The R Book

Logical Arithmetic

Arithmetic involving logical expressions is very useful in programming and in selection of variables. If logical arithmetic is unfamiliar to you, then persevere with it, because it will become clear how useful it is, once the penny has dropped. The key thing to understand is that logical expressions evaluate to either true or false (represented in R by TRUE or FALSE), and that R can coerce TRUE or FALSE into numerical values: 1 for TRUE and 0 for FALSE. Suppose that x is a sequence from 0 to 6 like this:

x<-0:6

Now we can ask questions about the contents of the vector called x. Is x less than 4?

x<4

[1]  TRUE  TRUE  TRUE  TRUE  FALSE  FALSE  FALSE

The answer is yes for the first four values (0, 1, 2 and 3) and no for the last three (4, 5 and 6). Two important logical functions are all and any. They check an entire vector but return a single logical value: TRUE or FALSE. Are all the x values bigger than 0?

all(x>0)

[1]  FALSE

No. The first x value is a zero. Are any of the x values negative?

any(x<0)

[1]  FALSE

No. The smallestx value is a zero. We can use the answers of logical functions in arithmetic. We can count the true values of (x<4), using sum

sum(x<4)

[1] 4

or we can multiply (x<4) by other vectors

(x<4)*runif(7)

[1]  0.9433433  0.9382651  0.6248691  0.9786844  0.0000000  0.0000000
     0.0000000

Logical arithmetic is particularly useful in generating simplified factor levels during statistical modelling. Suppose we want to reduce a five-level factor called ...