626 lines
40 KiB
HTML
626 lines
40 KiB
HTML
<section data-type="chapter" id="chp-logicals">
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<h1><span id="sec-logicals" class="quarto-section-identifier d-none d-lg-block"><span class="chapter-title">Logical vectors</span></span></h1>
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<section id="introduction" data-type="sect1">
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<h1>
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Introduction</h1>
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<p>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: <code>TRUE</code>, <code>FALSE</code>, and <code>NA</code>. It’s relatively rare to find logical vectors in your raw data, but you’ll create and manipulate in the course of almost every analysis.</p>
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<p>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 <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code> and <code><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when()</a></code>, two useful functions for making conditional changes powered by logical vectors.</p>
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<section id="prerequisites" data-type="sect2">
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<h2>
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Prerequisites</h2>
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<p>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 <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code>, <code><a href="https://dplyr.tidyverse.org/reference/filter.html">filter()</a></code>, and friends to work with data frames. We’ll also continue to draw examples from the nycflights13 dataset.</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">library(tidyverse)
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library(nycflights13)</pre>
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</div>
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<p>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 <code><a href="https://rdrr.io/r/base/c.html">c()</a></code>:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">x <- c(1, 2, 3, 5, 7, 11, 13)
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x * 2
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#> [1] 2 4 6 10 14 22 26</pre>
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</div>
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<p>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 free-floating vector, you can do to a variable inside data frame with <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code> and friends.</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">df <- tibble(x)
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df |>
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mutate(y = x * 2)
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#> # A tibble: 7 × 2
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#> x y
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#> <dbl> <dbl>
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#> 1 1 2
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#> 2 2 4
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#> 3 3 6
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#> 4 5 10
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#> 5 7 14
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#> 6 11 22
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#> # … with 1 more row</pre>
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</div>
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</section>
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</section>
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<section id="comparisons" data-type="sect1">
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<h1>
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Comparisons</h1>
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<p>A very common way to create a logical vector is via a numeric comparison with <code><</code>, <code><=</code>, <code>></code>, <code>>=</code>, <code>!=</code>, and <code>==</code>. So far, we’ve mostly created logical variables transiently within <code><a href="https://dplyr.tidyverse.org/reference/filter.html">filter()</a></code> — they are computed, used, and then thrown away. For example, the following filter finds all daytime departures that leave roughly on time:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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filter(dep_time > 600 & dep_time < 2000 & abs(arr_delay) < 20)
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#> # A tibble: 172,286 × 19
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#> year month day dep_time sched_…¹ dep_d…² arr_t…³ sched…⁴ arr_d…⁵ carrier
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#> <int> <int> <int> <int> <int> <dbl> <int> <int> <dbl> <chr>
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#> 1 2013 1 1 601 600 1 844 850 -6 B6
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#> 2 2013 1 1 602 610 -8 812 820 -8 DL
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#> 3 2013 1 1 602 605 -3 821 805 16 MQ
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#> 4 2013 1 1 606 610 -4 858 910 -12 AA
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#> 5 2013 1 1 606 610 -4 837 845 -8 DL
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#> 6 2013 1 1 607 607 0 858 915 -17 UA
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#> # … with 172,280 more rows, 9 more variables: flight <int>, tailnum <chr>,
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#> # origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
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#> # minute <dbl>, time_hour <dttm>, and abbreviated variable names
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#> # ¹sched_dep_time, ²dep_delay, ³arr_time, ⁴sched_arr_time, ⁵arr_delay</pre>
