831 lines
54 KiB
HTML
831 lines
54 KiB
HTML
<section data-type="chapter" id="chp-numbers">
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<h1><span id="sec-numbers" class="quarto-section-identifier d-none d-lg-block"><span class="chapter-title">Numbers</span></span></h1><p>::: status callout-note You are reading the work-in-progress second edition of R for Data Science. This chapter should be readable but is currently undergoing final polishing. You can find the complete first edition at <a href="https://r4ds.had.co.nz" class="uri">https://r4ds.had.co.nz</a>. :::</p>
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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>Numeric vectors are the backbone of data science, and you’ve already used them a bunch of times earlier in the book. Now it’s time to systematically survey what you can do with them in R, ensuring that you’re well situated to tackle any future problem involving numeric vectors.</p>
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<p>We’ll start by giving you a couple of tools to make numbers if you have strings, and then going into a little more detail of <code><a href="https://dplyr.tidyverse.org/reference/count.html">count()</a></code>. Then we’ll dive into various numeric transformations that pair well with <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code>, including more general transformations that can be applied to other types of vector, but are often used with numeric vectors. We’ll finish off by covering the summary functions that pair well with <code><a href="https://dplyr.tidyverse.org/reference/summarise.html">summarise()</a></code> and show you how they can also be used with <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code>.</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>This chapter mostly uses functions from base R, which are available without loading any packages. But we still need the tidyverse because we’ll use these base R functions inside of tidyverse functions like <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code> and <code><a href="https://dplyr.tidyverse.org/reference/filter.html">filter()</a></code>. Like in the last chapter, we’ll use real examples from nycflights13, as well as toy examples made with <code><a href="https://rdrr.io/r/base/c.html">c()</a></code> and <code><a href="https://tibble.tidyverse.org/reference/tribble.html">tribble()</a></code>.</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">library(tidyverse)
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library(nycflights13)</pre>
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</div>
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</section>
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</section>
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<section id="making-numbers" data-type="sect1">
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<h1>
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Making numbers</h1>
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<p>In most cases, you’ll get numbers already recorded in one of R’s numeric types: integer or double. In some cases, however, you’ll encounter them as strings, possibly because you’ve created them by pivoting from column headers or something has gone wrong in your data import process.</p>
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<p>readr provides two useful functions for parsing strings into numbers: <code><a href="https://readr.tidyverse.org/reference/parse_atomic.html">parse_double()</a></code> and <code><a href="https://readr.tidyverse.org/reference/parse_number.html">parse_number()</a></code>. Use <code><a href="https://readr.tidyverse.org/reference/parse_atomic.html">parse_double()</a></code> when you have numbers that have been written as strings:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">x <- c("1.2", "5.6", "1e3")
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parse_double(x)
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#> [1] 1.2 5.6 1000.0</pre>
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</div>
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<p>Use <code><a href="https://readr.tidyverse.org/reference/parse_number.html">parse_number()</a></code> when the string contains non-numeric text that you want to ignore. This is particularly useful for currency data and percentages:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">x <- c("$1,234", "USD 3,513", "59%")
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parse_number(x)
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#> [1] 1234 3513 59</pre>
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</div>
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</section>
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<section id="counts" data-type="sect1">
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<h1>
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Counts</h1>
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<p>It’s surprising how much data science you can do with just counts and a little basic arithmetic, so dplyr strives to make counting as easy as possible with <code><a href="https://dplyr.tidyverse.org/reference/count.html">count()</a></code>. This function is great for quick exploration and checks during analysis:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |> count(dest)
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#> # A tibble: 105 × 2
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#> dest n
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#> <chr> <int>
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#> 1 ABQ 254
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#> 2 ACK 265
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#> 3 ALB 439
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#> 4 ANC 8
