STK 573 Metode Grafik untuk Analisis dan Penyajian Data

Transcription

1 STK 573 Metode Grafik untuk Analisis dan Penyajian Data Pertemuan 3 4 Penyajian Grafik dari Informasi Tim Dosen: Prof. Dr. Khairil Anwar Notodiputro Dr. Ir. Aji Hamim Wigena Dr. Agus M Soleh

2 Outline Introduction Know the Intended Audience Principles of Effective Statistical Graphs Graphicacy Graphical Statistics Conclusion Exercises

3 Introduction Graphs and charts Focus to provide the basic principles of statistical graphics, the rules-of-theroad for graphical presentation as it were.

4 Introduction (2) To communication with visual media, there are three generally accepted skills that are required literacy the ability to exchange information with letters; numeracy the ability to exchange information with numbers; and graphicacy the ability to exchange information with graphics. It must be appreciated that the power of statistical graphics comes from the viewer being able to visualize the data.

5 Example We have a data names prevs 1 Epidermals Dust Mites Weeds Grasses Molds Trees 26.7 Trees Molds Grasses Weeds ust Mites idermals Visualization???? Percent

6 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: ,labels=names,tick=false,outer=false, las=2,hadj=1,padj=1)

7 Or? Data names prevs 1 Epidermals Dust Mites Weeds Grasses Molds Trees 26.7 Percent Epidermals Dust Mites Weeds Grasses Molds Trees

8 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???

9 Know the Intended Audience It is essential when presenting graphical displays to have a reasonable expectation of the intended audience. Selecting an appropriate graphical display requires recognizing three distinct groups of audiences: the public; users of data in policy, administrative, legislative positions; and professional colleagues.

10 For public Example For professional colleagues For administrators

11 Principles of Effective Statistical Graphs A statistical graph is a visual representation of data. This could be the original raw data or a summary of the data produced by statistical analysis, or a combination of the two. Statistical methods typically involve data reduction, also known as data compression. One of the underlying principles of effective statistical graphics is that there ought to be a formula or prescription for the layout of figure presenting statistical information.

12 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 a quantitative variable, such as logarithmic, exponential, or none at all; selecting an ordinal scale for a categorical variable.

13 The Design of Graphical Displays 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 universal standard. Efficiency concerns the ability of a graph to portray data in as simple a way as possible. Necessity concerns the need for the graph or certain of its elements. Truthfulness concerns whether the data are correctly plotted in a welldefined coordinate system.

14 Graphicacy the communication of data by producing graphical displays of quantitative data or quantitative aspects of 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.

15 Graphical Statistics The human eye, vision-corrected if necessary, can make visual distinctions with 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 of intersection in a square 1.0 centimeter on edge consisting of 100 fine lines that 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 be assessed by the following statistic:

16 Graphical Statistics (2) The goal with respect to the Truth Coefficient is to achieve a maximum value of one. Truth Coefficients less than 0.95are 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 or more than 1.05 indicative of distortion in the presentation of the data by the statistical graph. Compared to the Lie Factor, the Truth Coefficient is insensitive to the direction of the distortion.

17 Graphical Statistics (3) Greater in width than height how much greater the width than the height? One rule for determining the optimum aesthetic rectangular proportions, albeit from the fifth-century before the current era, is that of the so-called Golden Section a b = b a + b x = b a x2 x 1 = 0 Golden Ratio h w h = height w = width

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

19 Conclusion Burn The real point of graphic design, which comprises both pictures and text, is clear communication. Graphics are not merely cosmetic. When they are clear and consistent, they contribute greatly to ease of learning, communication, and understanding. The success of graphic design is measured in terms of the user s satisfaction and success in understanding... Tufte Graphical excellence is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space.

20 Exercises Review 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 the popular 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 your answer. h) Explain how the graph visually depicts the information. i) Estimate the ratio between height and width of the graph. Was the Rule of the Golden Section apparently used? j) Suggest how the graph could be improved in ways other than already described.

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