13 Logical vectors
You are reading the workinprogress second edition of R for Data Science. This chapter is largely complete and just needs final proof reading. You can find the complete first edition at https://r4ds.had.co.nz.
13.1 Introduction
In this chapter, you’ll learn tools for working with logical vectors. Logical vectors are the simplest type of vector because each element can only be one of three possible values: TRUE
, FALSE
, and NA
. It’s relatively rare to find logical vectors in your raw data, but you’ll create and manipulate them in the course of almost every analysis.
We’ll begin by discussing the most common way of creating logical vectors: with numeric comparisons. Then you’ll learn about how you can use Boolean algebra to combine different logical vectors, as well as some useful summaries. We’ll finish off with if_else()
and case_when()
, two useful functions for making conditional changes powered by logical vectors.
13.1.1 Prerequisites
Most of the functions you’ll learn about in this chapter are provided by base R, so we don’t need the tidyverse, but we’ll still load it so we can use mutate()
, filter()
, and friends to work with data frames. We’ll also continue to draw examples from the nycflights13::flights
dataset.
However, as we start to cover more tools, there won’t always be a perfect real example. So we’ll start making up some dummy data with c()
:
x < c(1, 2, 3, 5, 7, 11, 13)
x * 2
#> [1] 2 4 6 10 14 22 26
This makes it easier to explain individual functions at the cost of making it harder to see how it might apply to your data problems. Just remember that any manipulation we do to a freefloating vector, you can do to a variable inside a data frame with mutate()
and friends.
13.2 Comparisons
A very common way to create a logical vector is via a numeric comparison with <
, <=
, >
, >=
, !=
, and ==
. So far, we’ve mostly created logical variables transiently within filter()
— they are computed, used, and then thrown away. For example, the following filter finds all daytime departures that arrive roughly on time:
flights >
filter(dep_time > 600 & dep_time < 2000 & abs(arr_delay) < 20)
#> # A tibble: 172,286 × 19
#> year month day dep_time sched_dep_time dep_delay arr_time sched_arr_time
#> <int> <int> <int> <int> <int> <dbl> <int> <int>
#> 1 2013 1 1 601 600 1 844 850
#> 2 2013 1 1 602 610 8 812 820
#> 3 2013 1 1 602 605 3 821 805
#> 4 2013 1 1 606 610 4 858 910
#> 5 2013 1 1 606 610 4 837 845
#> 6 2013 1 1 607 607 0 858 915
#> # ℹ 172,280 more rows
#> # ℹ 11 more variables: arr_delay <dbl>, carrier <chr>, flight <int>, …
It’s useful to know that this is a shortcut and you can explicitly create the underlying logical variables with mutate()
:
flights >
mutate(
daytime = dep_time > 600 & dep_time < 2000,
approx_ontime = abs(arr_delay) < 20,
.keep = "used"
)
#> # A tibble: 336,776 × 4
#> dep_time arr_delay daytime approx_ontime
#> <int> <dbl> <lgl> <lgl>
#> 1 517 11 FALSE TRUE
#> 2 533 20 FALSE FALSE
#> 3 542 33 FALSE FALSE
#> 4 544 18 FALSE TRUE
#> 5 554 25 FALSE FALSE
#> 6 554 12 FALSE TRUE
#> # ℹ 336,770 more rows
This is particularly useful for more complicated logic because naming the intermediate steps makes it easier to both read your code and check that each step has been computed correctly.
All up, the initial filter is equivalent to:
13.2.1 Floating point comparison
Beware of using ==
with numbers. For example, it looks like this vector contains the numbers 1 and 2:
But if you test them for equality, you get FALSE
:
x == c(1, 2)
#> [1] FALSE FALSE
What’s going on? Computers store numbers with a fixed number of decimal places so there’s no way to exactly represent 1/49 or sqrt(2)
and subsequent computations will be very slightly off. We can see the exact values by calling print()
with the digits
^{1} argument:
print(x, digits = 16)
#> [1] 0.9999999999999999 2.0000000000000004
You can see why R defaults to rounding these numbers; they really are very close to what you expect.