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</div>
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<p>It’s useful to know that this is a shortcut and you can explicitly create the underlying logical variables with <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code>:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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mutate(
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daytime = dep_time > 600 & dep_time < 2000,
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approx_ontime = abs(arr_delay) < 20,
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.keep = "used"
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)
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#> # A tibble: 336,776 × 4
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#> dep_time arr_delay daytime approx_ontime
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#> <int> <dbl> <lgl> <lgl>
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#> 1 517 11 FALSE TRUE
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#> 2 533 20 FALSE FALSE
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#> 3 542 33 FALSE FALSE
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#> 4 544 -18 FALSE TRUE
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#> 5 554 -25 FALSE FALSE
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#> 6 554 12 FALSE TRUE
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#> # … with 336,770 more rows</pre>
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</div>
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<p>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.</p>
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<p>All up, the initial filter is equivalent to:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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mutate(
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daytime = dep_time > 600 & dep_time < 2000,
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approx_ontime = abs(arr_delay) < 20,
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) |>
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filter(daytime & approx_ontime)</pre>
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</div>
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<section id="sec-fp-comparison" data-type="sect2">
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<h2>
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Floating point comparison</h2>
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<p>Beware of using <code>==</code> with numbers. For example, it looks like this vector contains the numbers 1 and 2:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">x <- c(1 / 49 * 49, sqrt(2) ^ 2)
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x
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#> [1] 1 2</pre>
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</div>
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<p>But if you test them for equality, you get <code>FALSE</code>:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">x == c(1, 2)
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#> [1] FALSE FALSE</pre>
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</div>
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<p>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 <code>sqrt(2)</code> and subsequent computations will be very slightly off. We can see the exact values by calling <code><a href="https://rdrr.io/r/base/print.html">print()</a></code> with the the <code>digits</code><span data-type="footnote">R normally calls print for you (i.e. <code>x</code> is a shortcut for <code>print(x)</code>), but calling it explicitly is useful if you want to provide other arguments.</span> argument:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">print(x, digits = 16)
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#> [1] 0.9999999999999999 2.0000000000000004</pre>
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</div>
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<p>You can see why R defaults to rounding these numbers; they really are very close to what you expect.</p>
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<p>Now that you’ve seen why <code>==</code> is failing, what can you do about it? One option is to use <code><a href="https://dplyr.tidyverse.org/reference/near.html">dplyr::near()</a></code> which ignores small differences:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">near(x, c(1, 2))
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#> [1] TRUE TRUE</pre>
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</div>
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</section>
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<section id="sec-na-comparison" data-type="sect2">
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<h2>
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Missing values</h2>
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<p>Missing values represent the unknown so they are “contagious”: almost any operation involving an unknown value will also be unknown:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">NA > 5
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#> [1] NA
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10 == NA
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#> [1] NA</pre>
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</div>
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<p>The most confusing result is this one:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">NA == NA
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#> [1] NA</pre>
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</div>
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<p>It’s easiest to understand why this is true if we artificially supply a little more context:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r"># Let x be Mary's age. We don't know how old she is.
