Graphically Enhancing the Visual Presentation and Analysis of Univariate Data Using SAS Software

Transcription

1 Graphically Enhancing the Visual Presentation and Analysis of Univariate Data Using SAS Software James R. O Hearn, Pfizer Inc., New York, NY ABSTRACT The problem of analyzing univariate data is investigated. In this paper an enhanced graphical approach based on a template of numerical summary statistics and graphical plots using SAS/GRAPH, SAS/QC, and SAS/STAT is presented. It is shown that this template provides a more powerful tool for assessing statistical assumptions, for suggesting corrective actions when assumptions are not met, and for elucidating patterns and relationships than the UNIVARIATE procedure. It is anticipated that this template will be of some use for the data analyst in gaining greater insight into the structure of univariate data. An example using fictitious exercise test data will be given to illustrate this methodology. INTRODUCTION The first step in any statistical analysis is to generate univariate descriptive statistics on the primary analysis variables. The most commonly used and comprehensive method for performing univariate analysis in SAS is the UNIVARIATE procedure. However, except for a couple of minor statistical enhancements, the output from this procedure has hardly changed for nearly twenty years. This is most glaringly evident in the graphical plots where a number of shortcomings exist by today s standards: (1) line-printer style graphics, (2) plots rotated sideways with unnatural reverse ordering of horizontal axis values, (3) lack of control in the scaling of the vertical axis, and (4) lack of graphical sophistication in plot appearance. The objective of this paper is to enhance the visual display, and subsequently, improve the statistical analysis and understanding of univariate data using SAS software. Our strategy is to first generate and save the descriptive statistics along with a title and a footnote to a graphics catalog, to next create a seven panel template, and then to replay (re-display) the graphical output back into the template. The SAS code used in this paper will be based on the SAS for Windows 6.11 operating system. GENERATION OF GRAPHICAL OUTPUT Numerical Summary Statistics The first step in developing our statistical template is to create a graphics output file of summary statistics from a corresponding text input file. To accomplish this, we first generate the descriptive statistics from the UNIVARIATE procedure, and then direct the output to 1 an external text file referenced by the fileref on the PRINTTO procedure. Next, we invoke the GPRINT procedure, which inputs this text file and converts it into a graphics file, and then saves it to a graphics catalog. The following SAS code outlines this process more clearly and completely. libname gph c:\data\phsug98 ; filename univ c:\data\phsug98\univ.out ; options nocenter nodate nonumber ls=130 ps=25; goptions reset=all device=win gunit=cells chartype=007 hpos=130 vpos=25 htext=1.1 nodisplay; proc printto print=univ new; proc univariate data=univ normal; var &var; id pat; /* output SAS data set for creation of histogram */ output out=stats n=nobs median=median qrange=qrange mean=mean std=std probn=probn normal=normal min=min max=max range=range; proc printto; proc gprint fileref=univ gout=gph.univ name='stats'; DEVICE=WIN identifies the Microsoft Windows device driver used to produce/view graphical output on the monitor screen. GUNIT=CELLS specifies the graphical unit of measurement for the numerical statistical output. CHARTYPE=007 defines the hardware/true Type font number (007=SAS Monospace) for the summary statistics. (See (4) for instructions in adding True Type fonts with the WINPRTx series of device drivers. )