Now that you’ve seen why ==
is failing, what can you do about it? One option is to use dplyr::near()
which ignores small differences:
13.2.2 Missing values
Missing values represent the unknown so they are “contagious”: almost any operation involving an unknown value will also be unknown:
NA > 5
#> [1] NA
10 == NA
#> [1] NA
The most confusing result is this one:
NA == NA
#> [1] NA
It’s easiest to understand why this is true if we artificially supply a little more context:
# We don't know how old Mary is
age_mary < NA
# We don't know how old John is
age_john < NA
# Are Mary and John the same age?
age_mary == age_john
#> [1] NA
# We don't know!
So if you want to find all flights where dep_time
is missing, the following code doesn’t work because dep_time == NA
will yield NA
for every single row, and filter()
automatically drops missing values:
flights >
filter(dep_time == NA)
#> # A tibble: 0 × 19
#> # ℹ 19 variables: year <int>, month <int>, day <int>, dep_time <int>,
#> # sched_dep_time <int>, dep_delay <dbl>, arr_time <int>, …
Instead we’ll need a new tool: is.na()
.
13.2.3 is.na()
is.na(x)
works with any type of vector and returns TRUE
for missing values and FALSE
for everything else:
We can use is.na()
to find all the rows with a missing dep_time
:
flights >
filter(is.na(dep_time))
#> # A tibble: 8,255 × 19
#> year month day dep_time sched_dep_time dep_delay arr_time sched_arr_time
#> <int> <int> <int> <int> <int> <dbl> <int> <int>
#> 1 2013 1 1 NA 1630 NA NA 1815
#> 2 2013 1 1 NA 1935 NA NA 2240
#> 3 2013 1 1 NA 1500 NA NA 1825
#> 4 2013 1 1 NA 600 NA NA 901
#> 5 2013 1 2 NA 1540 NA NA 1747
#> 6 2013 1 2 NA 1620 NA NA 1746
#> # ℹ 8,249 more rows
#> # ℹ 11 more variables: arr_delay <dbl>, carrier <chr>, flight <int>, …
is.na()
can also be useful in arrange()
. arrange()
usually puts all the missing values at the end but you can override this default by first sorting by is.na()
:
flights >
filter(month == 1, day == 1) >
arrange(dep_time)
#> # A tibble: 842 × 19
#> year month day dep_time sched_dep_time dep_delay arr_time sched_arr_time
#> <int> <int> <int> <int> <int> <dbl> <int> <int>
#> 1 2013 1 1 517 515 2 830 819
#> 2 2013 1 1 533 529 4 850 830
#> 3 2013 1 1 542 540 2 923 850
#> 4 2013 1 1 544 545 1 1004 1022
#> 5 2013 1 1 554 600 6 812 837
#> 6 2013 1 1 554 558 4 740 728
#> # ℹ 836 more rows
#> # ℹ 11 more variables: arr_delay <dbl>, carrier <chr>, flight <int>, …
flights >
filter(month == 1, day == 1) >
arrange(desc(is.na(dep_time)), dep_time)
#> # A tibble: 842 × 19
#> year month day dep_time sched_dep_time dep_delay arr_time sched_arr_time
#> <int> <int> <int> <int> <int> <dbl> <int> <int>
#> 1 2013 1 1 NA 1630 NA NA 1815
#> 2 2013 1 1 NA 1935 NA NA 2240
#> 3 2013 1 1 NA 1500 NA NA 1825
#> 4 2013 1 1 NA 600 NA NA 901
#> 5 2013 1 1 517 515 2 830 819
#> 6 2013 1 1 533 529 4 850 830
#> # ℹ 836 more rows
#> # ℹ 11 more variables: arr_delay <dbl>, carrier <chr>, flight <int>, …
We’ll come back to cover missing values in more depth in Chapter 19.
13.2.4 Exercises
 How does
dplyr::near()
work? Typenear
to see the source code. Issqrt(2)^2
near 2?  Use
mutate()
,is.na()
, andcount()
together to describe how the missing values indep_time
,sched_dep_time
anddep_delay
are connected.
