111Cholesterol Level20644112339

Cholesterol Level205.5443.74112339Weight18939112298Revised Table

Coping Score-0.130.31-0.780.97Systolic Blood Pressure13817107182Table 1.Summary Statistics of the Independent Variables

Type BDiastolic Blood Pressure801154111VariableType AType BTotal`

Weight170.5739.22104300Coping Score-0.10.3-0.81.0Mean

Systolic Blood Pressure123.6112.1793155

Diastolic Blood Pressure74.5310.3752102Type BCholesterol Level206184194

Cholesterol Level183.9638.46107316Cholesterol Level18438107316Weight189171179

Coping Score0.570.260.101.41Weight17139104300Systolic Blood Pressure138124131

Systolic Blood Pressure1241293155Diastolic Blood Pressure807577

Diastolic Blood Pressure751052102Coping Score-0.10.60.2

Coping Score0.60.30.11.4Range

Cholesterol Level112-339107-316107-339

Weight112-298104-300104-300

Systolic Blood Pressure107-18293-15593-182

Diastolic Blood Pressure54-11152-10252-111

Coping Score-0.8 to 1.00.1 to 1.4-0.8 to 1.4

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Correlation Demo

Correlations

(From SPSS)Trial 1Trail 2Trial 3Trial 4

Trial 11.0000.4880.2460.223

Trial 20.4881.0000.8120.803

Trial 30.2460.8121.0000.785

Trial 40.2230.8030.7851.000

**Correlation is significant at the 0.01 level (2-tailed).

RevisedCorrelations

(Option #1)Trial 2Trial 3Trial 4Trial 1

Trial 20.80.80.5

Trial 30.80.80.2

Trial 40.80.80.2

Trial 10.50.20.2

(Option #2)RevisedCorrelations

Trial 2Trial 3Trial 4Trial 1

Trial 20.810.800.49

Trial 30.780.25

Trial 40.22

Trial 1

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Universal Graph

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Universal Graph

1532.13279.21702880

2084169.71542520

2018.4205.951622700

1999.5255.48135.53240

2238.0594942700

2217.25248.42582700

2414.05263.288.252895

2015.2518760.254860

82582.4524900

132.3110.99495040

137199.9128900

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Graph Types

Case1Case2Case3Case4Case5Case6Case5Case2Case1Case4Case3Case6

A354215244910494235241510

B21142341322

C215026867

D14338182644

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F93519413125

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Colors

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Patient Metaphor

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Continuum

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Expressive Values of Color

ColorSymbolismAltered ColorSymbolism

YellowUnderstandingMuted Yellowuntruth

Knowledgedistrust

"Heavenly"betrayal

RedPassion

Burning

Blood

BlueNervous SystemShadowy Bluefear

Immortalitysuperstition

Faithgrief

GreenContentmentdecay

Fruitfulness

Hope

VioletPiety

Regal

&A

Page &P

Unusual

Information

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Page &P

Head

Xray and Imaging

Respiratory

Routine Blood Work

Cardiac

Gastrointestinal

I&O

Old Lab Work

UniversalLiteral

Line GraphMetaphorVideo

Bar GraphGraphicsPicture

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Page &P

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Page &P

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Metaphor Graphics: Database Display (Cole, 1988)MaleFemale


Clinical Data Display


Metaphor Icon Graph: Example


Metaphor Icon Graph: Questionable Example


Clinical Data DisplayPowsner, S. & Tufte,E.R., 1994


Schneiderman Model

DataVisualForm

Data TransformationsVisual MappingsView Transformations

Human Interaction

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Page &P

Raw Data

Data Tables

Visual Structures

Views

Task

Bugs

&A

Page &P

Cole DB Single

&A

Page &P

Patient Died


Metastases



Lymph nodes removed

Cole DB Screen

High

Integrality

Low

LowHigh

Meaningfulness

Male

Female

&A

Page &P


Tufte EMR Single






reduced-

critically reduced-

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Page &P






Today's value

Tufte EMR Screen

Public, John Q.admitted 6/4/996/10/996th Intermediate Care

Right lower lobe pneumonia, new onset diabetes, history of manic depressive disorder