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#> 5 ATL 17215
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#> 6 AUS 2439
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#> # … with 99 more rows</pre>
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</div>
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<p>(Despite the advice in <a href="#chp-workflow-style" data-type="xref">#chp-workflow-style</a>, we usually put <code><a href="https://dplyr.tidyverse.org/reference/count.html">count()</a></code> on a single line because it’s usually used at the console for a quick check that a calculation is working as expected.)</p>
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<p>If you want to see the most common values add <code>sort = TRUE</code>:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |> count(dest, sort = TRUE)
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#> # A tibble: 105 × 2
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#> dest n
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#> <chr> <int>
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#> 1 ORD 17283
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#> 2 ATL 17215
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#> 3 LAX 16174
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#> 4 BOS 15508
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#> 5 MCO 14082
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#> 6 CLT 14064
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#> # … with 99 more rows</pre>
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</div>
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<p>And remember that if you want to see all the values, you can use <code>|> View()</code> or <code>|> print(n = Inf)</code>.</p>
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<p>You can perform the same computation “by hand” with <code><a href="https://dplyr.tidyverse.org/reference/group_by.html">group_by()</a></code>, <code><a href="https://dplyr.tidyverse.org/reference/summarise.html">summarise()</a></code> and <code><a href="https://dplyr.tidyverse.org/reference/context.html">n()</a></code>. This is useful because it allows you to compute other summaries at the same time:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |>
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group_by(dest) |>
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summarise(
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n = n(),
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delay = mean(arr_delay, na.rm = TRUE)
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)
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#> # A tibble: 105 × 3
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#> dest n delay
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#> <chr> <int> <dbl>
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#> 1 ABQ 254 4.38
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#> 2 ACK 265 4.85
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#> 3 ALB 439 14.4
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#> 4 ANC 8 -2.5
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#> 5 ATL 17215 11.3
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#> 6 AUS 2439 6.02
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#> # … with 99 more rows</pre>
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</div>
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<p><code><a href="https://dplyr.tidyverse.org/reference/context.html">n()</a></code> is a special summary function that doesn’t take any arguments and instead accesses information about the “current” group. This means that it only works inside dplyr verbs:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">n()
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#> Error in `n()`:
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#> ! Must only be used inside data-masking verbs like `mutate()`,
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#> `filter()`, and `group_by()`.</pre>
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</div>
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<p>There are a couple of variants of <code><a href="https://dplyr.tidyverse.org/reference/context.html">n()</a></code> that you might find useful:</p>
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<ul><li>
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<p><code>n_distinct(x)</code> counts the number of distinct (unique) values of one or more variables. For example, we could figure out which destinations are served by the most carriers:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |>
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group_by(dest) |>
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summarise(
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carriers = n_distinct(carrier)
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) |>
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arrange(desc(carriers))
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#> # A tibble: 105 × 2
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#> dest carriers
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#> <chr> <int>
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#> 1 ATL 7
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#> 2 BOS 7
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#> 3 CLT 7
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#> 4 ORD 7
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#> 5 TPA 7
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#> 6 AUS 6
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#> # … with 99 more rows</pre>
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</div>
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</li>
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<li>