13.3 Boolean algebra
Once you have multiple logical vectors, you can combine them together using Boolean algebra. In R, &
is “and”, 
is “or”, !
is “not”, and xor()
is exclusive or^{2}. For example, df > filter(!is.na(x))
finds all rows where x
is not missing and df > filter(x < 10  x > 0)
finds all rows where x
is smaller than 10 or bigger than 0. Figure 13.1 shows the complete set of Boolean operations and how they work.
As well as &
and 
, R also has &&
and 
. Don’t use them in dplyr functions! These are called shortcircuiting operators and only ever return a single TRUE
or FALSE
. They’re important for programming, not data science.
13.3.1 Missing values
The rules for missing values in Boolean algebra are a little tricky to explain because they seem inconsistent at first glance:
To understand what’s going on, think about NA  TRUE
(NA
or TRUE
). A missing value in a logical vector means that the value could either be TRUE
or FALSE
. TRUE  TRUE
and FALSE  TRUE
are both TRUE
because at least one of them is TRUE
. NA  TRUE
must also be TRUE
because NA
can either be TRUE
or FALSE
. However, NA  FALSE
is NA
because we don’t know if NA
is TRUE
or FALSE
. Similar reasoning applies with NA & FALSE
.
13.3.2 Order of operations
Note that the order of operations doesn’t work like English. Take the following code that finds all flights that departed in November or December:
flights >
filter(month == 11  month == 12)
You might be tempted to write it like you’d say in English: “Find all flights that departed in November or December.”:
flights >
filter(month == 11  12)
#> # A tibble: 336,776 × 19
#> year month day dep_time sched_dep_time dep_delay arr_time sched_arr_time
#> <int> <int> <int> <int> <int> <dbl> <int> <int>
#> 1 2013 1 1 517 515 2 830 819
#> 2 2013 1 1 533 529 4 850 830
#> 3 2013 1 1 542 540 2 923 850
#> 4 2013 1 1 544 545 1 1004 1022
#> 5 2013 1 1 554 600 6 812 837
#> 6 2013 1 1 554 558 4 740 728
#> # ℹ 336,770 more rows
#> # ℹ 11 more variables: arr_delay <dbl>, carrier <chr>, flight <int>, …
This code doesn’t error but it also doesn’t seem to have worked. What’s going on? Here, R first evaluates month == 11
creating a logical vector, which we call nov
. It computes nov  12
. When you use a number with a logical operator it converts everything apart from 0 to TRUE
, so this is equivalent to nov  TRUE
which will always be TRUE
, so every row will be selected:
flights >
mutate(
nov = month == 11,
final = nov  12,
.keep = "used"
)
#> # A tibble: 336,776 × 3
#> month nov final
#> <int> <lgl> <lgl>
#> 1 1 FALSE TRUE
#> 2 1 FALSE TRUE
#> 3 1 FALSE TRUE
#> 4 1 FALSE TRUE
#> 5 1 FALSE TRUE
#> 6 1 FALSE TRUE
#> # ℹ 336,770 more rows
13.3.3 %in%
An easy way to avoid the problem of getting your ==
s and 
s in the right order is to use %in%
. x %in% y
returns a logical vector the same length as x
that is TRUE
whenever a value in x
is anywhere in y
.
So to find all flights in November and December we could write:
Note that %in%
obeys different rules for NA
to ==
, as NA %in% NA
is TRUE
.
This can make for a useful shortcut:
flights >
filter(dep_time %in% c(NA, 0800))
#> # A tibble: 8,803 × 19
#> year month day dep_time sched_dep_time dep_delay arr_time sched_arr_time
#> <int> <int> <int> <int> <int> <dbl> <int> <int>
#> 1 2013 1 1 800 800 0 1022 1014
#> 2 2013 1 1 800 810 10 949 955
#> 3 2013 1 1 NA 1630 NA NA 1815
#> 4 2013 1 1 NA 1935 NA NA 2240
#> 5 2013 1 1 NA 1500 NA NA 1825
#> 6 2013 1 1 NA 600 NA NA 901
#> # ℹ 8,797 more rows
#> # ℹ 11 more variables: arr_delay <dbl>, carrier <chr>, flight <int>, …
13.3.4 Exercises
 Find all flights where
arr_delay
is missing butdep_delay
is not. Find all flights where neitherarr_time
norsched_arr_time
are missing, butarr_delay
is.  How many flights have a missing
dep_time
? What other variables are missing in these rows? What might these rows represent?  Assuming that a missing
dep_time
implies that a flight is cancelled, look at the number of cancelled flights per day. Is there a pattern? Is there a connection between the proportion of cancelled flights and the average delay of noncancelled flights?