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x <- NA
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# Let y be John's age. We don't know how old he is.
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y <- NA
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# Are John and Mary the same age?
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x == y
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#> [1] NA
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# We don't know!</pre>
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</div>
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<p>So if you want to find all flights with <code>dep_time</code> is missing, the following code doesn’t work because <code>dep_time == NA</code> will yield a <code>NA</code> for every single row, and <code><a href="https://dplyr.tidyverse.org/reference/filter.html">filter()</a></code> automatically drops missing values:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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filter(dep_time == NA)
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#> # A tibble: 0 × 19
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#> # … with 19 variables: year <int>, month <int>, day <int>, dep_time <int>,
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#> # sched_dep_time <int>, dep_delay <dbl>, arr_time <int>,
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#> # sched_arr_time <int>, arr_delay <dbl>, carrier <chr>, flight <int>,
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#> # tailnum <chr>, origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>,
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#> # hour <dbl>, minute <dbl>, time_hour <dttm></pre>
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</div>
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<p>Instead we’ll need a new tool: <code><a href="https://rdrr.io/r/base/NA.html">is.na()</a></code>.</p>
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</section>
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<section id="is.na" data-type="sect2">
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<h2>
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<code>is.na()</code>
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</h2>
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<p><code>is.na(x)</code> works with any type of vector and returns <code>TRUE</code> for missing values and <code>FALSE</code> for everything else:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">is.na(c(TRUE, NA, FALSE))
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#> [1] FALSE TRUE FALSE
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is.na(c(1, NA, 3))
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#> [1] FALSE TRUE FALSE
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is.na(c("a", NA, "b"))
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#> [1] FALSE TRUE FALSE</pre>
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</div>
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<p>We can use <code><a href="https://rdrr.io/r/base/NA.html">is.na()</a></code> to find all the rows with a missing <code>dep_time</code>:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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filter(is.na(dep_time))
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#> # A tibble: 8,255 × 19
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#> year month day dep_time sched_…¹ dep_d…² arr_t…³ sched…⁴ arr_d…⁵ carrier
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#> <int> <int> <int> <int> <int> <dbl> <int> <int> <dbl> <chr>
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#> 1 2013 1 1 NA 1630 NA NA 1815 NA EV
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#> 2 2013 1 1 NA 1935 NA NA 2240 NA AA
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#> 3 2013 1 1 NA 1500 NA NA 1825 NA AA
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#> 4 2013 1 1 NA 600 NA NA 901 NA B6
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#> 5 2013 1 2 NA 1540 NA NA 1747 NA EV
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#> 6 2013 1 2 NA 1620 NA NA 1746 NA EV
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#> # … with 8,249 more rows, 9 more variables: flight <int>, tailnum <chr>,
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#> # origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
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#> # minute <dbl>, time_hour <dttm>, and abbreviated variable names
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#> # ¹sched_dep_time, ²dep_delay, ³arr_time, ⁴sched_arr_time, ⁵arr_delay</pre>
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</div>
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<p><code><a href="https://rdrr.io/r/base/NA.html">is.na()</a></code> can also be useful in <code><a href="https://dplyr.tidyverse.org/reference/arrange.html">arrange()</a></code>. <code><a href="https://dplyr.tidyverse.org/reference/arrange.html">arrange()</a></code> usually puts all the missing values at the end but you can override this default by first sorting by <code><a href="https://rdrr.io/r/base/NA.html">is.na()</a></code>:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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filter(month == 1, day == 1) |>
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arrange(dep_time)
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#> # A tibble: 842 × 19
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#> year month day dep_time sched_…¹ dep_d…² arr_t…³ sched…⁴ arr_d…⁵ carrier
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#> <int> <int> <int> <int> <int> <dbl> <int> <int> <dbl> <chr>
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#> 1 2013 1 1 517 515 2 830 819 11 UA