2 The HPOS and VPOS graphics output options are equal to the LINESIZE and PAGESIZE text output options. HTEXT=1.1 specifies the height of all statistical text. The PRINTTO procedure directs all statistical output to the external text file UNIV.OUT while the NEW option removes any previous output. The NODISPLAY option suppresses the display of the summary statistics. GOUT=GPH.UNIV defines the location of the graphics catalog where the graphical output from the GPRINT procedure is stored. NAME= STATS specifies the name of the graph in the graphics catalog (GPH.UNIV). Histogram The histogram is the most familiar and widely used plot for summarizing a data distribution. Unfortunately, it is often the most difficult to create given the complexity associated with choosing the appropriate (or optimal) binwidth/number of bins to display. To deal with this problem, a more precise theoretical/adhoc approach is proposed, and then incorporated into the CAPABILITY procedure of SAS/QC (see p. 52 of (5) for advantages of this procedure over the GCHART procedure). First, we calculate the number of bins using one of the upper bound formulas of Emerson and Hoaglin (1983), depending on the number of observations in the data set. Then, we modify this upper bound based on the normality of the data given by the p-value of the Shapiro- Wilk Test of Normality from the summary statistics. In particular, if the data is normal (p.05), we reduce the upper bound by 40% of the range from the upper bound to the default CAPABILITY lower bound of Terrell and Scott (1985). (The value of 40% refers to the adhoc element of this technique. It has been chosen for the expressed purpose of smoothing the data a little, while at the same time retaining a great amount of detail.) If the data is not normal (p <.05), we don t modify the upper bound, since it is recommended to use more bins than fewer under such circumstances (Scott, 1992). The following SAS code outlines the CAPABILITY part used to create the histogram and includes as well a nonparametric kernel density curve superimposed onto the histogram to examine features possibly obscured by the choice of histogram bins or sampling variation. (See pp of (7) for more details on kernel density estimates.) goptions dev=win gunit=pct ftext=zapf nodisplay; proc capability data=plots gout=gph.univ graphics noprint; 2 var &var; hist &var/midpoints=(&first to &last by &binwidth) vaxis=axis1 haxis=axis2 vscale=percent kernel (k=normal c=mise l=1 w=2) noframe nolegend name='hist'; axis1 label=(j=c h=&lh a=90 r=0 'Relative Frequency (%)') axis2 offset=(10,) label=(j=c h=&lh "&varlabel (&unit)") value=(h=&vh) order=(&first to &last by &binwidth) minor=none; title1 j=c h=&th 'Histogram Plot'; GUNIT=PCT defines the graphical unit of measurement for the plots. FTEXT=zapf is the software font used in the plots. GRAPHICS invokes high-resolution graphics. MIDPOINTS specifies the bin midpoints, where &first and &last are designated as the true first and last midpoints of the data, respectively, whose values are calculated by subtracting and adding a small percentage of the binwidth to the min and max values, respectively, and where &binwidth is equal to the range of the data divided by the # of calculated bins. Note this quantity, the small percentage, will probably have to be adjusted depending on the range of the data and the binwidth. KERNEL superimposes a nonparametric density curve onto the histogram using the normal kernel function (K=normal) to estimate the density function with the degree of smoothness (or bandwidth) indirectly specified by the default C= value, the value that minimizes the approximate mean integrated square error (MISE). (See p. 116 of (7).) Box-and-Whisker Plot The box-and-whisker plot presents a quick overview of a number of prominent features (center, middle 50% of the data, tail spread, and extreme values) of a distribution. Even though it is not customary in quality control work, the SHEWHART procedure in SAS/QC can be utilized to create an individual box-and-whisker plot. The following SAS code outlines this process. %let vnbrlo=%eval(&vnbr-2); %let vnbrup=%eval(&vnbr+2); goptions dev=win hsize=4 in vsize=3.15 in nodisplay; proc shewhart data=plots &gout graphics;

