Stat 515 - Fall 2001 - SAS Templates

The Basics of SAS:

There are three main windows that are used in SAS. The Log window, the Program Editor window, and the Output window. The Log and Program Editor window are the two on the screen when you start up the program. The Output window isn't visible yet because you haven't created anything to output. If you happen to lose one of these windows they usually have a bar at the bottom of the SAS window. You can also find them under the View menu.

The Program Editor is where you tell SAS what you want done. The Output window is where it puts the results, and the Log window is where it tells you what it did and if there are any errors. It is important to note that the Output window often gets very long! You usually want to copy the parts you want to print into MS-Word and print from there. It is also important to note that you should check the Log window everytime you run anything. (The error SAS Syntax Editor control is not installed is ok though.) The errors will appear in maroon. Successful runs appear in Blue. Hitting the [F3] key will run the program currently in the Program Editor window.

This will however erase whatever was written in the Program Editor window. To recall whatever was there, make sure you are in that window, and hit the [F4] key.

If you keep running more programs it will keep adding it all to the Output window. To clear the Output window, make sure you are in that window, and choose Clear text under the Edit menu.

If you happen to lose a window, try looking under the Globals menu.

The following is the SAS code for entering data about the starting salaries of a group of bank employees. The data consists of the beginning salaries of all 32 male and 61 female entry level clerical workers hired between 1969 and 1977 by a bank. The data is reported in the book The Statistical Sleuth by Ramsey and Schafer, and is originally from: H.V. Roberts, "Harris Trust and Savings Bank: An Analysis of Employee Compensation" (1979), Report 7946, Center for Mathematical Studies in Business and Economics, University of Chicago Graduate School of Business.

The data is formatted in two columns, the first is the starting salary, the second is an id code, m for male, and f for female.
 

OPTIONS pagesize=50 linesize=64;



DATA bankdata;

INPUT salary gender $ @@;

LABEL salary = "Starting Salary" 

   gender = "m=male, f=female";

CARDS;

3900 f 4020 f 4290 f 4380 f 4380 f 4380 f

4380 f 4380 f 4440 f 4500 f 4500 f 4620 f

4800 f 4800 f 4800 f 4800 f 4800 f 4800 f

4800 f 4800 f 4800 f 4800 f 4980 f 5100 f

5100 f 5100 f 5100 f 5100 f 5100 f 5160 f

5220 f 5220 f 5280 f 5280 f 5280 f 5400 f

5400 f 5400 f 5400 f 5400 f 5400 f 5400 f 

5400 f 5400 f 5400 f 5400 f 5400 f 5520 f 

5520 f 5580 f 5640 f 5700 f 5700 f 5700 f 

5700 f 5700 f 6000 f 6000 f 6120 f 6300 f 

6300 f 4620 m 5040 m 5100 m 5100 m 5220 m 

5400 m 5400 m 5400 m 5400 m 5400 m 5700 m 

6000 m 6000 m 6000 m 6000 m 6000 m 6000 m 

6000 m 6000 m 6000 m 6000 m 6000 m 6000 m

6000 m 6300 m 6600 m 6600 m 6600 m 6840 m

6900 m 6900 m 8100 m

; 

The OPTIONS line only needs to be used once during a session. It sets the length of the page and the length of the lines for viewing on the screen and printing. The font can be set by using the Options menu along the top of the screen. When you cut and paste from SAS to a word processor, the font Courier New works well.

The DATA line defines what the name of the data set is. The name should be eight characters or less, with no spaces, and only letters, numbers, and underscores. It must start with a letter. The INPUT line gives the names of the variables, and they must be in the order that the data will be entered. The $ after gender on the INPUT line means that the variable gender is qualitative instead of quantitative. The @@ at the end of the INPUT line means that the variables will be entered right after each other on the same line with no returns. (Instead of needing one row for each person.)

If we hit F3 at this point to enter what we put above, nothing new will appear on the output screen. This is no big surprise however once we realize that we haven't told SAS to return any output! The code below simply tells SAS to print back out the data we entered.