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#> 2 2013 1 1 533 529 4 850 830 20 UA
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#> 3 2013 1 1 542 540 2 923 850 33 AA
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#> 4 2013 1 1 544 545 -1 1004 1022 -18 B6
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#> 5 2013 1 1 554 600 -6 812 837 -25 DL
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#> 6 2013 1 1 554 558 -4 740 728 12 UA
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#> # … with 836 more rows, 9 more variables: flight <int>, tailnum <chr>,
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#> # origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
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#> # minute <dbl>, time_hour <dttm>, and abbreviated variable names
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#> # ¹sched_dep_time, ²dep_delay, ³arr_time, ⁴sched_arr_time, ⁵arr_delay
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flights |>
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filter(month == 1, day == 1) |>
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arrange(desc(is.na(dep_time)), dep_time)
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#> # A tibble: 842 × 19
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#> year month day dep_time sched_…¹ dep_d…² arr_t…³ sched…⁴ arr_d…⁵ carrier
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#> <int> <int> <int> <int> <int> <dbl> <int> <int> <dbl> <chr>
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#> 1 2013 1 1 NA 1630 NA NA 1815 NA EV
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#> 2 2013 1 1 NA 1935 NA NA 2240 NA AA
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#> 3 2013 1 1 NA 1500 NA NA 1825 NA AA
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#> 4 2013 1 1 NA 600 NA NA 901 NA B6
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#> 5 2013 1 1 517 515 2 830 819 11 UA
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#> 6 2013 1 1 533 529 4 850 830 20 UA
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#> # … with 836 more rows, 9 more variables: flight <int>, tailnum <chr>,
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#> # origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
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#> # minute <dbl>, time_hour <dttm>, and abbreviated variable names
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#> # ¹sched_dep_time, ²dep_delay, ³arr_time, ⁴sched_arr_time, ⁵arr_delay</pre>
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</div>
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<p>We’ll come back to cover missing values in more depth in <a href="#chp-missing-values" data-type="xref">#chp-missing-values</a>.</p>
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</section>
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<section id="exercises" data-type="sect2">
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<h2>
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Exercises</h2>
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<ol type="1"><li>How does <code><a href="https://dplyr.tidyverse.org/reference/near.html">dplyr::near()</a></code> work? Type <code>near</code> to see the source code.</li>
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<li>Use <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code>, <code><a href="https://rdrr.io/r/base/NA.html">is.na()</a></code>, and <code><a href="https://dplyr.tidyverse.org/reference/count.html">count()</a></code> together to describe how the missing values in <code>dep_time</code>, <code>sched_dep_time</code> and <code>dep_delay</code> are connected.</li>
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</ol></section>
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</section>
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<section id="boolean-algebra" data-type="sect1">
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<h1>
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Boolean algebra</h1>
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<p>Once you have multiple logical vectors, you can combine them together using Boolean algebra. In R, <code>&</code> is “and”, <code>|</code> is “or”, and <code>!</code> is “not”, and <code><a href="https://rdrr.io/r/base/Logic.html">xor()</a></code> is exclusive or<span data-type="footnote">That is, <code>xor(x, y)</code> 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?”.</span>. <a href="#fig-bool-ops" data-type="xref">#fig-bool-ops</a> shows the complete set of Boolean operations and how they work.</p>
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<div class="cell">
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<div class="cell-output-display">
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<figure id="fig-bool-ops"><p><img src="diagrams/transform.png" alt="Six Venn diagrams, each explaining a given logical operator. The circles (sets) in each of the Venn diagrams represent x and y. 1. y & !x is y but none of x; x & y is the intersection of x and y; x & !y is x but none of y; x is all of x none of y; xor(x, y) is everything except the intersection of x and y; y is all of y and none of x; and x | y is everything." width="395"/></p>
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<figcaption>The complete set of boolean operations. <code>x</code> is the left-hand circle, <code>y</code> is the right-hand circle, and the shaded region show which parts each operator selects.</figcaption>
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</figure>
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</div>
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</div>
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<p>As well as <code>&</code> and <code>|</code>, R also has <code>&&</code> and <code>||</code>. Don’t use them in dplyr functions! These are called short-circuiting operators and only ever return a single <code>TRUE</code> or <code>FALSE</code>. They’re important for programming, not data science</p>