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<p>A weighted count is a sum. For example you could “count” the number of miles each plane flew:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |>
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group_by(tailnum) |>
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summarise(miles = sum(distance))
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#> # A tibble: 4,044 × 2
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#> tailnum miles
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#> <chr> <dbl>
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#> 1 D942DN 3418
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#> 2 N0EGMQ 250866
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#> 3 N10156 115966
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#> 4 N102UW 25722
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#> 5 N103US 24619
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#> 6 N104UW 25157
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#> # … with 4,038 more rows</pre>
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</div>
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<p>Weighted counts are a common problem so <code><a href="https://dplyr.tidyverse.org/reference/count.html">count()</a></code> has a <code>wt</code> argument that does the same thing:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |> count(tailnum, wt = distance)
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#> # A tibble: 4,044 × 2
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#> tailnum n
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#> <chr> <dbl>
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#> 1 D942DN 3418
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#> 2 N0EGMQ 250866
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#> 3 N10156 115966
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#> 4 N102UW 25722
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#> 5 N103US 24619
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#> 6 N104UW 25157
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#> # … with 4,038 more rows</pre>
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</div>
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</li>
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<li>
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<p>You can count missing values by combining <code><a href="https://rdrr.io/r/base/sum.html">sum()</a></code> and <code><a href="https://rdrr.io/r/base/NA.html">is.na()</a></code>. In the <code>flights</code> dataset this represents flights that are cancelled:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |>
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group_by(dest) |>
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summarise(n_cancelled = sum(is.na(dep_time)))
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#> # A tibble: 105 × 2
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#> dest n_cancelled
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#> <chr> <int>
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#> 1 ABQ 0
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#> 2 ACK 0
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#> 3 ALB 20
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#> 4 ANC 0
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#> 5 ATL 317
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#> 6 AUS 21
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#> # … with 99 more rows</pre>
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</div>
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</li>
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</ul>
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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 can you use <code><a href="https://dplyr.tidyverse.org/reference/count.html">count()</a></code> to count the number rows with a missing value for a given variable?</li>
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<li>Expand the following calls to <code><a href="https://dplyr.tidyverse.org/reference/count.html">count()</a></code> to instead use <code><a href="https://dplyr.tidyverse.org/reference/group_by.html">group_by()</a></code>, <code><a href="https://dplyr.tidyverse.org/reference/summarise.html">summarise()</a></code>, and <code><a href="https://dplyr.tidyverse.org/reference/arrange.html">arrange()</a></code>:
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<ol type="1"><li><p><code>flights |> count(dest, sort = TRUE)</code></p></li>
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<li><p><code>flights |> count(tailnum, wt = distance)</code></p></li>
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</ol></li>
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</ol></section>
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</section>
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<section id="numeric-transformations" data-type="sect1">
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<h1>
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Numeric transformations</h1>
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<p>Transformation functions work well with <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code> because their output is the same length as the input. The vast majority of transformation functions are already built into base R. It’s impractical to list them all so this section will show the most useful ones. As an example, while R provides all the trigonometric functions that you might dream of, we don’t list them here because they’re rarely needed for data science.</p>
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<section id="sec-recycling" data-type="sect2">
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<h2>