13.4 Summaries
The following sections describe some useful techniques for summarizing logical vectors. As well as functions that only work specifically with logical vectors, you can also use functions that work with numeric vectors.
13.4.1 Logical summaries
There are two main logical summaries: any()
and all()
. any(x)
is the equivalent of 
; it’ll return TRUE
if there are any TRUE
’s in x
. all(x)
is equivalent of &
; it’ll return TRUE
only if all values of x
are TRUE
’s. Like all summary functions, they’ll return NA
if there are any missing values present, and as usual you can make the missing values go away with na.rm = TRUE
.
For example, we could use all()
and any()
to find out if every flight was delayed on departure by at most an hour or if any flights were delayed on arrival by five hours or more. And using group_by()
allows us to do that by day:
flights >
group_by(year, month, day) >
summarize(
all_delayed = all(dep_delay <= 60, na.rm = TRUE),
any_long_delay = any(arr_delay >= 300, na.rm = TRUE),
.groups = "drop"
)
#> # A tibble: 365 × 5
#> year month day all_delayed any_long_delay
#> <int> <int> <int> <lgl> <lgl>
#> 1 2013 1 1 FALSE TRUE
#> 2 2013 1 2 FALSE TRUE
#> 3 2013 1 3 FALSE FALSE
#> 4 2013 1 4 FALSE FALSE
#> 5 2013 1 5 FALSE TRUE
#> 6 2013 1 6 FALSE FALSE
#> # ℹ 359 more rows
In most cases, however, any()
and all()
are a little too crude, and it would be nice to be able to get a little more detail about how many values are TRUE
or FALSE
. That leads us to the numeric summaries.
13.4.2 Numeric summaries of logical vectors
When you use a logical vector in a numeric context, TRUE
becomes 1 and FALSE
becomes 0. This makes sum()
and mean()
very useful with logical vectors because sum(x)
gives the number of TRUE
s and mean(x)
gives the proportion of TRUE
s (because mean()
is just sum()
divided by length()
.
That, for example, allows us to see the proportion of flights that were delayed on departure by at most an hour and the number of flights that were delayed on arrival by five hours or more:
flights >
group_by(year, month, day) >
summarize(
all_delayed = mean(dep_delay <= 60, na.rm = TRUE),
any_long_delay = sum(arr_delay >= 300, na.rm = TRUE),
.groups = "drop"
)
#> # A tibble: 365 × 5
#> year month day all_delayed any_long_delay
#> <int> <int> <int> <dbl> <int>
#> 1 2013 1 1 0.939 3
#> 2 2013 1 2 0.914 3
#> 3 2013 1 3 0.941 0
#> 4 2013 1 4 0.953 0
#> 5 2013 1 5 0.964 1
#> 6 2013 1 6 0.959 0
#> # ℹ 359 more rows
13.4.3 Logical subsetting
There’s one final use for logical vectors in summaries: you can use a logical vector to filter a single variable to a subset of interest. This makes use of the base [
(pronounced subset) operator, which you’ll learn more about in Section 28.2.
Imagine we wanted to look at the average delay just for flights that were actually delayed. One way to do so would be to first filter the flights and then calculate the average delay:
flights >
filter(arr_delay > 0) >
group_by(year, month, day) >
summarize(
behind = mean(arr_delay),
n = n(),
.groups = "drop"
)
#> # A tibble: 365 × 5
#> year month day behind n
#> <int> <int> <int> <dbl> <int>
#> 1 2013 1 1 32.5 461
#> 2 2013 1 2 32.0 535
#> 3 2013 1 3 27.7 460
#> 4 2013 1 4 28.3 297
#> 5 2013 1 5 22.6 238
#> 6 2013 1 6 24.4 381
#> # ℹ 359 more rows
This works, but what if we wanted to also compute the average delay for flights that arrived early? We’d need to perform a separate filter step, and then figure out how to combine the two data frames together^{3}. Instead you could use [
to perform an inline filtering: arr_delay[arr_delay > 0]
will yield only the positive arrival delays.