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<section id="sec-na-boolean" data-type="sect2">
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<h2>
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Missing values</h2>
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<p>The rules for missing values in Boolean algebra are a little tricky to explain because they seem inconsistent at first glance:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">df <- tibble(x = c(TRUE, FALSE, NA))
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df |>
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mutate(
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and = x & NA,
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or = x | NA
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)
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#> # A tibble: 3 × 3
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#> x and or
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#> <lgl> <lgl> <lgl>
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#> 1 TRUE NA TRUE
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#> 2 FALSE FALSE NA
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#> 3 NA NA NA</pre>
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</div>
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<p>To understand what’s going on, think about <code>NA | TRUE</code>. A missing value in a logical vector means that the value could either be <code>TRUE</code> or <code>FALSE</code>. <code>TRUE | TRUE</code> and <code>FALSE | TRUE</code> are both <code>TRUE</code>, so <code>NA | TRUE</code> must also be <code>TRUE</code>. Similar reasoning applies with <code>NA & FALSE</code>.</p>
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</section>
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<section id="order-of-operations" data-type="sect2">
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<h2>
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Order of operations</h2>
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<p>Note that the order of operations doesn’t work like English. Take the following code finds all flights that departed in November or December:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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filter(month == 11 | month == 12)</pre>
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</div>
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<p>You might be tempted to write it like you’d say in English: “find all flights that departed in November or December”:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="r">flights |>
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filter(month == 11 | 12)
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#> # A tibble: 336,776 × 19
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#> year month day dep_time sched_…¹ dep_d…² arr_t…³ sched…⁴ arr_d…⁵ carrier
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#> <int> <int> <int> <int> <int> <dbl> <int> <int> <dbl> <chr>
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#> 1 2013 1 1 517 515 2 830 819 11 UA
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#> 2 2013 1 1 533 529 4 850 830 20 UA
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#> 3 2013 1 1 542 540 2 923 850 33 AA
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#> 4 2013 1 1 544 545 -1 1004 1022 -18 B6
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#> 5 2013 1 1 554 600 -6 812 837 -25 DL
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#> 6 2013 1 1 554 558 -4 740 728 12 UA
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#> # … with 336,770 more rows, 9 more variables: flight <int>, tailnum <chr>,
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#> # origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
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#> # minute <dbl>, time_hour <dttm>, and abbreviated variable names
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#> # ¹sched_dep_time, ²dep_delay, ³arr_time, ⁴sched_arr_time, ⁵arr_delay</pre>
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</div>
|
||
<p>This code doesn’t error but it also doesn’t seem to have worked. What’s going on? Here R first evaluates <code>month == 11</code> creating a logical vector, which we call <code>nov</code>. It computes <code>nov | 12</code>. When you use a number with a logical operator it converts everything apart from 0 to TRUE, so this is equivalent to <code>nov | TRUE</code> which will always be <code>TRUE</code>, so every row will be selected:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">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
|
||
#> # … with 336,770 more rows</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="in" data-type="sect2">
|
||
<h2>
|
||
<code>%in%</code>
|
||
</h2>
|
||
<p>An easy way to avoid the problem of getting your <code>==</code>s and <code>|</code>s in the right order is to use <code>%in%</code>. <code>x %in% y</code> returns a logical vector the same length as <code>x</code> that is <code>TRUE</code> whenever a value in <code>x</code> is anywhere in <code>y</code> .</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">1:12 %in% c(1, 5, 11)
|
||
#> [1] TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE FALSE TRUE FALSE
|
||
letters[1:10] %in% c("a", "e", "i", "o", "u")
|
||
#> [1] TRUE FALSE FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE</pre>
|
||
</div>
|
||
<p>So to find all flights in November and December we could write:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
filter(month %in% c(11, 12))</pre>
|
||
</div>
|
||
<p>Note that <code>%in%</code> obeys different rules for <code>NA</code> to <code>==</code>, as <code>NA %in% NA</code> is <code>TRUE</code>.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">c(1, 2, NA) == NA