PROC PRINT DATA=bankdata;

TITLE "Gender Equity in Salaries";

RUN;

The only difficulty we have now, is that it would be nice to look at both the men and women separately, so we need to be able to split the data up based on whats in the second column. The following lines will make two separate data sets male and female, and then print out the second one to make sure it is working right:

DATA male;

SET bankdata;

KEEP salary;

WHERE gender='m';

RUN;



DATA female;

SET bankdata;

KEEP salary;

WHERE gender='f';

RUN;



PROC PRINT DATA=female;

TITLE "Female Salaries";

RUN;

Whenever you have a DATA line, that means you are creating a new dataset with that name. The SET line tells it that we are making this new data set from an old one. The KEEP line says the only variables we want in this new data set are the ones on that line. The lines after that say any special commands that go into the making of the new data set. In this case the WHERE command is used to make sure we only keep one gender or the other. Later we will see examples of making datasets that involve using mathematical functions. In any case, it should be pretty straight-forward when you just stop and read through what the lines say.

The most basic procedure to give out some actual graphs and statistics is PROC UNIVARIATE:

PROC UNIVARIATE DATA=female PLOT FREQ ;

VAR salary;

TITLE 'Summary of the Female Salaries';

RUN;

The VAR line says which of the variables you want a summary of. Also note that the graphs here are pretty awful. The INSIGHT procedure will do most of the things that the UNIVARIATE procedure will, and a lot more. The one thing it won't do is be open to programming it to do new things. Later in the semester we'll see how some of the other procedures in SAS can be used to do things that aren't already programmed in.

PROC INSIGHT;

OPEN female;

DIST salary;

RUN;

You can cut and paste the graphs from PROC INSIGHT right into microsoft word. Simply click on the border of the box you want to copy with the right mouse button to select it. You can then cut and paste like normal. Clicking on the arrow in the bottom corner of each of the boxes gives you options for adjusting the graphs format. To quit PROC INSIGHT, click on the X in the upper right portion of the spreadsheet.

The graph at the top is a Box Plot or a Box and Whisker Plot. The wide line in the middle is the median. The edges of the box are the 25th percentile = 1st Quartile = Q1 and the 75th percentile = 3rd Quartile = Q3. The distance between these two values is called the Interquartile Range = IQR = Q3-Q1. It is another measure of spread. As a rule of thumb, if the data is from a bell curve then IQR/s should be approximately 1.3. Because it isn't affected as much by outliers, the IQR is sometimes more useful for describing the spread of a data set than the standard deviation is.

Extending beyond the edge of the box are the whiskers. The whiskers are allowed to go up to 1.5 IQRs from the edge of the box, and must end at a data point. The values beyond that are displayed as dots. They are possible outliers. The box plot has the advantage that it is always drawn the same way (unlike a histogram), but the disadvantage that it doesn't show as much detail.

One thing that we can notice from the histogram and box plot is that the data does not look very symmetric, instead it looks slightly skewed to the left. We can add a curve over the histogram to make it easier to compare to a bell-shaped (or normal) curve. Under the Curves menu, choose Parametric Density.... Just hit ok on the box that pops up.

As mentioned before, one of the problems with the histogram is that the way it looks can be affected a lot by how the width of the bars is selected, and where they start and begin. The box with the arrow in it, at the lower left side of the histogram lets you control that. Click on that box, and then select Ticks.... Change the 3800 to 3600, and the 6600 to 6400, and then click ok. Now try 3700 and 6700, and set the Tick Increment to 600.

Unlike the histogram, the Q-Q plot is not subject to options chosen by the user. Under the Graphs menu select QQ Plot... and then click ok in the window that comes up. Then under Curves select QQ Ref Line.... The idea of the Q-Q plot is that it plots the actual data along the y-axis, and the values that the data would have if they were exactly the percentiles of a normal curve. So if the data is approximately like that of a bell curve, the line should look fairly close to straight. If not, it should be off. Notice that this looks very close to a straight line. Because the data is bell-curved, the empirical rule should hold, and it does fairly well for this data. Notice that the mean and median differ by less than 100. Also notice that IQR/s = 1.11, which isn't very far from 1.3.