This leads to:
flights >
group_by(year, month, day) >
summarize(
behind = mean(arr_delay[arr_delay > 0], na.rm = TRUE),
ahead = mean(arr_delay[arr_delay < 0], na.rm = TRUE),
n = n(),
.groups = "drop"
)
#> # A tibble: 365 × 6
#> year month day behind ahead n
#> <int> <int> <int> <dbl> <dbl> <int>
#> 1 2013 1 1 32.5 12.5 842
#> 2 2013 1 2 32.0 14.3 943
#> 3 2013 1 3 27.7 18.2 914
#> 4 2013 1 4 28.3 17.0 915
#> 5 2013 1 5 22.6 14.0 720
#> 6 2013 1 6 24.4 13.6 832
#> # ℹ 359 more rows
Also note the difference in the group size: in the first chunk n()
gives the number of delayed flights per day; in the second, n()
gives the total number of flights.
13.4.4 Exercises
 What will
sum(is.na(x))
tell you? How aboutmean(is.na(x))
?  What does
prod()
return when applied to a logical vector? What logical summary function is it equivalent to? What doesmin()
return when applied to a logical vector? What logical summary function is it equivalent to? Read the documentation and perform a few experiments.
13.5 Conditional transformations
One of the most powerful features of logical vectors are their use for conditional transformations, i.e. doing one thing for condition x, and something different for condition y. There are two important tools for this: if_else()
and case_when()
.
13.5.1 if_else()
If you want to use one value when a condition is TRUE
and another value when it’s FALSE
, you can use dplyr::if_else()
^{4}. You’ll always use the first three argument of if_else()
. The first argument, condition
, is a logical vector, the second, true
, gives the output when the condition is true, and the third, false
, gives the output if the condition is false.
Let’s begin with a simple example of labeling a numeric vector as either “+ve” (positive) or “ve” (negative):
There’s an optional fourth argument, missing
which will be used if the input is NA
:
if_else(x > 0, "+ve", "ve", "???")
#> [1] "ve" "ve" "ve" "ve" "+ve" "+ve" "+ve" "???"
You can also use vectors for the the true
and false
arguments. For example, this allows us to create a minimal implementation of abs()
:
if_else(x < 0, x, x)
#> [1] 3 2 1 0 1 2 3 NA
So far all the arguments have used the same vectors, but you can of course mix and match. For example, you could implement a simple version of coalesce()
like this:
You might have noticed a small infelicity in our labeling example above: zero is neither positive nor negative. We could resolve this by adding an additional if_else()
:
This is already a little hard to read, and you can imagine it would only get harder if you have more conditions. Instead, you can switch to dplyr::case_when()
.
13.5.2 case_when()
dplyr’s case_when()
is inspired by SQL’s CASE
statement and provides a flexible way of performing different computations for different conditions. It has a special syntax that unfortunately looks like nothing else you’ll use in the tidyverse. It takes pairs that look like condition ~ output
. condition
must be a logical vector; when it’s TRUE
, output
will be used.
This means we could recreate our previous nested if_else()
as follows:
This is more code, but it’s also more explicit.
To explain how case_when()
works, let’s explore some simpler cases. If none of the cases match, the output gets an NA
:
case_when(
x < 0 ~ "ve",
x > 0 ~ "+ve"
)
#> [1] "ve" "ve" "ve" NA "+ve" "+ve" "+ve" NA
If you want to create a “default”/catch all value, use TRUE
on the left hand side:
case_when(
x < 0 ~ "ve",
x > 0 ~ "+ve",
TRUE ~ "???"
)
#> [1] "ve" "ve" "ve" "???" "+ve" "+ve" "+ve" "???"