|
||
#> [1] NA NA NA
|
||
c(1, 2, NA) %in% NA
|
||
#> [1] FALSE FALSE TRUE</pre>
|
||
</div>
|
||
<p>This can make for a useful shortcut:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
filter(dep_time %in% c(NA, 0800))
|
||
#> # A tibble: 8,803 × 19
|
||
#> year month day dep_time sched_…¹ dep_d…² arr_t…³ sched…⁴ arr_d…⁵ carrier
|
||
#> <int> <int> <int> <int> <int> <dbl> <int> <int> <dbl> <chr>
|
||
#> 1 2013 1 1 800 800 0 1022 1014 8 DL
|
||
#> 2 2013 1 1 800 810 -10 949 955 -6 MQ
|
||
#> 3 2013 1 1 NA 1630 NA NA 1815 NA EV
|
||
#> 4 2013 1 1 NA 1935 NA NA 2240 NA AA
|
||
#> 5 2013 1 1 NA 1500 NA NA 1825 NA AA
|
||
#> 6 2013 1 1 NA 600 NA NA 901 NA B6
|
||
#> # … with 8,797 more rows, 9 more variables: flight <int>, tailnum <chr>,
|
||
#> # origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
|
||
#> # minute <dbl>, time_hour <dttm>, and abbreviated variable names
|
||
#> # ¹sched_dep_time, ²dep_delay, ³arr_time, ⁴sched_arr_time, ⁵arr_delay</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="exercises-1" data-type="sect2">
|
||
<h2>
|
||
Exercises</h2>
|
||
<ol type="1"><li>Find all flights where <code>arr_delay</code> is missing but <code>dep_delay</code> is not. Find all flights where neither <code>arr_time</code> nor <code>sched_arr_time</code> are missing, but <code>arr_delay</code> is.</li>
|
||
<li>How many flights have a missing <code>dep_time</code>? What other variables are missing in these rows? What might these rows represent?</li>
|
||
<li>Assuming that a missing <code>dep_time</code> 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 average delay of non-cancelled flights?</li>
|
||
</ol></section>
|
||
</section>
|
||
|
||
<section id="sec-logical-summaries" data-type="sect1">
|
||
<h1>
|
||
Summaries</h1>
|
||
<p>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.</p>
|
||
|
||
<section id="logical-summaries" data-type="sect2">
|
||
<h2>
|
||
Logical summaries</h2>
|
||
<p>There are two main logical summaries: <code><a href="https://rdrr.io/r/base/any.html">any()</a></code> and <code><a href="https://rdrr.io/r/base/all.html">all()</a></code>. <code>any(x)</code> is the equivalent of <code>|</code>; it’ll return <code>TRUE</code> if there are any <code>TRUE</code>’s in <code>x</code>. <code>all(x)</code> is equivalent of <code>&</code>; it’ll return <code>TRUE</code> only if all values of <code>x</code> are <code>TRUE</code>’s. Like all summary functions, they’ll return <code>NA</code> if there are any missing values present, and as usual you can make the missing values go away with <code>na.rm = TRUE</code>.</p>
|
||
<p>For example, we could use <code><a href="https://rdrr.io/r/base/all.html">all()</a></code> to find out if there were days where every flight was delayed:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
all_delayed = all(arr_delay >= 0, na.rm = TRUE),
|
||
any_delayed = any(arr_delay >= 0, na.rm = TRUE),
|
||
.groups = "drop"
|
||
)
|
||
#> # A tibble: 365 × 5
|
||
#> year month day all_delayed any_delayed
|
||
#> <int> <int> <int> <lgl> <lgl>
|
||
#> 1 2013 1 1 FALSE TRUE
|
||
#> 2 2013 1 2 FALSE TRUE
|
||
#> 3 2013 1 3 FALSE TRUE
|
||
#> 4 2013 1 4 FALSE TRUE
|
||
#> 5 2013 1 5 FALSE TRUE
|
||
#> 6 2013 1 6 FALSE TRUE
|
||
#> # … with 359 more rows</pre>
|
||
</div>
|
||
<p>In most cases, however, <code><a href="https://rdrr.io/r/base/any.html">any()</a></code> and <code><a href="https://rdrr.io/r/base/all.html">all()</a></code> are a little too crude, and it would be nice to be able to get a little more detail about how many values are <code>TRUE</code> or <code>FALSE</code>. That leads us to the numeric summaries.</p>
|
||
</section>
|
||
|
||
<section id="numeric-summaries-of-logical-vectors" data-type="sect2">
|
||
<h2>
|
||
Numeric summaries of logical vectors</h2>
|
||
<p>When you use a logical vector in a numeric context, <code>TRUE</code> becomes 1 and <code>FALSE</code> becomes 0. This makes <code><a href="https://rdrr.io/r/base/sum.html">sum()</a></code> and <code><a href="https://rdrr.io/r/base/mean.html">mean()</a></code> very useful with logical vectors because <code>sum(x)</code> will give the number of <code>TRUE</code>s and <code>mean(x)</code> the proportion of <code>TRUE</code>s. That lets us see the distribution of delays across the days of the year as shown in <a href="#fig-prop-delayed-dist" data-type="xref">#fig-prop-delayed-dist</a>.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
prop_delayed = mean(arr_delay > 0, na.rm = TRUE),
|
||
.groups = "drop"
|
||
) |>
|
||
ggplot(aes(prop_delayed)) +
|
||
geom_histogram(binwidth = 0.05)</pre>
|
||
<div class="cell-output-display">
|
||
|
||
<figure id="fig-prop-delayed-dist"><p><img src="logicals_files/figure-html/fig-prop-delayed-dist-1.png" alt="The distribution is unimodal and mildly right skewed. The distribution peaks around 30% delayed flights." width="576"/></p>
|
||
<figcaption>A histogram showing the proportion of delayed flights each day.</figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
<p>Or we could ask how many flights left before 5am, which are often flights that were delayed from the previous day:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
n_early = sum(dep_time < 500, na.rm = TRUE),
|
||
.groups = "drop"
|
||
) |>
|
||
arrange(desc(n_early))
|
||
#> # A tibble: 365 × 4
|
||
#> year month day n_early
|
||
#> <int> <int> <int> <int>
|
||
#> 1 2013 6 28 32
|
||
#> 2 2013 4 10 30
|
||
#> 3 2013 7 28 30
|
||
#> 4 2013 3 18 29
|
||
#> 5 2013 7 7 29
|
||
#> 6 2013 7 10 29
|
||
#> # … with 359 more rows</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="logical-subsetting" data-type="sect2">
|
||
<h2>
|
||
Logical subsetting</h2>
|
||
<p>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 <code>[</code> (pronounced subset) operator, which you’ll learn more about in <a href="#sec-subset-many" data-type="xref">#sec-subset-many</a>.</p>
|
||