Lets change one of the values though, so that the data appears less normal. Click on the spreadsheet, and change the 3900 to 8900, the 4020 to 8020, the 4290 to the 8290, and the first 4380 to 8380. Now note that those three points are rather exterme as indicated on the box plot. You can also see the change in the Q-Q plot. Now, the empirical rule does not work nearly as well. Notice that the mean is over 100 larger than the median (we only changed 4 out of 61 values, and not by _that_ much) which isn't too bad. However, notice that IQR/s is only 0.84!

To compare both men and women, we could open PROC INSIGHT with the original data set. (It is probably quickest to close it using the X in the spreadsheet, then go to the Solutions menu, the Analysis submenu, and then Interactive Data Analysis. Select Work and then Bank Data and then hit Open.) Under the Analyze menu choose Box Plot/Mosaic Plot (Y). Pick Salary for Y and Gender for X.

Homework 3 Notes

This assignment is basically just repeating part of what we did in class, but with a different data set. The data set SLI.DAT can be found either on the disk that came with your text book, or can be found on the web.

Once you've opened up a window (e.g. Internet Explorer) with the data in it, you can copy it into the program editor window of SAS. Just like was done for the bankdata set from in class, you'll need to add a DATA line with the name you want to give the data set (leaving a period in the name won't work!), an INPUT line with the names of the variables (having spaces and % signs won't work for a name), a CARDS line, and a semi-colon at the end. Remember on the INPUT line to put a space and $ after the names of any variables that are qualitative instead of quantitative (like we did for gender on the in class example. (Make sure you got rid of the little square that appears at the bottom of the data set on the web page.)

Parts c-e of the homework now want you to compute measures of center for the variable DIQ for each of three different groups. The first step is to create three different data sets (one for YND, one for SLI, and one for OND), just like we created separate data sets for male and female in class. You need to come up with a name for each of the three new data sets, and put that on the DATA line, the SET is whatever you called the data from SLI.DAT, you need to at least KEEP the DIQ variable, and you need to use the WHERE command correctly. Using PROC PRINT can tell you if you correctly made the right data sets.

Once you've made the three new data sets, you can get the measures of central tendency (section 2.4 of the text) using either PROC UNIVARIATE or PROC INSIGHT. Getting the side by side box plots is the last thing we did in class on the 4th.

Remember to include a copy of what you put in the program editor window with your finished homework.

Homework 6 Notes

The following instructions and code will construct confidence intervals for the mean, variance, and standard deviation of the data in Example 7.2 on page 292. (Your homework should probably be similar, but using the data in problem 7.34 on page 299, and not the data thats used here as an example.)

The first step is to enter the data.

DATA examp7p2;
INPUT numb_chars @@;
CARDS;
1.13	1.55	1.43	0.92	1.25	1.36	1.32	0.85	
1.07	1.48	1.20	1.33	1.18	1.22	1.29
;

We could then use PROC INSIGHT to analyze this data. You could start PROC INSIGHT by going to the Solutions menu, and then the Analysis submenu, then choose Interactive Data Analysis. In the box that comes up, choose WORK and examp7p2 and hit Open. You could also start PROC INSIGHT by using the following:

PROC INSIGHT;
OPEN examp7p2;
DIST numb_chars;
RUN;   

To construct the confidence intervals, go to the Tables menu and select Basic Confidence Intervals. If you choose your desired percent, all three will be added to the output window.

To report the results of this example, the easiest thing to do would be to open Microsoft word and copy into it the code from the Program Editor window, the box containing the Q-Q plot, and the box containing the confidence intervals.

Homework 8 Notes

Note: For "by hand" problems you may use SAS or a calculator to calculate the means and standard deviations. For the two-sample t-test by hand you should still calculate s²_p by hand from the two individual standard deviations (even though you can use SAS to check the result.)

