The document discusses applications of the DOW loop in SAS. It describes how DOW loops can be used to perform Cartesian joins, calculate geometric means, and conduct bivariate linear regression. The DOW loop structure involves a DO loop with a SET statement to iterate through a dataset. It provides examples of using single and multiple DOW loops to summarize data and perform calculations that require multiple passes through the data.

1. Applications of the DOW LoopApplications of the DOW Loop

2. Table of Contents
• Introduction
• Structure of DOW Loop
• Application 1: Cartesian Join
• Application 2: Geometric Mean
• Multiple DOW Loop
• Application 3: Bivariate Regression
• Conclusion

3. Introduction
• A simple data step concept first proposed
by Ian Whitlock on the SAS – L list with
Don Henderson.
• Detail analysis by Paul Dorfman and
Howard Schreier.
• The term DOW (DO – Whitlock) loop was
coined by Dorfman.

4. Structure of the DOW Loop
• The original DOW loop is a simple do
loop with a set statement in the structure.
Data ... ;
<Stuff done before break-event> ;
Do <Index Specs> Until ( Break-Event ) ;
Set A ;
<Stuff done for each record> ;
End ;
<Stuff done after break-event... > ;
Run ;

5. Application 1: Cartesian Join
• Cartesian Join is one of the simple things
that can be easily achieved in a single
SQL statement.
PROC SQL;
CREATE TABLE DATA AS SELECT * FROM
A,B;
QUIT;

6. Application 1: Cartesian Join
• Cartesian Joins can also be done
using a simple DOW loop.
• Not as simple and as elegant as the
SQL statement
• Applicable to all versions of SAS
DATA CART_JOIN;
SET A;
DO J = 1 TO COUNT;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

7. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

8. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

9. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

10. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

11. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

12. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

13. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

14. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

15. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

16. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

17. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

18. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

19. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

20. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

21. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

22. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

23. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

24. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

25. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

26. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

27. The engine
A B C D
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
DATA CART_JOIN;
SET A;
DO J = 1 TO 4;
SET B NOBS=COUNT POINT=J;
OUTPUT;
END;
RUN;

28. Application 2: Geometric Mean
• Most of the mathematical and statistical
functions in SAS are column based and
deriving a calculation for just a single
column can be very troublesome.
• The DOW loop provides a simple
solution to these problems.
• We can use a DOW loop to loop through
the observations and derive the answer.

29. Application 2: Geometric Mean
/*LOOP RUN*/
DATA _NULL_;
/*SINGLE DO LOOP*/
DO UNTIL (EOF);
SET HAVE END=EOF;
BY CATEGORY;
/*RESETING THE PREVIOUS VALUE*/
IF FIRST.CATEGORY THEN DO;
TOTAL = 1;
COUNT = 0;
END;
/*CALCULATING THE TOTAL SUM AND COUNTS VALUE*/
TOTAL = TOTAL*NUMBER;
COUNT = SUM(COUNT,1);
/*OUTPUTING THE RESULTS AND THE GEOMETRIC MEAN CALCULATION*/
IF LAST.CATEGORY THEN DO;
/*CALCULATION FORMULA AS PER THE INSTRUCTION IN SAS HELP*/
GEOMEAN = TOTAL**(1/COUNT);
/*OUTPUTING THE SOLUTION*/
PUT CATEGORY= GEOMEAN=;
OUTPUT;
END;
END;
RUN;

30. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value

31. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1

32. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1

33. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1

34. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2

35. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2 3

36. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2 3

37. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2 3
3

38. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2 3
3 6

39. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2 3
3 6

40. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2 3
3 6
4

41. DATA _NULL_;
DO UNTIL (EOF);
SET A END = EOF;
COUNT = SUM(COUNT,1);
VALUE = SUM(VALUE,A);
END;
RUN;
The engine
A B C D
1 2 3 4
2 2 3 4
3 2 3 4
4 2 3 4
Count Value
1 1
2 3
3 6
4 10

42. Multiple DOW Loop
• The double DOW loop structure
was first proposed by Howard
Scherier on the SAS – L as a
variation of the original technique.
• There have been several
approaches which use multiple
DOW loops to achieve various
calculations which requires multiple
iterations through the data.

43. Application 3: Bivariate Regression
• In order to calculate the
parameters of the regression, we
have to first calculate the mean of
both the x and y variables.
• After running through this, we will
then use the mean to calculate the
sum of square for both x-squares
and xy which are essential for the
regression parameter estimation.

44. Application 3: Bivariate Regression
/******************************************************************************
-------------------------------------------------------------------------------
DOW LOOP REGRESSION
-------------------------------------------------------------------------------
THIS MACRO IS A SIMPLE DEMONSTRATION THE USE OF DOUBLE DOW LOOP TO COMPUTE THE
SLOPE AND INTERCEPT OF A SIMPLE LINEAR REGRESSION MODEL.
-------------------------------------------------------------------------------
INPUT DESCRIPTION
-------------------------------------------------------------------------------
INPUT INPUT DATASET
Y DEPEDENT VARIABLE
X INDEPENDENT VARIABLE
-------------------------------------------------------------------------------
*******************************************************************************/
%LET INPUT = HTWT;
%LET Y = HEIGHT;
%LET X = WEIGHT;
/******************************************************************************/

45. Application 3: Bivariate Regression
/******************************************************************************
MAIN MACRO
*******************************************************************************/
%MACRO DOW_REG();
/******************************************************************************/
/******************************************************************************
*******************************************************************************/
DATA _NULL_;
/******************************************************************************
FIRST DOW LOOP FOR MEANS CALCULATION SUMMARIZATION
*******************************************************************************/
DO I = 1 BY 1 UNTIL (EOF);
SET &INPUT END=EOF;
SUM_Y = SUM(SUM_Y,&Y);
SUM_X = SUM(SUM_X,&X);
COUNT = SUM(COUNT,1);
END;
/******************************************************************************
MEANS CALCULATION
*******************************************************************************/
MEAN_Y = SUM_Y/COUNT;
MEAN_X = SUM_X/COUNT;

46. Application 3: Bivariate Regression
/******************************************************************************
LOOP TO CALCULATE SUM OF SQUARES AND XY
*******************************************************************************/
DO _N_ = 1 TO COUNT;
SET &INPUT;
XY = (&Y - MEAN_Y)*(&X - MEAN_X);
XX = (&X - MEAN_X)**2;
SUM_XY = SUM(SUM_XY,XY);
SUM_XX = SUM(SUM_XX,XX);
END;
/******************************************************************************
CALCULATION OF SLOPES
*******************************************************************************/
SLOPE = SUM_XY/SUM_XX;
INTERCEPT = MEAN_Y - SLOPE*MEAN_X;
PUT SLOPE = INTERCEPT = ;
/******************************************************************************
*******************************************************************************/
RUN;
%MEND;
/******************************************************************************
MACRO CALLING
*******************************************************************************/
%DOW_REG();

47. Conclusion
• One of the most versatile programming
structures in SAS
• Can be used on a variety of scenario to
achieve the required results
• Beside data manipulation, DOW loops
are also useful for summarization of
data, mathematical calculations and
even model parameter estimations.