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Arithmetic and recycling rules</h2>
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<p>We introduced the basics of arithmetic (<code>+</code>, <code>-</code>, <code>*</code>, <code>/</code>, <code>^</code>) in <a href="#chp-workflow-basics" data-type="xref">#chp-workflow-basics</a> and have used them a bunch since. These functions don’t need a huge amount of explanation because they do what you learned in grade school. But we need to briefly talk about the <strong>recycling rules</strong> which determine what happens when the left and right hand sides have different lengths. This is important for operations like <code>flights |> mutate(air_time = air_time / 60)</code> because there are 336,776 numbers on the left of <code>/</code> but only one on the right.</p>
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<p>R handles mismatched lengths by <strong>recycling,</strong> or repeating, the short vector. We can see this in operation more easily if we create some vectors outside of a data frame:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">x <- c(1, 2, 10, 20)
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x / 5
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#> [1] 0.2 0.4 2.0 4.0
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# is shorthand for
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x / c(5, 5, 5, 5)
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#> [1] 0.2 0.4 2.0 4.0</pre>
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</div>
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<p>Generally, you only want to recycle single numbers (i.e. vectors of length 1), but R will recycle any shorter length vector. It usually (but not always) gives you a warning if the longer vector isn’t a multiple of the shorter:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">x * c(1, 2)
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#> [1] 1 4 10 40
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x * c(1, 2, 3)
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#> Warning in x * c(1, 2, 3): longer object length is not a multiple of shorter
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#> object length
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#> [1] 1 4 30 20</pre>
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</div>
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<p>These recycling rules are also applied to logical comparisons (<code>==</code>, <code><</code>, <code><=</code>, <code>></code>, <code>>=</code>, <code>!=</code>) and can lead to a surprising result if you accidentally use <code>==</code> instead of <code>%in%</code> and the data frame has an unfortunate number of rows. For example, take this code which attempts to find all flights in January and February:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |>
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filter(month == c(1, 2))
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#> # A tibble: 25,977 × 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 1 542 540 2 923 850 33 AA
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#> 3 2013 1 1 554 600 -6 812 837 -25 DL
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#> 4 2013 1 1 555 600 -5 913 854 19 B6
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#> 5 2013 1 1 557 600 -3 838 846 -8 B6
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#> 6 2013 1 1 558 600 -2 849 851 -2 B6
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#> # … with 25,971 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>The code runs without error, but it doesn’t return what you want. Because of the recycling rules it finds flights in odd numbered rows that departed in January and flights in even numbered rows that departed in February. And unforuntately there’s no warning because <code>flights</code> has an even number of rows.</p>
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<p>To protect you from this type of silent failure, most tidyverse functions use a stricter form of recycling that only recycles single values. Unfortunately that doesn’t help here, or in many other cases, because the key computation is performed by the base R function <code>==</code>, not <code><a href="https://dplyr.tidyverse.org/reference/filter.html">filter()</a></code>.</p>
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</section>
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<section id="minimum-and-maximum" data-type="sect2">
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<h2>
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Minimum and maximum</h2>
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<p>The arithmetic functions work with pairs of variables. Two closely related functions are <code><a href="https://rdrr.io/r/base/Extremes.html">pmin()</a></code> and <code><a href="https://rdrr.io/r/base/Extremes.html">pmax()</a></code>, which when given two or more variables will return the smallest or largest value in each row:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">df <- tribble(
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~x, ~y,
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1, 3,
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5, 2,
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7, NA,
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)
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df |>
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mutate(
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min = pmin(x, y, na.rm = TRUE),
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max = pmax(x, y, na.rm = TRUE)
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)
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#> # A tibble: 3 × 4
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#> x y min max