WBC 11100c/ulGlucose 237 mg/dlMood 0

+++Discharge RS MD 1200 6/10/99

+++

[[[Note 2

---

---Note 3

T 98.8* FReg Insulin 3unitsLi .56 mmol/l

+++Note 4

+++

[[[

---

---

R 18 resp/minCa 8.7 md/dlCl 100 mmol/l

+++

+++

[[[

---

---

Cefuroxime 1.5gNa 136 mmol/lCO2 23.7 mmol/l

+++

+++

[[[

---

---

Clindamycin900mcg

+

+

[

-

-

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Vessey

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Problem Solution

Table Demo


Revised Table



Total Sample







Weight188.5139.16112298















Weight112-298104-300104-300




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Correlation Demo

Correlations


Trial 11.0000.4880.2460.223

Trial 20.4881.0000.8120.803

Trial 30.2460.8121.0000.785

Trial 40.2230.8030.7851.000


RevisedCorrelations


Trial 20.80.80.5

Trial 30.80.80.2

Trial 40.80.80.2

Trial 10.50.20.2



Trial 20.810.800.49

Trial 30.780.25

Trial 40.22

Trial 1

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Universal Graph

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Universal Graph

1532.13279.21702880

2084169.71542520

2018.4205.951622700

1999.5255.48135.53240

2238.0594942700

2217.25248.42582700

2414.05263.288.252895

2015.2518760.254860

82582.4524900

132.3110.99495040

137199.9128900

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Page &P

Graph Types


A354215244910494235241510

B21142341322

C215026867

D14338182644

E4327153313

F93519413125

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Graph Types

0

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0

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Case1

Colors

00000

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A

B

C

D

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GIFIC

000

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000

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Continuum

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Knowledgedistrust

"Heavenly"betrayal

RedPassion

Burning

Blood



Faithgrief


Fruitfulness

Hope

VioletPiety

Regal

&A

Page &P

Unusual

Information

&A

Page &P

Head

Xray and Imaging

Respiratory

Routine Blood Work

Cardiac

Gastrointestinal

I/O

Old Lab Work

UniversalLiteral



&A

Page &P

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Page &P

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Page &P

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Page &P

Tufte, 1997Clinical Data Display


Schneiderman Model

DataVisualForm

Data TransformationsVisual MappingsView Transformations

Human Interaction

&A

Page &P

Raw Data

Data Tables

Visual Structures

Views

Task

Bugs

&A

Page &P

Cole DB Single

&A

Page &P

Patient Died


Metastases



Lymph nodes removed

Cole DB Screen

High

Integrality

Low

LowHigh

Meaningfulness

Male

Female

&A

Page &P


Tufte EMR Single






reduced-

critically reduced-

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Page &P






Today's value

Tufte EMR Screen

Public, John Q.admitted 6/4/996/10/996th Intermediate Care

Right lower lobe pneumonia, new onset diabetes, history of manic depressive disorder

WBC 11100c/ulGlucose 237 mg/dlMood 0

+++Discharge RS MD 1200 6/10/99

+++

[[[Note 2

---

---Note 3

T 98.8* FReg Insulin 3unitsLi .56 mmol/l

+++Note 4

+++

[[[

---

---

R 18 resp/minCa 8.7 md/dlCl 100 mmol/l

+++

+++

[[[

---

---

Cefuroxime 1.5gNa 136 mmol/lCO2 23.7 mmol/l

+++

+++

[[[

---

---

Clindamycin900mcg

+

+

[

-

-

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Page &P

Vessey

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Page &P




Problem Solution

Table Demo


Revised Table



Total Sample







Weight188.5139.16112298















Weight112-298104-300104-300




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Page &P

Correlation Demo

Correlations


Trial 11.0000.4880.2460.223

Trial 20.4881.0000.8120.803

Trial 30.2460.8121.0000.785

Trial 40.2230.8030.7851.000


RevisedCorrelations


Trial 20.80.80.5

Trial 30.80.80.2

Trial 40.80.80.2

Trial 10.50.20.2



Trial 20.810.800.49

Trial 30.780.25

Trial 40.22

Trial 1

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Universal Graph

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Universal Graph

1532.13279.21702880

2084169.71542520

2018.4205.951622700

1999.5255.48135.53240

2238.0594942700

2217.25248.42582700

2414.05263.288.252895

2015.2518760.254860

82582.4524900

132.3110.99495040

137199.9128900

&A

Page &P

Graph Types


A354215244910494235241510

B21142341322

C215026867

D14338182644

E4327153313

F93519413125

A_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

B_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

C_ _ _ _ _ _ _ _ _

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Case1

Colors

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A

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GIFIC

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Sheet14

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Knowledgedistrust

"Heavenly"betrayal

RedPassion

Burning

Blood



Faithgrief


Fruitfulness

Hope

VioletPiety

Regal

&A

Page &P

Unusual

Information

&A

Page &P

Head

Xray and Imaging

Respiratory

Routine Blood Work

Cardiac

Gastrointestinal

I/O

Old Lab Work

UniversalLiteral



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Color


Why Do We Use Color?Formatting PurposesGroup data (patterns)Create focused attention to specific data (highlight data)Semantic Purpose (encode data)Create RealismAesthetic Purpose (visual appeal)