<p>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:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
filter(arr_delay > 0) |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
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
|
||
#> # … with 359 more rows</pre>
|
||
</div>
|
||
<p>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<span data-type="footnote">We’ll cover this in <a href="#chp-joins" data-type="xref">#chp-joins</a>]</span>. Instead you could use <code>[</code> to perform an inline filtering: <code>arr_delay[arr_delay > 0]</code> will yield only the positive arrival delays.</p>
|
||
<p>This leads to:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
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
|
||
#> # … with 359 more rows</pre>
|
||
</div>
|
||
<p>Also note the difference in the group size: in the first chunk <code><a href="https://dplyr.tidyverse.org/reference/context.html">n()</a></code> gives the number of delayed flights per day; in the second, <code><a href="https://dplyr.tidyverse.org/reference/context.html">n()</a></code> gives the total number of flights.</p>
|
||
</section>
|
||
|
||
<section id="exercises-2" data-type="sect2">
|
||
<h2>
|
||
Exercises</h2>
|
||
<ol type="1"><li>What will <code>sum(is.na(x))</code> tell you? How about <code>mean(is.na(x))</code>?</li>
|
||
<li>What does <code><a href="https://rdrr.io/r/base/prod.html">prod()</a></code> return when applied to a logical vector? What logical summary function is it equivalent to? What does <code><a href="https://rdrr.io/r/base/Extremes.html">min()</a></code> return applied to a logical vector? What logical summary function is it equivalent to? Read the documentation and perform a few experiments.</li>
|
||
</ol></section>
|
||
</section>
|
||
|
||
<section id="conditional-transformations" data-type="sect1">
|
||
<h1>
|
||
Conditional transformations</h1>
|
||
<p>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: <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code> and <code><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when()</a></code>.</p>
|
||
|
||
<section id="if_else" data-type="sect2">
|
||
<h2>
|
||
<code>if_else()</code>
|
||
</h2>
|
||
<p>If you want to use one value when a condition is true and another value when it’s <code>FALSE</code>, you can use <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">dplyr::if_else()</a></code><span data-type="footnote">dplyr’s <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code> is very similar to base R’s <code><a href="https://rdrr.io/r/base/ifelse.html">ifelse()</a></code>. There are two main advantages of <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code>over <code><a href="https://rdrr.io/r/base/ifelse.html">ifelse()</a></code>: you can choose what should happen to missing values, and <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code> is much more likely to give you a meaningful error if you variables have incompatible types.</span>. You’ll always use the first three argument of <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code>. The first argument, <code>condition</code>, is a logical vector, the second, <code>true</code>, gives the output when the condition is true, and the third, <code>false</code>, gives the output if the condition is false.</p>
|
||
<p>Let’s begin with a simple example of labeling a numeric vector as either “+ve” or “-ve”:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">x <- c(-3:3, NA)
|
||
if_else(x > 0, "+ve", "-ve")
|
||
#> [1] "-ve" "-ve" "-ve" "-ve" "+ve" "+ve" "+ve" NA</pre>
|
||
</div>
|
||
<p>There’s an optional fourth argument, <code>missing</code> which will be used if the input is <code>NA</code>:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">if_else(x > 0, "+ve", "-ve", "???")
|
||
#> [1] "-ve" "-ve" "-ve" "-ve" "+ve" "+ve" "+ve" "???"</pre>
|
||
</div>
|
||
<p>You can also use vectors for the the <code>true</code> and <code>false</code> arguments. For example, this allows us to create a minimal implementation of <code><a href="https://rdrr.io/r/base/MathFun.html">abs()</a></code>:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">if_else(x < 0, -x, x)
|
||
#> [1] 3 2 1 0 1 2 3 NA</pre>
|
||
</div>
|
||
<p>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 <code><a href="https://dplyr.tidyverse.org/reference/coalesce.html">coalesce()</a></code> like this:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">x1 <- c(NA, 1, 2, NA)
|
||
y1 <- c(3, NA, 4, 6)
|
||
if_else(is.na(x1), y1, x1)
|
||
#> [1] 3 1 2 6</pre>
|
||
</div>
|
||
<p>You might have noticed a small infelicity in our labeling: zero is neither positive nor negative. We could resolve this by adding an additional <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code>:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">if_else(x == 0, "0", if_else(x < 0, "-ve", "+ve"), "???")
|
||
#> [1] "-ve" "-ve" "-ve" "0" "+ve" "+ve" "+ve" "???"</pre>
|
||
</div>
|
||
<p>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 <code><a href="https://dplyr.tidyverse.org/reference/case_when.html">dplyr::case_when()</a></code>.</p>
|
||
</section>
|
||
|
||
<section id="case_when" data-type="sect2">
|
||
<h2>
|
||
<code>case_when()</code>
|
||
</h2>
|
||
<p>dplyr’s <code><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when()</a></code> is inspired by SQL’s <code>CASE</code> statement and provides a flexible way of performing different computations for different computations. It has a special syntax that unfortunately looks like nothing else you’ll use in the tidyverse. It takes pairs that look like <code>condition ~ output</code>. <code>condition</code> must be a logical vector; when it’s <code>TRUE</code>, <code>output</code> will be used.</p>
|
||
<p>This means we could recreate our previous nested <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code> as follows:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">case_when(
|
||
x == 0 ~ "0",
|
||
x < 0 ~ "-ve",
|
||
x > 0 ~ "+ve",
|
||
is.na(x) ~ "???"