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#> <dbl> <dbl> <dbl> <dbl>
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#> 1 1 3 1 3
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#> 2 5 2 2 5
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#> 3 7 NA 7 7</pre>
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</div>
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<p>Note that these are different to the summary functions <code><a href="https://rdrr.io/r/base/Extremes.html">min()</a></code> and <code><a href="https://rdrr.io/r/base/Extremes.html">max()</a></code> which take multiple observations and return a single value. You can tell that you’ve used the wrong form when all the minimums and all the maximums have the same value:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">df |>
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mutate(
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min = min(x, y, na.rm = TRUE),
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max = max(x, y, na.rm = TRUE)
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)
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#> # A tibble: 3 × 4
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#> x y min max
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#> <dbl> <dbl> <dbl> <dbl>
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#> 1 1 3 1 7
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#> 2 5 2 1 7
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#> 3 7 NA 1 7</pre>
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</div>
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</section>
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<section id="modular-arithmetic" data-type="sect2">
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<h2>
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Modular arithmetic</h2>
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<p>Modular arithmetic is the technical name for the type of math you did before you learned about real numbers, i.e. division that yields a whole number and a remainder. In R, <code>%/%</code> does integer division and <code>%%</code> computes the remainder:</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">1:10 %/% 3
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#> [1] 0 0 1 1 1 2 2 2 3 3
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1:10 %% 3
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#> [1] 1 2 0 1 2 0 1 2 0 1</pre>
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</div>
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<p>Modular arithmetic is handy for the flights dataset, because we can use it to unpack the <code>sched_dep_time</code> variable into and <code>hour</code> and <code>minute</code>:</p>
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||
<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |>
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mutate(
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hour = sched_dep_time %/% 100,
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minute = sched_dep_time %% 100,
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.keep = "used"
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)
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#> # A tibble: 336,776 × 3
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#> sched_dep_time hour minute
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#> <int> <dbl> <dbl>
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#> 1 515 5 15
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#> 2 529 5 29
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#> 3 540 5 40
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#> 4 545 5 45
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#> 5 600 6 0
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#> 6 558 5 58
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#> # … with 336,770 more rows</pre>
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</div>
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<p>We can combine that with the <code>mean(is.na(x))</code> trick from <a href="#sec-logical-summaries" data-type="xref">#sec-logical-summaries</a> to see how the proportion of cancelled flights varies over the course of the day. The results are shown in <a href="#fig-prop-cancelled" data-type="xref">#fig-prop-cancelled</a>.</p>
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<div class="cell">
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<pre data-type="programlisting" data-code-language="downlit">flights |>
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group_by(hour = sched_dep_time %/% 100) |>
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summarise(prop_cancelled = mean(is.na(dep_time)), n = n()) |>
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filter(hour > 1) |>
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ggplot(aes(hour, prop_cancelled)) +
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geom_line(color = "grey50") +
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geom_point(aes(size = n))</pre>
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<div class="cell-output-display">
|
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<figure id="fig-prop-cancelled"><p><img src="numbers_files/figure-html/fig-prop-cancelled-1.png" alt="A line plot showing how proportion of cancelled flights changes over the course of the day. The proportion starts low at around 0.5% at 6am, then steadily increases over the course of the day until peaking at 4% at 7pm. The proportion of cancelled flights then drops rapidly getting down to around 1% by midnight." width="576"/></p>
|
||
