Descriptive Statistics: Using Indicator Variables

Transcription

1 Descriptive Statistics: sing ndicator Variables Juliana. a" NC Highway Safety Research Center Tamara R. Fischell, NC Highway Safety Research Center ntroduction ndicator variables have proved useful in certain categorical studies of highway safety data when counts and percentages are computed and displayed. Alternative methods of producing these statistics can be based on the special properties of indicator variables. Examples presented in this paper demonstrate the variety of ways indicator variables can be used. We will present a brief description of highway safety studies where these techniques are effective, and use several examples to illustrate common applications. An intermediate-level knowledge of SAS@ basics (DATA step, SHARY, FREQ, CHART, EANS, WEGHT statement) is assumed. Definition An indicator variable is a very simple variable with special properties. t has two specific non-missing values: one and zero. The value is defined as one for an observation that satisfies some criterion of interest, and zero for one that does not. The criterion may be simple (the driver was using a seat belt) or complex (the car overturned and the driver was not belted). A variable defined as an indicator variable has two useful properties: 1. The sum is a count of the number of observations satisfying the criterion. 2. The mean, which is the sum divided by the total number of observations, is the percentage satisfying the criterion. The five observations below illustrate the properties of an indicator variable ELT (O-not belted, -belted) and its relationship to ELTSE (-unbelted, -belted), a standard categorical variable. Three people, sixty percent (3/5), were belted. OS ELTSE ELT S of ELT ~ EAN of ELT = These properties hold whether the statistics are calculated for an entire file, or for subgroups. Subgroups may be specified using Y variables (PROe EANS), elass variables (PROe SARY), or GROP variables (PROe CHART). Applications We use indicator variables for categorical studies that focus on one characteristic while controlling for other variables. One standard analysis compares different types of cars with regard to rare events, such as overturning or post-crash fires. Another example is the consideration of changes in seat belt usage over time controlling for variables like sex and race. Our vehicle studies of rare events involve large files, where four or five variables are sufficient to define the subgroups of interest. The analysis may be based on 100,000 to 1,000,000 observations. We use indicator variables to count the rare events so that more classification variables can be used to define subgroups. The statistics are computed by PROC SARY as discussed by a and Leininger (1984). Example 1 This example shows how PROC SARY and PROe FREQ can be used to produce tables based on the sum of an indicator variable. The difficulty is that PROC FREQ tables based on the sum cannot be produced directly from summary data. The analysis compares the frequency of post-crash fire in cars, where the different car types are defined by four classification variables. An extra DATA step is required to change the summary data into appropriate input for PROC FREQ. Two counts for each combination of the CLASS variables exist in the summary dataset, SSTAT, created in Figure 1. The overall count is the value of FREQ, while FRE is the count of the-number of post-crash fires. The TASTAT dataset has two observations for each subgroup combination, with an appropriate value for the categorical variable FRETYPE. The first observation is weighted by the number of non-fire cases and the second is weighted by the number of fire cases. 1026

2 Figure 1 PROC SARY DATA=CARS NWAYi CLASS CARGROP YEAR ODYTYPE PACT, VAR FRE: OTPT OT=ddname.SSTAT S= /* CARS is a large file /* defines subgroups /* indicator variable (0,1) /* S=count of fires DATA TASTAT, SET ddname.sstati FRETYPE='NO 'i CONT = FREQ - FRE, FRETYPE='YES'; - CONT = FRE, OTPT, OTPT, /* No fire /* Fire PROC FREQ DATA=TASTAT; WEGHT CONT; TALES (CARGROP ODYTYPE PACT) * FRETYPE, Tables could be produced for any combination of the classification variables using 'PROC FREQ DATA=TASTAT;' and 'WEGHT CONT;'. Example 2 ndicator variables are useful when the possibility exists that a special class of observations will eventually be omitted from a large file analysis. An easy and inexpensive method of producing tables with or without the "special" observations requires planning ahead. oth analyses can be based on summary data that includes the sum of an indicator variable. Tables for two populations are produced from one summary dataset in the example in Figure 2. nitially, all cars were included, but we expected that the final analysis would not include overturn cases. The large file does not need to be re-processed for tables of only non-overturn cases since the summary data includes the sum of an indicator variable (OVERTRN). sing a CLASS variable to separate the overturn cases was not possible for this analysis because of the number of other classification variables required. NEWCONT is the appropriate weight variable for non-overturn tables since it is defined as the difference of FREQ, the total for the entire file, and OVERTRN, the number of overturned cars. Figure 2 PROC SARY DATA=CARS NWAY, CLASS CARGROP YEAR ELT SEX NJRY, VAR OVERTRN, OTPT OT=STAT S= i /* CARS is a large file /* defines subgroups -/* indicator variable (0,1) /* S=count of overturn cases J DATA ddname.stat; SET STAT, NEWCONT = FREQ - OVERTRN, LAEL NEWCONT =-'NON-OVERTRN CONT'; PROC FREQ DATA=ddname.STAT; WEGHT FREQ; /* all cars TALES CARGROP * ELT * NJRY; TTLE ALL CARS; PROC FREQ DATA=ddname.STATi WEGHT NEWCONTi /* non-overturn only TALES CARGROP * ELT * NJRY; TTLE NON-OVERTRN CARS ONLY; 1027

