SAS WHERE statement with several conditions - sas

Question

In SAS PROC FREQ, using a WHERE statement with multiple conditions, I would like to understand why adding a condition causes a frequency to increase.
The first instance:
PROC FREQ;
WHERE X=1 AND Y=1;
TABLE YEARS;
RUN;
Outputs N=100 for a particular year.
But:
PROC FREQ;
WHERE (X=1 AND Y=1) AND A=2 OR B=2;
TABLE YEARS;
RUN;
Outputs larger N than the previous WHERE for the same year, e.g., N=200.
In the second FREQ and WHERE statement I think the condition in parentheses should be evaluated first, before the AND...OR, and should select the same N=100 as the first WHERE statement. And then the remaining criteria in the line, AND A=2 OR B=2, should select a subset of N=100 have either A=2 or B=2. And consequently, selected N should be less than or equal to 100, but not greater than 100.
This is what I want--the subset of (X=1 AND Y=1)
that also has either A=2 OR B=2--but it does not seem to be what I am getting. Suggestions?
Is this the correct statement for what I want?
WHERE (X=1 AND Y=1 AND A=2) OR (X=1 AND Y=1 AND B=2);
Thank you.

Answer 1

Adding an un-nested OR to a logical expression will always cause the result set to remain the same or become larger.
You need the parenthesis to change the order of evaluation. When there are no parentheses all the and expressions will be evaluated first, then the or expressions
From the documentation Combining Expressions By Using Logical Operators
Processing Compound Expressions
When SAS encounters a compound WHERE
expression (multiple conditions), the software follows rules to
determine the order in which to evaluate each expression. When WHERE
expressions are combined, SAS processes the conditions in a specific
order:
The NOT expression is processed first.
Then the expressions joined by AND are processed.
Finally, the expressions joined by OR are processed.
Using Parentheses to Control Order of Evaluation
Even though SAS evaluates logical operators in a specific order, you can
control the order of evaluation by nesting expressions in parentheses.
That is, an expression enclosed in parentheses is processed before one
not enclosed. The expression within the innermost set of parentheses
is processed first, followed by the next deepest, moving outward until
all parentheses have been processed.
For example, suppose you want a
list of all the Canadian sites that have both SAS/GRAPH and SAS/STAT
software, so you issue the following expression:
where product='GRAPH' or product='STAT' and country='Canada';
The result, however, includes all sites that license SAS/GRAPH software along with the Canadian
sites that license SAS/STAT software. To obtain the correct results,
you can use parentheses, which causes SAS to evaluate the comparisons
within the parentheses first, providing a list of sites with either
product licenses, then the result is used for the remaining condition:
where (product='GRAPH' or product='STAT') and country='Canada';
So your
WHERE (X=1 AND Y=1) AND A=2 OR B=2;
is the same as
WHERE (X=1 AND Y=1 AND A=2) OR B=2;
your this is what I want described in the question is
WHERE (X=1 AND Y=1) AND (A=2 OR B=2);
which is the same (by distributive law of logic)
WHERE (X=1 AND Y=1 AND A=2) OR (X=1 AND Y=1 AND B=2);
No matter how you state the expression, adding an OR will always have the possibility of increasing the number of items meeting the expression. The un-nested OR will have the possibility of selecting more items than a nested (or parentheticalized) OR