Tim Dosen:

Prof. Dr. Khairil Anwar Notodiputro

Dr. Ir. Aji Hamim Wigena

Dr. Agus M Soleh

STK 573Metode Grafik untuk Analisis dan Penyajian Data

Pertemuan 3 – 4Penyajian Grafik dari Informasi

Outline

• Introduction

• Know the Intended Audience

• Principles of Effective Statistical Graphs

• Graphicacy

• Graphical Statistics

• Conclusion

• Exercises

Introduction

Graphs and charts

Focusto provide the basic principles ofstatistical graphics, the rules-of-the-road for graphical presentation as itwere.

Introduction (2)

• To communication with visual media, there are threegenerally accepted skills that are required

– literacy—the ability to exchange information with letters;

– numeracy—the ability to exchange information withnumbers; and

– graphicacy—the ability to exchange information withgraphics.

• It must be appreciated that the power of statisticalgraphics comes from the viewer being able tovisualize the data.

Example

We have a data

names prevs

1 Epidermals 38.2

2 Dust Mites 37.8

3 Weeds 31.1

4 Grasses 31.1

5 Molds 29.3

6 Trees 26.7

Visualization????

Percent

0 10 20 30 40 50

Epidermals

Dust Mites

Weeds

Grasses

Molds

Trees

Sintax

names<-c("Epidermals","Dust Mites", "Weeds", "Grasses",

"Molds", "Trees")

prevs<-c(38.2,37.8,31.1,31.1,29.3,26.7)

plot(prevs,1:6,type="n",xaxt="n",yaxt="n",xlim=c(0,50),

ylim=c(0,7), xlab='Percent',ylab='',xaxs="i",yaxs="i")

for (i in 1:6) lines(x=c(0,prevs[i]),y=c(i,i),lty=3)

points(x=prevs,y=1:6,pch=19,cex=1.0)

axis(1,at=10*(0:5),labels=TRUE,tick=TRUE,outer=FALSE)

axis(2,at=1:6+0.1875,labels=names,tick=FALSE,outer=FALSE,

las=2,hadj=1,padj=1)

Or ?

names prevs

1 Epidermals 38.2

2 Dust Mites 37.8

3 Weeds 31.1

4 Grasses 31.1

5 Molds 29.3

6 Trees 26.7

Pe

rce

nt

01

02

03

04

05

0

Ep

ide

rma

ls

Du

st M

ite

s

We

ed

s

Gra

sse

s

Mo

lds

Tre

es

Data

Sintax (2)

barplot(prevs,space=0.5,names.arg=NULL,horiz=FALSE,a

xes=FALSE,ylim=c(0,50), ylab="Percent",col="black")

yy<-1.5*(1:length(prevs)-0.33)

axis(2,tick=TRUE,xaxp=c(0,50,5))

yy<-1.5*(1:length(prevs)-.375)

axis(1,at=yy,labels=names,tck=0,tcl=0,col=1,las=3)

Which one better???

Know the Intended Audience

• It is essential when presenting graphical displays to have areasonable expectation of the intended audience.

• Selecting an appropriate graphical display requires recognizingthree distinct groups of audiences:– the public;

– users of data in policy, administrative, legislative positions; and

– professional colleagues.

ExampleFor public

For professional colleagues

For administrators

Principles of Effective Statistical Graphs

• A statistical graph is a visual representation of data. This couldbe the original raw data or a summary of the data producedby statistical analysis, or a combination of the two.

• Statistical methods typically involve data reduction, alsoknown as data compression.

• One of the underlying principles of effective statisticalgraphics is that there ought to be a formula or prescription forthe layout of figure presenting statistical information.

The Layout of a Graphical Display

• What is necessary?

– scale and graphical frame

• selecting a scale to cover the extremes of the data;

• selecting an appropriate transformation of scale for aquantitative variable, such as logarithmic, exponential,or none at all;

• selecting an ordinal scale for a categorical variable.

• ACCENT– Apprehension concerns the ability to correctly perceive

relations among the data.– Clarity concerns the ability to visually distinguish the elements

of a graph.– Consistency concerns the ability to interpret a graph based on

exposure to similar graphs in the past or a reasonably universalstandard.

– Efficiency concerns the ability of a graph to portray data in assimple a way as possible.

– Necessity concerns the need for the graph or certain of itselements.

– Truthfulness concerns whether the data are correctly plotted ina welldefined coordinate system.

The Design of Graphical Displays

Graphicacy

• the communication of data by producing graphicaldisplays of quantitative data or quantitative aspectsof qualitative data.

Three distinct processes:• the production of graphical information;• the consumption of graphical information;

and• the increase in awareness or knowledge of

a subject.

Graphical Statistics

• The human eye, vision-corrected if necessary, can make visual distinctionswith gaps as small as 0.1 millimeter at a distance of 0.5 meter.

• Equivalently, the human eye can discern as many as 100 points ofintersection in a square 1.0 centimeter on edge consisting of 100 fine linesthat are equally spaced and parallel to the edges.

• Few statistical graphs approach this degree of data density in practice.

• Violations of the Truthfulness principle of the ACCENT rule can beassessed by the following statistic:

Graphical Statistics (2)

The goal with respect to the Truth Coefficient is to achieve a maximum valueof one. Truth Coefficients less than 0.95 are to be considered suspect.

Closely related to the Truth Coefficient is the Lie Factor defined by

The goal is to achieve a Lie Factor of one with Lie Factors of less than 0.95 ormore than 1.05 indicative of distortion in the presentation of the data by thestatistical graph. Compared to the Lie Factor, the Truth Coefficient isinsensitive to the direction of the distortion.

Graphical Statistics (3)

• Greater in width than height

– how much greater the width than the height?

• One rule for determining the optimum aestheticrectangular proportions, albeit from the fifth-centurybefore the current era, is that of the so-called GoldenSection

𝑎

𝑏=

𝑏

𝑎 + 𝑏→ 𝑥 =

𝑏

𝑎→ 𝑥2 − 𝑥 − 1 = 0

Golden Ratioℎ

𝑤

2

1 + 5

ℎ = height𝑤 = width

Example

Comparison of a rectangle 50% wider than tall (on the left) witha rectangle with dimensions defined by the Golden Section (onthe right)

Conclusion

• Burn– “The real point of graphic design, which comprises both

pictures and text, is clear communication. Graphics are notmerely cosmetic. When they are clear and consistent, theycontribute greatly to ease of learning, communication, andunderstanding. The success of graphic design is measuredin terms of the user’s satisfaction and success inunderstanding....”

• Tufte– “Graphical excellence is that which gives to the viewer the

greatest number of ideas in the shortest time with theleast ink in the smallest space.”

ExercisesReview one issue of a journal in statistics for the graphics that are used.

a) How many graphics are used?

b) Are they descriptive or analytical?

c) Do the graphs appear to contain more or less information than the graphs of thepopular press?

d) Describe the clarity of titles and labels, purpose of the graphs, and visual appeal.

e) Pick out the best example of a graph that illustrates the text.

f) Analyze the graph in relation to the ACCENT rule.

g) Could the graph stand alone and make the point without the text? Justify youranswer.

h) Explain how the graph visually depicts the information.

i) Estimate the ratio between height and width of the graph. Was the Rule of theGolden Section apparently used?

j) Suggest how the graph could be improved in ways other than already described.

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