3 Example 3 The purpose of this example is to compare two methods of displaying percentages. PROC CHART is used with an indicator variable and a standard categorical variable. The advantage of displaying percentages as the mean of an indicator variable, is that charts do not include the "other category.~ The charts are based on a dataset containing information about drivers (SEX, ELTSE), with time periods defined by ONTH and an indicator variable named ELT. Figu.res 3a and 3b show the difference between using the mean of ELT (0,1) and. using the standard categorical variable ELTSE (,). The trend for belt usage is clearer using the indicator variable. Example 4 Computing percentages for subgroups is simple using an indicator variable. For small datasets either PROC CHART or a combination of PROC EANS and PROC PLOT can be used. sing PROC SARY to compute the statistics is more efficient for large files. Suppose the difference between males and females was of interest in the data from Example 3. Figures 4a and 4b show two ways of computing and displaying the same statistics. Less coding and processing are required with PROC CHART, while computing the statistics using PROC EANS requires sorting the dataset. Advantages and Disadvantages Some of the advantages of using indicator variables, when the study type is appropriate, are: 1) ncreased flexibility in choosing classification variables to define subgroups when PROC SARY is used to compute statistics. sing an indicator variable may allow an additional CLASS variable. 2) ncreased potential foi generating a variety of tables from summary data of a large file. For example, we could count both the number of overturn and post-crash fire cases for the same car subgroups. 3) Graphic displays of percentages can be based on the mean of an indicator variable. PRoe CHART may be used directly or means may be generated as input for PROe PLOT. oth statistics and a chart can be shown on one page using the HAR statement of PROC CHART. The only disadvantage we have found is the knowledge required to recognize and implement analyses based on statistics calculated from indicator variables. Additional DATA steps may be required before procedures like FREO or PLOT Can produce desired results. A good method for understanding the processing stages is to inclde PROC PRNT after every step (with the OS option) during program testing. using indicator variables effectively takes planning and practice! Conclusion ndicator variables are useful for many of our categorical studies. Efficient analyses of large files are possible when they are used with PROC SARY. The ideas presented here are meant as an introduction to the possibilities created by indicator variables. We hope others will find applications for these techniques when they consider how to analyze their data. References Hamilton, Elizabeth, Single Variable Tabulations for North Carolina Accidents. NC Hlghway Safety Research Center, Chapel Hill, NC, a, J.. and Leininger, C., PROC SHARY as the asis for Efficient Analyses of Large Files." Proc. of the Ninth Annual SG Conference. SAS nst.i tute nc., Cary, NC, SAS is the registered trademark of SAS nstitute nc., Cary, NC For more information, contact: Juliana. a NC Highway Safety Research Center CTP 197A Chapel Hill, NC

4 ELT EAN *"''''* *"''''''' "'*"'... JL *"''''* ** "'''''''* *"''''* AG Figure 311 AR CHART OF EANS "'''''''* ""*. SEP ONTH **>k* "'*"'''' "'''''''''' ***'" """""'* NO *"''''''' "'''''''''' *"'*'" ",,,,,,,oil """'*'" *""*'" PROC CHART OAT A=DR VERS; VAR ONTH TVPE=EAN SVAR=EL T; PEACENTAGE ** 20 + ** 10+ ** *... JL ** * ** "'' A Figure 3b PERCENTAGE AR CHART *'" ** ** "'* SEP ** NOV ** "'*.... ELTSE ONTH PROC CHART DAT A=DR VERS; VAR ELTSE GROP=ONTH TVPE=PERCENT DSCRETE G 00; 1029

5 Figure 4a AR CHART Of EANS C»TH SEX FREQ 6EL T EAN JL ALE ".. 1", t f S00 FEAlE ~l" ** ** AG AlE ~... *** FEALE SEP ALE " ii WH FEAlE ~ * * ** ** AlE ~*** * ** ** FEALE t.w. ii NOV ALE ~. * FEALE 1,, l1li * [) C AlE ~ ***** ** FEALE ELT EAN PROC CHART DATA=DRVERS; HAR SEX / TYPE =EAN SV AR=EL T GROP=ONTH DSCRETE; Figure 4b ELT EAN PLOT Of 6El TEAN'C»TH SYOl S VALlJ Of SEX JL AG SEP C»TH NOV PROC SORT DATA=DRVERS; Y ONTH SEX; PROC EANS DAT A=DR VERS; VAR ELT; OTPT OT=STAT EAN=ELTEAN; PROC PLOT DATA=STAT; PLOT EL TEAN.. ONTH = SEX; 1030