Test for a Single Mean: The following code is an example of how you can get a test of hypotheses for a single mean. It is example 8.4 on page 337. Please note that PROC INSIGHT always gives the p-value for the alternate hypothesis "not equals too". If you want the p-value for < or > then you must draw the picture and see how you need to change the p-value. (The text gives instructions for this on page 338 in its Note.)

DATA examp8p3;
INPUT hstays @@;
CARDS;
2	3	8	6	4	4	6	4	2	5
8	10	4	4	4	2	1	3	2	10
1	3	2	3	4	3	5	2	4	1
2	9	1	7	17	9	9	9	4	4
1	1	1	3	1	6	3	3	2	5
1	3	3	14	2	3	9	6	6	3
5	1	4	6	11	22	1	9	6	5
2	2	5	4	3	6	1	5	1	6
17	1	2	4	5	4	4	3	2	3
3	5	2	3	3	2	10	2	4	2
;

PROC INSIGHT;
OPEN examp8p3;
DIST hstays;
RUN;

To conduct the test of hypotheses, we can simply go to Tests for Location... under the Tables menu. Select mu=5 (our null hypothesis value in this example) and hit ok. This gives the results of three tests. The first is our t-test for testing the alternate hypothesis of "not equals to". The other two tests (the Sign Test and the Signed Rank test) are discussed in STAT 518.

Looking at the p-value we can see that it is 0.2042 with a t-statistic of 1.28. Following the instructions on page 338 we cut that p-value in half for our hypotheses and get that the p-value is 0.1021. Comparing this to our alpha=0.05 we fail to reject the alternate hypothesis.

Another way to get the one-sided p-values is to use the following code. It returns all three p-values (one for each possible alternate hypothesis) and you have to choose the correct one. The only portions you need to change are the name of the data set, the name of the variable, and the value after the cards line. The value after the cards line should be the value for the null hypothesis.

If you read through the code, you should be able to make out several of the formulas.

PROC MEANS NOPRINT DATA=examp8p3;

VAR hstays;

OUTPUT OUT=temp MEAN=xbar STD=sd N=n

RUN;

DATA temp2;

SET temp;

KEEP xbar mu sd n t pgreater pless ptwoside;

INPUT mu;

t  = (xbar-mu)/(sd/sqrt(n));

df = n - 1;

pgreater = 1 - probt(t,df);

pless = probt(t,df);

ptwoside = 2*MIN(1-ABS(probt(t,df)),ABS(probt(t,df)));

cards;

5

;

PROC PRINT;

RUN;

Test for Two Means and Two Variances: The following sample code would analyze the data in Example 9.4 on page 380. Notice that we have to enter the group and the value for each observation, and that the group name is a word (and so it needs a $).

DATA examp9p4;

INPUT group $ value @@;

CARDS;

new	80      new     80      new     79      new     81

stand	79      stand   62      stand   70      stand   68

new	76      new     66      new     71      new     76

stand	73      stand   76      stand   86      stand   73

new	70      new     85

stand	72      stand   68      stand   75      stand   66

;





PROC TTEST DATA=examp9p4;

CLASS group;

VAR value;

RUN;

The order you enter the groups determines which hypothesis is being tested. Because the new group was entered first, the procedure will look at the difference new-stand. By default the procedure tests the hypothesis that this difference is equal to zero. To test that the difference is equal to some other value, say 5, you would add H0=5 to the first line between examp9p4 and the semi-colon (in PROC TTEST).

The first three rows of the output contain the means, confidence intervals for the means, standard deviations, and confidence intervals for the standard deviations for the two groups individually, and for the difference of the two groups. Notice that the third row gives the confidence interval (-1.399, 9.5327) that matches what the text found in the middle of page 381... SAS uses 95% for CIs by default. Also notice that we can find s²_p on the third line; 6.119 is the square root of 37.45.

