## 2.6 Logicals

All programming languages have ways of tracking whether variables meet certain criteria. These are often called Booleans or Logicals. For us, this will particularly come up in the context of subsetting data (i.e., selecting data based on some condition) and in running particular portions of code based on some condition.

Some main logical operators are ==, <=, >=, <, > corresponding to whether or not two things are equal, less than or equal to, greater than or equal, strictly less than, and strictly greater than. These can be applied to vectors. And the comparisons result in either TRUE or FALSE. Here are some examples

five <- c(1,2,3,4,5)

# only 3 is equal to 3
five == 3
#> [1] FALSE FALSE  TRUE FALSE FALSE

# 1,2,3 are all less than or equal to 3
five <= 3
#> [1]  TRUE  TRUE  TRUE FALSE FALSE

# 3,4,5, are all greater than or equal to 3
five >= 3
#> [1] FALSE FALSE  TRUE  TRUE  TRUE

# 1,2 are strictly less than 3
five < 3
#> [1]  TRUE  TRUE FALSE FALSE FALSE

# 4,5 are strictly greater than 3
five > 3
#> [1] FALSE FALSE FALSE  TRUE  TRUE

Example 2.3 Often, we might be interested in learning about a subset of our data. As a simple example, using our firm_data from earlier, you could imagine being interested in average employment for manufacturing firms.

We can do this using the subset function along with the logical operations we’ve learned in this section.

manufacturing_firms <- subset(firm_data, industry=="Manufacturing")
mean(manufacturing_firms\$employees)
#> [1] 252.3333

As practice, try creating a subset of firm_data based on firms having more than 100 employees.

There are a number of additional logical operators that can be useful in practice. Here, we quickly cover several more.

• != — not equal

c(1,2,3) != 3
#> [1]  TRUE  TRUE FALSE
• We can link together multiple logical comparisons. If we want to check whether multiple conditions hold, we can use “logical AND” &; if we want to check whether any of multiple conditions hold, we can use “logical OR” |.

# AND
( c(1,2,3,4,5) >= 3 ) & ( c(1,2,3,4,5) < 5 )
#> [1] FALSE FALSE  TRUE  TRUE FALSE

# OR
( c(1,2,3,4,5) >= 4 ) | ( c(1,2,3,4,5) < 2 )
#> [1]  TRUE FALSE FALSE  TRUE  TRUE
• %in% — checks whether the elements of one vector show up in another vector

# 1 is in the 2nd vector, but 7 is not
c(1,7) %in% c(1,2,3,4,5)
#> [1]  TRUE FALSE
• Often it is useful to check whether any logical conditions are true or all logical conditions are true. This can be done as follows

# this one is TRUE because 1 is in the 2nd vector
any(c(1,7) %in% c(1,2,3,4,5))
#> [1] TRUE

# this one is FALSE because 7 is not in the 2nd vector
all(c(1,7) %in% c(1,2,3,4,5))
#> [1] FALSE