<figcaption>A line plot with scheduled departure hour on the x-axis, and proportion of cancelled flights on the y-axis. Cancellations seem to accumulate over the course of the day until 8pm, very late flights are much less likely to be cancelled.</figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="logarithms" data-type="sect2">
|
||
<h2>
|
||
Logarithms</h2>
|
||
<p>Logarithms are an incredibly useful transformation for dealing with data that ranges across multiple orders of magnitude. They also convert exponential growth to linear growth. For example, take compounding interest — the amount of money you have at <code>year + 1</code> is the amount of money you had at <code>year</code> multiplied by the interest rate. That gives a formula like <code>money = starting * interest ^ year</code>:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">starting <- 100
|
||
interest <- 1.05
|
||
|
||
money <- tibble(
|
||
year = 2000 + 1:50,
|
||
money = starting * interest^(1:50)
|
||
)</pre>
|
||
</div>
|
||
<p>If you plot this data, you’ll get an exponential curve:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">ggplot(money, aes(year, money)) +
|
||
geom_line()</pre>
|
||
<div class="cell-output-display">
|
||
<p><img src="numbers_files/figure-html/unnamed-chunk-22-1.png" width="576"/></p>
|
||
</div>
|
||
</div>
|
||
<p>Log transforming the y-axis gives a straight line:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">ggplot(money, aes(year, money)) +
|
||
geom_line() +
|
||
scale_y_log10()</pre>
|
||
<div class="cell-output-display">
|
||
<p><img src="numbers_files/figure-html/unnamed-chunk-23-1.png" width="576"/></p>
|
||
</div>
|
||
</div>
|
||
<p>This a straight line because a little algebra reveals that <code>log(money) = log(starting) + n * log(interest)</code>, which matches the pattern for a line, <code>y = m * x + b</code>. This is a useful pattern: if you see a (roughly) straight line after log-transforming the y-axis, you know that there’s underlying exponential growth.</p>
|
||
<p>If you’re log-transforming your data with dplyr you have a choice of three logarithms provided by base R: <code><a href="https://rdrr.io/r/base/Log.html">log()</a></code> (the natural log, base e), <code><a href="https://rdrr.io/r/base/Log.html">log2()</a></code> (base 2), and <code><a href="https://rdrr.io/r/base/Log.html">log10()</a></code> (base 10). We recommend using <code><a href="https://rdrr.io/r/base/Log.html">log2()</a></code> or <code><a href="https://rdrr.io/r/base/Log.html">log10()</a></code>. <code><a href="https://rdrr.io/r/base/Log.html">log2()</a></code> is easy to interpret because difference of 1 on the log scale corresponds to doubling on the original scale and a difference of -1 corresponds to halving; whereas <code><a href="https://rdrr.io/r/base/Log.html">log10()</a></code> is easy to back-transform because (e.g) 3 is 10^3 = 1000.</p>
|
||
<p>The inverse of <code><a href="https://rdrr.io/r/base/Log.html">log()</a></code> is <code><a href="https://rdrr.io/r/base/Log.html">exp()</a></code>; to compute the inverse of <code><a href="https://rdrr.io/r/base/Log.html">log2()</a></code> or <code><a href="https://rdrr.io/r/base/Log.html">log10()</a></code> you’ll need to use <code>2^</code> or <code>10^</code>.</p>
|
||
</section>
|
||
|
||
<section id="sec-rounding" data-type="sect2">
|
||
<h2>
|
||
Rounding</h2>
|
||
<p>Use <code>round(x)</code> to round a number to the nearest integer:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">round(123.456)
|
||
#> [1] 123</pre>
|
||
</div>
|
||
<p>You can control the precision of the rounding with the second argument, <code>digits</code>. <code>round(x, digits)</code> rounds to the nearest <code>10^-n</code> so <code>digits = 2</code> will round to the nearest 0.01. This definition is useful because it implies <code>round(x, -3)</code> will round to the nearest thousand, which indeed it does:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">round(123.456, 2) # two digits
|
||
#> [1] 123.46
|
||
round(123.456, 1) # one digit
|
||
#> [1] 123.5
|
||
round(123.456, -1) # round to nearest ten
|
||
#> [1] 120
|
||
round(123.456, -2) # round to nearest hundred
|
||
#> [1] 100</pre>
|
||
</div>
|
||
<p>There’s one weirdness with <code><a href="https://rdrr.io/r/base/Round.html">round()</a></code> that seems surprising at first glance:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">round(c(1.5, 2.5))
|
||
#> [1] 2 2</pre>
|
||
</div>
|
||
<p><code><a href="https://rdrr.io/r/base/Round.html">round()</a></code> uses what’s known as “round half to even” or Banker’s rounding: if a number is half way between two integers, it will be rounded to the <strong>even</strong> integer. This is a good strategy because it keeps the rounding unbiased: half of all 0.5s are rounded up, and half are rounded down.</p>
|
||
<p><code><a href="https://rdrr.io/r/base/Round.html">round()</a></code> is paired with <code><a href="https://rdrr.io/r/base/Round.html">floor()</a></code> which always rounds down and <code><a href="https://rdrr.io/r/base/Round.html">ceiling()</a></code> which always rounds up:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">x <- 123.456
|
||
|
||
floor(x)
|
||
#> [1] 123
|
||
ceiling(x)
|
||
#> [1] 124</pre>
|
||
</div>
|
||
<p>These functions don’t have a digits argument, so you can instead scale down, round, and then scale back up:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit"># Round down to nearest two digits
|
||
floor(x / 0.01) * 0.01
|
||
#> [1] 123.45
|
||
# Round up to nearest two digits
|
||
ceiling(x / 0.01) * 0.01
|
||
#> [1] 123.46</pre>
|
||
</div>
|
||
<p>You can use the same technique if you want to <code><a href="https://rdrr.io/r/base/Round.html">round()</a></code> to a multiple of some other number:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit"># Round to nearest multiple of 4
|
||
round(x / 4) * 4
|
||
#> [1] 124
|
||
|
||
# Round to nearest 0.25
|
||
round(x / 0.25) * 0.25
|
||