The next two rows of the output are for the two t-tests. The Pooled line is the case where the variances are equal, and the Sattertwaite line is for unequal variances. For unequal variances in SAS, SAS uses a complicated formula to estimate the degrees of freedom. Notice that they are not an integer! Since we only use the unequal case for large sample sizes (where the z and t are nearly identical) this shouldn't be a problem. One important thing to note here is that SAS is doing the two-sided test for the alternate hypothesis "not equals to". If you are testing either < or >, then you will need to draw the picture and adjust the p-value by hand.

The final line is a test of the null hypothesis that the variances of the two groups are equal or not. The Pr>F column is the p-value for this test, so if it is a small value (less than alpha) you reject the null hypothesis that the variances are equal. For this example we see that the p-value is 0.8148, which is very large, and so we fail to reject that the variances are equal. (Remember that the F test for two vairances is not robust at all; if you have any question as to whether the two samples come from normal populations you shouldn't trust it!!!)

In checking the assumption that the data is normal, we need to make sure we check it for BOTH samples. We can still use PROC INSIGHT for this.

PROC INSIGHT;

OPEN examp9p4;

RUN;

When you choose Distribution (Y) under the Analyze menu, choose value for Y and choose group for group. This will put the information for both groups in the same window (use the scroll bar at the bottom to switch between them). If you add the q-q plot and q-q line, it will add them for both variables. In this case the second sample appears to look fairly normal, but the first one is a bit questionable. Because of this, I would trust the two sample t-test (it is robust against) slight violations, but I would not trust the result of the F-test.

A logical next question is "If I can't trust the F-test, then how do I know if I can use the test where we assume the variances are equal?" Because the two-sample t-test for two means is fairly robust (especially when the two samples are about equal sized, see pg. 383) we could just compare the standard deviations, or we could use two box-plots like they do on page 382 and see if we believe the variances are equal or not.

NOTE: There are more robust tests available to see if two variances are equal than the F test. One of these that SAS can be made to perform in PROC GLM is called the "Modified Levene's Test" or the "Brown and Forsythe Test". Similarly SAS can be made to perform tests of the null hypothesis "the data comes from a normally distributed population" vs. the alternate hypothesis that the population is not normal. Perhaps the best of these tests is the "Anderson-Darling Test". Because these tests are somewhat complicated we will not be covering them in STAT 515... but if you ever need a test of either of these hypotheses, feel free to stop by and ask either me or the Statistical Consulting lab.

Homework 10 Notes

The following code will analyze the data in examples 10.3 and 10.4. Notice that each observation must have both a group identifier and a measurement. Recall that the $ tells SAS that the variable before it is characters (not numbers) and the @@ means that more than one observation occurs on a line.

DATA iron;
INPUT brand $ dist @@;
CARDS;
A	251.2	B	263.2	C	269.7	D	251.6
A	245.1	B	262.9	C	263.2	D	248.6
A	248.0	B	265.0	C	277.5	D	249.4
A	251.1	B	254.5	C	267.4	D	242.0
A	260.5	B	264.3	C	270.5	D	246.5
A	250.0	B	257.0	C	265.5	D	251.3
A	253.9	B	262.8	C	270.7	D	261.8
A	244.6	B	264.4	C	272.9	D	249.0
A	254.6	B	260.6	C	275.6	D	247.1
A	248.8	B	255.9	C	266.5	D	245.9
;
           
PROC INSIGHT;
OPEN iron;
FIT dist = brand;
RUN;

This output gives you the ANOVA table automatically. To check the assumptions we need to verify that the variances seem to be approximately equal and that the distributions seem approximately normal.

Side by side box plots can be used to see if the groups seem to have the same variance (similar to Figure 10.10, but using Box Plots instead of Dot Plots). Under the Analyze menu choose Box Plot/Mosaic Plot (Y). Select dist for Y and brand for X. This plot shows us both how the means differ (C looks larger than the others) and that all have roughly the same variance (the size of each box plot isn't that much different from the others). You also could have chosen Distribution (Y) under the Analyze menu with dist for Y and brand for group. This will calculate the standard deviation for each group and we could conclude that since all the sds are between 3.8 and 5.2 that they are close enough that the procedure should work well.