|
||
)
|
||
#> [1] "-ve" "-ve" "-ve" "0" "+ve" "+ve" "+ve" "???"</pre>
|
||
</div>
|
||
<p>This is more code, but it’s also more explicit.</p>
|
||
<p>To explain how <code><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when()</a></code> works, lets explore some simpler cases. If none of the cases match, the output gets an <code>NA</code>:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">case_when(
|
||
x < 0 ~ "-ve",
|
||
x > 0 ~ "+ve"
|
||
)
|
||
#> [1] "-ve" "-ve" "-ve" NA "+ve" "+ve" "+ve" NA</pre>
|
||
</div>
|
||
<p>If you want to create a “default”/catch all value, use <code>TRUE</code> on the left hand side:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">case_when(
|
||
x < 0 ~ "-ve",
|
||
x > 0 ~ "+ve",
|
||
TRUE ~ "???"
|
||
)
|
||
#> [1] "-ve" "-ve" "-ve" "???" "+ve" "+ve" "+ve" "???"</pre>
|
||
</div>
|
||
<p>And note that if multiple conditions match, only the first will be used:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">case_when(
|
||
x > 0 ~ "+ve",
|
||
x > 3 ~ "big"
|
||
)
|
||
#> [1] NA NA NA NA "+ve" "+ve" "+ve" NA</pre>
|
||
</div>
|
||
<p>Just like with <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code> you can use variables on both sides of the <code>~</code> and you can mix and match variables as needed for your problem. For example, we could use <code><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when()</a></code> to provide some human readable labels for the arrival delay:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="r">flights |>
|
||
mutate(
|
||
status = case_when(
|
||
is.na(arr_delay) ~ "cancelled",
|
||
arr_delay > 60 ~ "very late",
|
||
arr_delay > 15 ~ "late",
|
||
abs(arr_delay) <= 15 ~ "on time",
|
||
arr_delay < -15 ~ "early",
|
||
arr_delay < -30 ~ "very early",
|
||
),
|
||
.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
|
||
#> # … with 336,770 more rows</pre>
|
||
</div>
|
||
</section>
|
||
</section>
|
||
|
||
<section id="summary" data-type="sect1">
|
||
<h1>
|
||
Summary</h1>
|
||
<p>The definition of a logical vector is simple because each value must be either <code>TRUE</code>, <code>FALSE</code>, or <code>NA</code>. But logical vectors provide a huge amount of power. In this chapter, you learned how to create logical vectors with <code>></code>, <code><</code>, <code><=</code>, <code>=></code>, <code>==</code>, <code>!=</code>, and <code><a href="https://rdrr.io/r/base/NA.html">is.na()</a></code>, how to combine them with <code>!</code>, <code>&</code>, and <code>|</code>, and how to summarize them with <code><a href="https://rdrr.io/r/base/any.html">any()</a></code>, <code><a href="https://rdrr.io/r/base/all.html">all()</a></code>, <code><a href="https://rdrr.io/r/base/sum.html">sum()</a></code>, and <code><a href="https://rdrr.io/r/base/mean.html">mean()</a></code>. You also learned the powerful <code><a href="https://dplyr.tidyverse.org/reference/if_else.html">if_else()</a></code> and <code><a href="https://dplyr.tidyverse.org/reference/case_when.html">case_when()</a></code> that allow you to return values depending on the value of a logical vector.</p>
|
||
<p>We’ll see logical vectors again and in the following chapters. For example in <a href="#chp-strings" data-type="xref">#chp-strings</a> you’ll learn about <code>str_detect(x, pattern)</code> which returns a logical vector that’s <code>TRUE</code> for the elements of <code>x</code> that match the <code>pattern</code>, and in <a href="#chp-datetimes" data-type="xref">#chp-datetimes</a> 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.</p>
|
||
|
||
|
||
</section>
|
||
</section>
|