#> [1] 123.5</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="cutting-numbers-into-ranges" data-type="sect2">
|
||
<h2>
|
||
Cutting numbers into ranges</h2>
|
||
<p>Use <code><a href="https://rdrr.io/r/base/cut.html">cut()</a></code><span data-type="footnote">ggplot2 provides some helpers for common cases in <code><a href="https://ggplot2.tidyverse.org/reference/cut_interval.html">cut_interval()</a></code>, <code><a href="https://ggplot2.tidyverse.org/reference/cut_interval.html">cut_number()</a></code>, and <code><a href="https://ggplot2.tidyverse.org/reference/cut_interval.html">cut_width()</a></code>. ggplot2 is an admittedly weird place for these functions to live, but they are useful as part of histogram computation and were written before any other parts of the tidyverse existed.</span> to break up a numeric vector into discrete buckets:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">x <- c(1, 2, 5, 10, 15, 20)
|
||
cut(x, breaks = c(0, 5, 10, 15, 20))
|
||
#> [1] (0,5] (0,5] (0,5] (5,10] (10,15] (15,20]
|
||
#> Levels: (0,5] (5,10] (10,15] (15,20]</pre>
|
||
</div>
|
||
<p>The breaks don’t need to be evenly spaced:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">cut(x, breaks = c(0, 5, 10, 100))
|
||
#> [1] (0,5] (0,5] (0,5] (5,10] (10,100] (10,100]
|
||
#> Levels: (0,5] (5,10] (10,100]</pre>
|
||
</div>
|
||
<p>You can optionally supply your own <code>labels</code>. Note that there should be one less <code>labels</code> than <code>breaks</code>.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">cut(x,
|
||
breaks = c(0, 5, 10, 15, 20),
|
||
labels = c("sm", "md", "lg", "xl")
|
||
)
|
||
#> [1] sm sm sm md lg xl
|
||
#> Levels: sm md lg xl</pre>
|
||
</div>
|
||
<p>Any values outside of the range of the breaks will become <code>NA</code>:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">y <- c(NA, -10, 5, 10, 30)
|
||
cut(y, breaks = c(0, 5, 10, 15, 20))
|
||
#> [1] <NA> <NA> (0,5] (5,10] <NA>
|
||
#> Levels: (0,5] (5,10] (10,15] (15,20]</pre>
|
||
</div>
|
||
<p>See the documentation for other useful arguments like <code>right</code> and <code>include.lowest</code>, which control if the intervals are <code>[a, b)</code> or <code>(a, b]</code> and if the lowest interval should be <code>[a, b]</code>.</p>
|
||
</section>
|
||
|
||
<section id="cumulative-and-rolling-aggregates" data-type="sect2">
|
||
<h2>
|
||
Cumulative and rolling aggregates</h2>
|
||
<p>Base R provides <code><a href="https://rdrr.io/r/base/cumsum.html">cumsum()</a></code>, <code><a href="https://rdrr.io/r/base/cumsum.html">cumprod()</a></code>, <code><a href="https://rdrr.io/r/base/cumsum.html">cummin()</a></code>, <code><a href="https://rdrr.io/r/base/cumsum.html">cummax()</a></code> for running, or cumulative, sums, products, mins and maxes. dplyr provides <code><a href="https://dplyr.tidyverse.org/reference/cumall.html">cummean()</a></code> for cumulative means. Cumulative sums tend to come up the most in practice:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">x <- 1:10
|
||
cumsum(x)
|
||
#> [1] 1 3 6 10 15 21 28 36 45 55</pre>
|
||
</div>
|
||
<p>If you need more complex rolling or sliding aggregates, try the <a href="https://davisvaughan.github.io/slider/">slider</a> package by Davis Vaughan. The following example illustrates some of its features.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">library(slider)
|
||
|
||
# Same as a cumulative sum
|
||
slide_vec(x, sum, .before = Inf)
|
||
#> [1] 1 3 6 10 15 21 28 36 45 55
|
||
# Sum the current element and the one before it
|
||
slide_vec(x, sum, .before = 1)
|
||
#> [1] 1 3 5 7 9 11 13 15 17 19
|
||
# Sum the current element and the two before and after it
|
||
slide_vec(x, sum, .before = 2, .after = 2)
|
||
#> [1] 6 10 15 20 25 30 35 40 34 27
|
||
# Only compute if the window is complete
|
||
slide_vec(x, sum, .before = 2, .after = 2, .complete = TRUE)
|
||
#> [1] NA NA 15 20 25 30 35 40 NA NA</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="exercises-1" data-type="sect2">
|
||
<h2>
|
||
Exercises</h2>
|
||
<ol type="1"><li><p>Explain in words what each line of the code used to generate <a href="#fig-prop-cancelled" data-type="xref">#fig-prop-cancelled</a> does.</p></li>
|
||
<li><p>What trigonometric functions does R provide? Guess some names and look up the documentation. Do they use degrees or radians?</p></li>
|
||
<li>
|
||
<p>Currently <code>dep_time</code> and <code>sched_dep_time</code> are convenient to look at, but hard to compute with because they’re not really continuous numbers. You can see the basic problem in this plot: there’s a gap between each hour.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
filter(month == 1, day == 1) |>
|
||
ggplot(aes(sched_dep_time, dep_delay)) +
|
||
geom_point()
|
||
#> Warning: Removed 4 rows containing missing values (`geom_point()`).</pre>
|
||
<div class="cell-output-display">
|
||
<p><img src="numbers_files/figure-html/unnamed-chunk-36-1.png" width="576"/></p>
|
||
</div>
|
||
</div>
|
||
<p>Convert them to a more truthful representation of time (either fractional hours or minutes since midnight).</p>
|
||
</li>
|
||
</ol></section>
|
||
</section>
|
||
|
||
<section id="general-transformations" data-type="sect1">
|
||
<h1>
|
||
General transformations</h1>
|
||
<p>The following sections describe some general transformations which are often used with numeric vectors, but can be applied to all other column types.</p>
|
||
|
||
<section id="ranks" data-type="sect2">
|
||
<h2>
|
||
Ranks</h2>
|
||
<p>dplyr provides a number of ranking functions inspired by SQL, but you should always start with <code><a href="https://dplyr.tidyverse.org/reference/row_number.html">dplyr::min_rank()</a></code>. It uses the typical method for dealing with ties, e.g. 1st, 2nd, 2nd, 4th.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">x <- c(1, 2, 2, 3, 4, NA)
|
||
min_rank(x)
|
||
#> [1] 1 2 2 4 5 NA</pre>
|
||
</div>
|
||