3 boxchart &var*vnbr/boxstyle=schematicid stddevs serifs nolegend nolimits noframe idsymbol=circle vminor=1vaxis=axis1 haxis=axis2 name='box'; axis1 label=( j=c a=90 r=0 h=&lh "&varlabel (&unit)") axis2 label=(j=c h=&lh 'Visit Week') order=(&vnbrlo to &vnbrup by 1) symbol1 v=star h=3 c=black; title1 j=c h=&th 'Box and Whisker Plot'; BOXSTYLE=SCHEMATICID extends the whiskers of the box plot 1.5 x IQR below the 25 th and above the 75 th percentiles, respectively. NOLIMITS suppresses the display of control limits. HSIZE= and VSIZE= options set the dimensions of the graphics output area. Their intended purpose here is to make the graphical output proportional to the size of the template panels, and thus prevent any distortion. The values above are chosen based on the default HSIZE and VSIZE values defined by the WINPRTM driver and the dimensions of the template panels. (Note these options were not applied to the histogram plot so as to prevent any potential confusion in interpretation caused by the appearance of two unforeseen axis values, one on each end, being added to the horizontal axis, even though all other aspects of the plot remained the same.) It should be noted that a WARNING message appears in the log when running this code. However, this message pertains not to the construction of the plot, but to the customary practice in using the SHEWHART procedure of comparing the distributions of more than one subgroup (defined by a subgroup variable, here vnbr ) of some analysis variable (&var) via side-by-side box-and-whisker plots. Normal and Detrended Normal Probability Plots The normal and detrended normal probability plots describe more systematically how an empirical (sample) distribution differs from a theoretical standard normal distribution. These plots are generated using a slightly modified version of the SAS System for Statistical Graphics NQPLOT macro. The following SAS code outlines only the normal probability plot, with standard errors lines added in order to examine the relative variability of points in different regions of the plot. data plots; set plots; sigma = σ _p_=round((_n_ -.5)/nobs,.0001); _z_=round(probit(_p_),.0001); _se_=(sigma/((1/sqrt(2* )) *exp(- (_z_**2)/2))) *sqrt(_p_*(1-_p_)/nobs); _normal_= sigma * _z_ + &mu ; _resid_ = &var - _normal_; _lower_ = _normal_ *_se_; _upper_ = _normal_ *_se_; _reslo_ = -1.96*_se_; _reshi_ = 1.96*_se_; label _z_='standard Normal (Z) Quantile' _resid_='deviation From Normal'; proc gplot data=plots &gout; plot &var * _z_= 1 _normal_ * _z_= 2 %if &stderr=yes %then %do; _lower_ * _z_= 3 _upper_ * _z_= 3 %end; / overlay vaxis=axis1 haxis=axis2 hminor=3 vminor=1 name='npp'; symbol1 v=dot h=2 i=none c=black l=1; symbol2 v=none i=join c=blue l=3 w=2; symbol3 v=none i=join c=green l=33 w=2; axis1 label=(j=c a=90 r=0 h=&lh "&varlabel (&unit)") axis2 label=(j=c h=&lh Standard Normal Quantiles') title1 j=c h=&th 'Normal Probability Plot'; Title and Footnote The title and footnote for this template are both created using the GSLIDE procedure. The following SAS code generates these two descriptive features. %let title = Univariate Descriptive Statistics: &varlabel (Treatment = &tg, Visit=&vnbr); goptions dev=win target=winprtm ftext=zapf gunit=cells nodisplay; proc gslide &gout name='title'; title1 j=c h=1.20 "&protid"; title2 j=c h=1.25 "&title"; proc gslide &gout name='foot'; 3