Color is superior to size, shape or brightness as a mechanism to target a feature in a display When to Use Color


Eleven Colors That Are Never ConfusedWhiteBlackGrayRed GreenYellowBluePinkBrownOrangePurple

Kosslyn, 1994


General Guidelines: Use of ColorUse warm colors in the foregroundHave a large luminance contrast between the foreground and backgroundAdjacent colors should have different levels of brightnessRedundant color coding improves search tasksColor should be a secondary cue (always design for monochrome first) Travis, 1991


Kinds of Color ContrastsLight - DarkCold - WarmContrast of :huesaturationComplimentary Contrast (from color wheel)


General Guidelines: ColorsColors have cultural significance. Each individual sees, feels, and evaluates color in a very personal way.


General Guidelines: ColorsRed: alert values, warningBlue: most easily distinguished but does not photocopy wellOptic Yellow: (a greenish yellow color) most visible to humansShades of Grey: Best for those who are color blind Use Conventional colors (e.g., forests are green)


Take Home MessageHow Data are displayed mattersDisplays should be configured around the data and not how it was obtained


Things to ConsiderHow much data do I have?What cognitive task is needed?Are the data continuous or discrete?Am I making an exact or a relative judgment?Are the data static or dynamic?Are there display conventions about the subject area?Is the domain familiar to the audience?


Current RecommendationsTables: good for small datasets & to depict quantitative data where specific data are neededPie Graphs: good for judging proportionBar Graphs:display change or trends; excellent universal graph (better than line)Icons: good for synthesis of data and meaning; may be best for qualitative (relative) judgmentsShapes / Figures: Best to display integrated data


We will attempt to address these questions:(state questions)

The take home message is that configuration of the display matters. If the method of presentation of your data has an format that 1) reduces visual searching, 2) facilitates recognizing patterns and exceptions to those patterns within the data, and, 3) if there is an understood meaning is the style of presentation, extracting information and knowledge tranfer are facilitated.

For example, most of us learned the saying On old olypmus terrace tops a Finn and German vaulted a hedge in order to remember the 12 cranial nerves. Analogy or a metaphor connects meaning and can be used within displays to enhance learning. Smith (1986) conducted a study where subjects were presented with perceptually random stimuli and asked to reproduce them. The reproduced set was then used as a stimulus for the second set of subjects who were also asked to reproduce what they were shown. By the twelfth trial, the stimuli had a definite structure to them. The subjects had imposed a structure on the random events. This experiment demonstrated the human tendency to organize phenomena in order to generate meaning.These are the goals of good display design.

So knowing how we process information and learn, and keeping in mind the goals of better data display, what can we do with displaying data that helps these processes?Today, we are faced with large volumes of data. The challenge is how to extract the information, and ultimately knowledge, available within these data. It is my opinion that three things can assist this process: tools, support systems and data displays. Humans are good analog data processors; computers are good digital data processors.

I will give you a few hints about words but the majority of this presentation focuses on the numeric side of this slide.Heres an example of the impact of font type.Data elements should be grouped by relationships, similarities, and levels of information (elements, subsets or sets).

How do you arrange data to convey meaning? The ways of doing this are:proximity of datause of white spacenavigationAnd you make patterns and exceptions to patterns visible throughroundinglabelling & spacingdisplay format

Redundancy in communication helpsRound to 2 significant or effective digits (not decimel points)If we are interrupted by any task, the number of digits we retain in short term memory generally drops to two (Simon, 1969, Compton lectures)Keep the exact data when performing calculations, round for presentation/reporting of results; can put exact data in an appendixPut figures to be compared in columns rather than in rowsThe design of a table is determined by the data, not the labelsDummy Tables with no data can lead to poor table design[Is this true???? Trends are viewed across rather than down]Add row & column averages (make the main effects explicit)Averages provide visual focus for inspecting the dataOrder rows & columns by sizeShow larger numbers above smaller numbers to make mental subtraction easier.Facilitating mental arithmetic is important when scanning large data sets.Ordering columns makes no differenceA statistical table is not a telephone directory ; labels need NOT be alphabetical or in time sequence (it is easier to find an isolated name than to interpret an isolated number from an unstructured table).