And note that if multiple conditions match, only the first will be used:
case_when(
x > 0 ~ "+ve",
x > 2 ~ "big"
)
#> [1] NA NA NA NA "+ve" "+ve" "+ve" NA
Just like with if_else()
you can use variables on both sides of the ~
and you can mix and match variables as needed for your problem. For example, we could use case_when()
to provide some human readable labels for the arrival delay:
flights >
mutate(
status = case_when(
is.na(arr_delay) ~ "cancelled",
arr_delay < 30 ~ "very early",
arr_delay < 15 ~ "early",
abs(arr_delay) <= 15 ~ "on time",
arr_delay < 60 ~ "late",
arr_delay < Inf ~ "very late",
),
.keep = "used"
)
#> # A tibble: 336,776 × 2
#> arr_delay status
#> <dbl> <chr>
#> 1 11 on time
#> 2 20 late
#> 3 33 late
#> 4 18 early
#> 5 25 early
#> 6 12 on time
#> # ℹ 336,770 more rows
Be wary when writing this sort of complex case_when()
statement; my first two attempts used a mix of <
and >
and I kept accidentally creating overlapping conditions.
13.5.3 Compatible types
Note that both if_else()
and case_when()
require compatible types in the output. If they’re not compatible, you’ll see errors like this:
Overall, relatively few types are compatible, because automatically converting one type of vector to another is a common source of errors. Here are the most important cases that are compatible:
 Numeric and logical vectors are compatible, as we discussed in Section 13.4.2.
 Strings and factors (Chapter 17) are compatible, because you can think of a factor as a string with a restricted set of values.
 Dates and datetimes, which we’ll discuss in Chapter 18, are compatible because you can think of a date as a special case of datetime.

NA
, which is technically a logical vector, is compatible with everything because every vector has some way of representing a missing value.
We don’t expect you to memorize these rules, but they should become second nature over time because they are applied consistently throughout the tidyverse.
13.5.4 Exercises
A number is even if it’s divisible by two, which in R you can find out with
x %% 2 == 0
. Use this fact andif_else()
to determine whether each number between 0 and 20 is even or odd.Given a vector of days like
x < c("Monday", "Saturday", "Wednesday")
, use anifelse()
statement to label them as weekends or weekdays.Use
ifelse()
to compute the absolute value of a numeric vector calledx
.Write a
case_when()
statement that uses themonth
andday
columns fromflights
to label a selection of important US holidays (e.g., New Years Day, 4th of July, Thanksgiving, and Christmas). First create a logical column that is eitherTRUE
orFALSE
, and then create a character column that either gives the name of the holiday or isNA
.
13.6 Summary
The definition of a logical vector is simple because each value must be either TRUE
, FALSE
, or NA
. But logical vectors provide a huge amount of power. In this chapter, you learned how to create logical vectors with >
, <
, <=
, =>
, ==
, !=
, and is.na()
, how to combine them with !
, &
, and 
, and how to summarize them with any()
, all()
, sum()
, and mean()
. You also learned the powerful if_else()
and case_when()
functions that allow you to return values depending on the value of a logical vector.
We’ll see logical vectors again and again in the following chapters. For example in Chapter 15 you’ll learn about str_detect(x, pattern)
which returns a logical vector that’s TRUE
for the elements of x
that match the pattern
, and in Chapter 18 you’ll create logical vectors from the comparison of dates and times. But for now, we’re going to move onto the next most important type of vector: numeric vectors.
R normally calls print for you (i.e.
x
is a shortcut forprint(x)
), but calling it explicitly is useful if you want to provide other arguments.↩︎That is,
xor(x, y)
is true if x is true, or y is true, but not both. This is how we usually use “or” In English. “Both” is not usually an acceptable answer to the question “would you like ice cream or cake?”.↩︎We’ll cover this in Chapter 20.↩︎
dplyr’s
if_else()
is very similar to base R’sifelse()
. There are two main advantages ofif_else()
overifelse()
: you can choose what should happen to missing values, andif_else()
is much more likely to give you a meaningful error if your variables have incompatible types.↩︎