4 title1; footnote1 j=left h =.6 "Program: &program"; footnote2 j=left h =.6 "Data Source: &srce"; footnote3 j=left h =.6 "Output Date: &today"; footnote4 j=left h =.6 Programmer: &name ; STATISTICAL TEMPLATE STRUCTURE Let us now create the structure of the statistical template. First, the graphics enivironment is reset to DEV=WIN, TARGET=WINPRTM, and DISPLAY so as to be able to preview the template on the monitor screen (WIN driver) as it should appear on a hard-copy device (WINPRTM driver). Second, the GREPLAY procedure is invoked with the NOFS, IGOUT, and TC options. The NOFS option allows us to use line-mode statements for creating templates, replaying graphics, and managing graphics catalogs. The IGOUT option specifies the location of the graphical catalog (GPH.UNIV) to be inputted into the GREPLAY procedure while the TC option identifies the storage location of the template (GPH.UNIVCAT). Third, the TDEF statement defines the template structure, including the name SPECS and the four (x, y) coordinates for each of the seven panels. Fourth, the TEMPLATE statement assigns the newly defined template as the current template while the DELETE statement deletes any graphical output from the input catalog. Lastly, the TREPLAY statement selects and replays the graphs into the template based on the panel number (1,2, ) and the graphical catalog entry name (stats, hist, ). See Figure 1 below. goptions reset=all dev=win target=winprtm hsize=0 vsize=0 display; proc greplay nofs igout=gph.univ tc=univcat; tdef specs 1/ llx=0 lly=0 ulx=0 uly=100 urx=100 ury=100 lrx=100 lry=0 2/ llx=0 lly=65 ulx=0 uly=95 urx=100 ury=95 lrx=100 lry=65 3/ llx=0 lly=35 ulx=0 uly=65 urx=50 ury=65 lrx=50 lry=35 4/ llx=50 lly=35 ulx=50 uly=65 urx=100 ury=65 lrx=100 lry=35 5/ llx=0 lly=5 ulx=0 uly=35 urx=50 ury=35 lrx=50 lry=5 6/ llx=50 lly=5 ulx=50 uly=35 urx=100 ry=35 lrx=100 lry=5 7/ llx=0 lly=0 ulx=0 uly=100 urx=100 ury=100 lrx=100 lry=0 ; template specs; treplay 1:title 2:stats 3:hist 4:box 5:npp 6:dpp 7:foot; CONCLUSION This paper has attempted to improve the visualization and analysis of univariate data. By enhancing the graphical features of the plots, the conveyance and summarization of quantitative information is more readily apparent and more easily interpretable. In general, these graphical enhancements are a good idea, however, they do require greater time and computer resources. Thus, it is up to the data analyst to determine whether or not the visual improvement of the template is worth the greater expense in production time for univariate statistical analyses. REFERENCES [1] Emerson, J.D. and Hoaglin, D.C. (1983). Understanding Robust and Exploratory Data Analysis, eds. D.C. Hoaglin, F. Mosteller, and J.W. Tukey, New York: John Wiley & Sons. [2] Scott, D.W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization, New York: John Wiley & Sons. [3] Terrell, G.R. and Scott, D.W. (1985). Oversmoothed Nonparametric Density Estimates, JASA, 80, [4] Producing Hardcopy Graphics Under Windows 95 and NT, TS-300C. Cary, NC: SAS Institute Inc. [5] SAS Institute Inc. (1991), SAS System for Statistical Graphics, First Edition, Cary, NC: SAS Institute Inc. [6] SAS Institute Inc. (1990), SAS /GRAPH Software; Reference, Version 6, Vols. 1, 2, Cary, NC: SAS Institute Inc., 1458 pp. [7] SAS Institute Inc. (1995), SAS /QC Software; Usage and Reference, Version 6, First Edition,Vols. 1, 2, Cary, NC: SAS Institute Inc., 1697 pp. NQPLOT macro is reprinted with permission of SAS Institute Inc. from SAS System for Statistical Graphics, First Edition. Copyright 1991 by SAS Institute Inc. AUTHOR CONTACT INFORMATION: James O Hearn Pfizer Inc. 235 E. 42 nd St., Mail Stop: 150/37/7, NY, NY (212) , ohearj@pfizer.com 4

5 SAS, SAS/GRAPH, SAS/QC, and SAS/STAT are registered trademarks of the SAS Institute Inc. in the USA and in other countries. indicates USA registration. Windows is a registered trademark of the Microsoft Corporation. 8QLYDULDWH 3URFHGXUH 9DULDEOH (;7,0( 7RWDO ([HUFLVH 7LPH VHF 0RPHQWV 4XDQWLOHV'HI ([WUHPHV 1 6XP :JWV 0D[ /RZHVW,' +LJKHVW,' 0HDQ 6XP 4 6WG 'HY 9DULDQFH 0HG 6NHZQHVV.XUWRVLV &66 0LQ &9 6WG 0HDQ 70HDQ 3U!_7_ 5DQJH 1XP A 1XP! 44 06LJQ 3U! _0_ 0RGH 6JQ 5DQN 3U! _6_ :1RUPDO 3U: 0LVVLQJ 9DOXH &RXQW &RXQW1REV Figure 1. Descriptive Statistics for Total Exercise Time (sec): Treatment = A, Visit = 10. 5