Spacing & layoutFrom Nursing Research Journal (1996).Round to 2 significant or effective digitseliminate leading 0 trailing 0 does not matterPut figures to be compared in columns rather than in rowsAdd row & column averages (make the main effects explicit)Order rows & columns by sizeShow larger numbers above smaller numbers (makes mental subtraction easier)Spacing & layoutsingle spacing guides the eye down the columnuse gaps (white space) between groups (columns or rows) to guide the eye across the data & to cluster datadata meant to be compared should be close togetherFrom SPSS Program: Correlation Statistics (1997).Format often found in the literature.Order of Trials changed to highest correlation to lowest.Only 2 effective digits displayedNo leading 0 displayedCan do a mirror image if desired for redundancy.Why use a graph rather than a table?Also used to trend data, especially dynamic data.

The advantages of analog properties may diminish with increasing size and complexity.Could build analogy into this:five aspects of a problemfive of something that fits together to make a whole.Cleveland & McGill (ordered from most to least accurate)Position along a common scalePositions along nonaligned scalesLength, Direction, AngleAreaVolume, CurvatureShading, Color SaturationBertin (1981)

Integrality relates to the degree to which a pattern is apparent. Meaningfulness relates to the degree to which a pattern, once detected, is interpretable.

Cole believes that these 2 concepts are key to design of a good graph: the goal is high-high.

The ability to estimate requires: ability to discriminate, rank order and to think in ratios.

Implications for Novice to Expert: Interesting and essentially untouched research field?Graph type should maximize accuracy; design for most accurate elemental type.

Very little research on this depiction.

Horizontal bar graphs and line graphs are the most frequently used types of graphs.These are the types of elemental judgments we make.

Position along a common scale

Positions along nonaligned scalesLengthDirectionAngleAreaVolumeCurvatureShadingColor SaturationGoal: Construct a graph that uses elementary tasks as high in the hierarchy as possible (the elements are in hierarchial form, read left to right)

Purpose (for Cleveland) of elementary perceptual tasks is to extract quantitative information from the graph; nothing is stated about qualitative information.

The power of a graph is its ability to enable one to take in quantitative information, organize it, and see patterns and structure not readily revealed by other means. [This may distinguish why sometimes other types of graphs seem to work better; i.e., those graphs may be representing qualitative amounts. ]

How does this apply in practice?

These are the types of graphs with their respect elemental task(s).

You can analyze a graph for its properties and either understand the accuracy of the graph as displayed or try to reduce the display to the most accurate elemental form that retains meaning. Also known as a Pareto Chart (when organized highest to lowest).Need to be careful using disk charts (3D Pie Charts) because they distort the proportion of the pieces and lead to judgment errorsuse flat pie graphs.Cognitive Fit reduces cognitive load.

Cognitive fit between the task (judgment) to be achieved and problem representation is believed to affect the efficiency and effectiveness of decision-making performance (Vessey, 1991). The following table depicts the attributes of cognitive fit:

Spatial / Continuous / Perception / Graphical (Analog)

Symbolic / Discrete / Analysis / Tabular (Digital)

Cognitive fit is achieved when attributes are consistent across each row. If attributes of the problem representation or task are mixed (attributes vary between rows), then the individual must transform the data in order to make a decision. This transformation increases cognitive load.

A picture is worth a thousand words.An example of good semantic mapping

Needs researchBelieved to aide in recall of information

The benefit of metaphor icons is that they have the capacity to carry much greater descritpive information using the same or less physical display space than other forms of presentation.They speed perceptual recognition, reduce cognitive load and are based on association (thus re-inforcing mental mapping).

Elting & Bodey (1991)

ICU Patient Display

The advantages of analog properties may diminish with increasing size and complexity. This may be the case here.Use colors that are wheel separated in the spectrum (not adjacent to each other)For colors juxtaposed, use colors separated by at least one distinct color in the color wheel

Avoid:1) cobalt or deep blue 2) red and blue in adjacent regions

Regions of the same color will be seen as a groupUse deeper saturations and greater intensities for hues to indicate greater amounts

Never use all eleven in one display ; people can only keep nine distinctions in mind at any one point in time

Is there a correst number to use: different opinions (generally 4-5 max).It probably depends on what you are trying to convey with color.

Warmer colors are perceived as closer.

Use the same color throughout to mean the same thing.

For example, white in the US is a good color; while in the middle east, white is used to signify death.Respect cultural norms for colors (In US, red means danger, blue means coolness, and green means life).Avoid blue if the graph is to be photocopied

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Data Display Techniques