To check if each of the samples looks like they came from normal distributions, we need to make a Q-Q plot for each one. Under the Analyze menu choose Distribution (Y). Select dist for Y and brand for group. You can then choose QQ Ref Line... under the curves menu. (To get rid of all the extra information, you could deselect the various "checked" tables and graphs under the Tables and Graphs menus.) For this example, Brands A and C look very close to normal, Brand B looks a little odd, and Brand D appears to have one outlier. Since the F test for ANOVA is robust however, none of these seem bad enough not to trust the test.

NOTE: PROC GLM is another commonly used method of performing both Analysis of Variance and regression. It will construct the ANOVA table and many other statistics that we will use in STAT 516... it won't construct the various graphs however. The code we would use with this data and PROC GLM would be:

PROC GLM DATA=iron;
CLASS brand;
MODEL dist=brand;
RUN; 

The last page of this output is the same as that on the bottom of page 446, except that it was generated using PROC GLM instead of PROC ANOVA.

Homework 11 Notes

Linear regression can be performed using PROC INSIGHT in the same way that ANOVA is (see Hmwk 10 above). Remember that the x variable must be numeric... so don't use a $ with it!

The only difference is in getting the plots to check the assumptions. The residual vs. predicted plot is already part of the output. The Q-Q plot for the residuals can be added by choosing Residual Normal QQ from the Graphs menu.

Homework 12 Notes

The following code will analyze the data in example 13.1 on page 717.

DATA ex13p1;

INPUT opinion $  count;

CARDS;

legal       39

decrim      99

exist       336

noopin      26

;

PROC FREQ DATA=ex13p1 ORDER=data;

TABLES opinion / TESTP=(.07,.18,.65,.10);

WEIGHT count;

RUN;

The following code will work example 13.2 on page 726.

DATA ex13p2;

INPUT rel $  marit $  count;

CARDS;

A   D       39

B   D       19

C   D       12

D   D       28

None        D       18

A   Never   172

B   Never   61

C   Never   44

D   Never   70

None        Never   37

;



PROC FREQ DATA=ex13p2;

  WEIGHT count;

  TABLES rel*marit / chisq expected nopercent;

RUN;

Downloading the Data from the Web

Note that if you are using Internet Explorer, it may work better to use "select all" under the edit menu, instead of highlighting the text manually). Also note that you don't want to leave the little box at the end of the data set in when you try to run SAS. Finally, in Internet Explorer, a box may pop up asking you if you wish to download or open the data. Just select open, and it should come up in some sort of document editor that you can cut and paste from.

Computer Trouble?

In most cases, help with the computers (NOT the programming) can be gained by e-mailing help@stat.sc.edu

For the printers on the first and second floor, printer paper is available in the Stat Department office. For printers on the third floor, paper is available in the Math Department office.

If you are using a PC restarting the machine will fix many problems, but obviously don't try that if you have a file that won't save or the like. DO NOT TURN OFF THE UNIX MACHINES.

If SAS won't start, one of the things to check is that your computer has loaded the X drive correctly (whatever that means). Go to My Computer and see if the apps on 'lc-nt' (X:) is listed as one of the drives. If it isn't, go to the Tools menu and select Map Network Drive.... Select X for the drive, and enter \\lc-nt\apps for the Folder. Then click Finish. This should connect your computer to the X drive and allow SAS to run. If you already had the X-drive connected, then you will need to e-mail help@stat.sc.edu.

If your graphs print out extremely small after you copy them to word, you might be able to fix the problem by "opening and closing" the image. In word, left click once on the image, and select Edit Picture or Open Picture Object under the Edit menu. A separate window will open with the image in it. Simply choose Close Picture. It should now print out ok. This will also make the spacing between the characters in the labels look right if they were somewhat off.

If the problem is an emergency requiring immediate attention see Wei Pan in room 209D.
If Wei Pan is not in, and it is an emergency see Jason Dew in room 415.
If neither Jason or Wei is available and it is an emergency see Minna Moore in room 417.
Flagrantly non-emergency cases may result in suspension of computer privileges.