<p>Note that the smallest values get the lowest ranks; use <code>desc(x)</code> to give the largest values the smallest ranks:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">min_rank(desc(x))
|
||
#> [1] 5 3 3 2 1 NA</pre>
|
||
</div>
|
||
<p>If <code><a href="https://dplyr.tidyverse.org/reference/row_number.html">min_rank()</a></code> doesn’t do what you need, look at the variants <code><a href="https://dplyr.tidyverse.org/reference/row_number.html">dplyr::row_number()</a></code>, <code><a href="https://dplyr.tidyverse.org/reference/row_number.html">dplyr::dense_rank()</a></code>, <code><a href="https://dplyr.tidyverse.org/reference/percent_rank.html">dplyr::percent_rank()</a></code>, and <code><a href="https://dplyr.tidyverse.org/reference/percent_rank.html">dplyr::cume_dist()</a></code>. See the documentation for details.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">df <- tibble(x = x)
|
||
df |>
|
||
mutate(
|
||
row_number = row_number(x),
|
||
dense_rank = dense_rank(x),
|
||
percent_rank = percent_rank(x),
|
||
cume_dist = cume_dist(x)
|
||
)
|
||
#> # A tibble: 6 × 5
|
||
#> x row_number dense_rank percent_rank cume_dist
|
||
#> <dbl> <int> <int> <dbl> <dbl>
|
||
#> 1 1 1 1 0 0.2
|
||
#> 2 2 2 2 0.25 0.6
|
||
#> 3 2 3 2 0.25 0.6
|
||
#> 4 3 4 3 0.75 0.8
|
||
#> 5 4 5 4 1 1
|
||
#> 6 NA NA NA NA NA</pre>
|
||
</div>
|
||
<p>You can achieve many of the same results by picking the appropriate <code>ties.method</code> argument to base R’s <code><a href="https://rdrr.io/r/base/rank.html">rank()</a></code>; you’ll probably also want to set <code>na.last = "keep"</code> to keep <code>NA</code>s as <code>NA</code>.</p>
|
||
<p><code><a href="https://dplyr.tidyverse.org/reference/row_number.html">row_number()</a></code> can also be used without any arguments when inside a dplyr verb. In this case, it’ll give the number of the “current” row. When combined with <code>%%</code> or <code>%/%</code> this can be a useful tool for dividing data into similarly sized groups:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">df <- tibble(x = runif(10))
|
||
|
||
df |>
|
||
mutate(
|
||
row0 = row_number() - 1,
|
||
three_groups = row0 %% 3,
|
||
three_in_each_group = row0 %/% 3,
|
||
)
|
||
#> # A tibble: 10 × 4
|
||
#> x row0 three_groups three_in_each_group
|
||
#> <dbl> <dbl> <dbl> <dbl>
|
||
#> 1 0.0808 0 0 0
|
||
#> 2 0.834 1 1 0
|
||
#> 3 0.601 2 2 0
|
||
#> 4 0.157 3 0 1
|
||
#> 5 0.00740 4 1 1
|
||
#> 6 0.466 5 2 1
|
||
#> # … with 4 more rows</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="offsets" data-type="sect2">
|
||
<h2>
|
||
Offsets</h2>
|
||
<p><code><a href="https://dplyr.tidyverse.org/reference/lead-lag.html">dplyr::lead()</a></code> and <code><a href="https://dplyr.tidyverse.org/reference/lead-lag.html">dplyr::lag()</a></code> allow you to refer the values just before or just after the “current” value. They return a vector of the same length as the input, padded with <code>NA</code>s at the start or end:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">x <- c(2, 5, 11, 11, 19, 35)
|
||
lag(x)
|
||
#> [1] NA 2 5 11 11 19
|
||
lead(x)
|
||
#> [1] 5 11 11 19 35 NA</pre>
|
||
</div>
|
||
<ul><li>
|
||
<p><code>x - lag(x)</code> gives you the difference between the current and previous value.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">x - lag(x)
|
||
#> [1] NA 3 6 0 8 16</pre>
|
||
</div>
|
||
</li>
|
||
<li>
|
||
<p><code>x == lag(x)</code> tells you when the current value changes.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">x == lag(x)
|
||
#> [1] NA FALSE FALSE TRUE FALSE FALSE</pre>
|
||
</div>
|
||
</li>
|
||
</ul><p>You can lead or lag by more than one position by using the second argument, <code>n</code>.</p>
|
||
</section>
|
||
|
||
<section id="exercises-2" data-type="sect2">
|
||
<h2>
|
||
Exercises</h2>
|
||
<ol type="1"><li><p>Find the 10 most delayed flights using a ranking function. How do you want to handle ties? Carefully read the documentation for <code><a href="https://dplyr.tidyverse.org/reference/row_number.html">min_rank()</a></code>.</p></li>
|
||
<li><p>Which plane (<code>tailnum</code>) has the worst on-time record?</p></li>
|
||
<li><p>What time of day should you fly if you want to avoid delays as much as possible?</p></li>
|
||
<li><p>What does <code>flights |> group_by(dest() |> filter(row_number() < 4)</code> do? What does <code>flights |> group_by(dest() |> filter(row_number(dep_delay) < 4)</code> do?</p></li>
|
||
<li><p>For each destination, compute the total minutes of delay. For each flight, compute the proportion of the total delay for its destination.</p></li>
|
||
<li>
|
||
<p>Delays are typically temporally correlated: even once the problem that caused the initial delay has been resolved, later flights are delayed to allow earlier flights to leave. Using <code><a href="https://dplyr.tidyverse.org/reference/lead-lag.html">lag()</a></code>, explore how the average flight delay for an hour is related to the average delay for the previous hour.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
mutate(hour = dep_time %/% 100) |>
|
||
group_by(year, month, day, hour) |>
|
||
summarise(
|
||
dep_delay = mean(dep_delay, na.rm = TRUE),
|
||
n = n(),
|
||
.groups = "drop"
|
||
) |>
|
||
filter(n > 5)</pre>
|
||
</div>
|
||
</li>
|
||
<li><p>Look at each destination. Can you find flights that are suspiciously fast? (i.e. flights that represent a potential data entry error). Compute the air time of a flight relative to the shortest flight to that destination. Which flights were most delayed in the air?</p></li>
|
||
<li><p>Find all destinations that are flown by at least two carriers. Use those destinations to come up with a relative ranking of the carriers based on their performance for the same destination.</p></li>
|
||
</ol></section>
|
||
</section>
|
||
|
||
<section id="numeric-summaries" data-type="sect1">
|
||
<h1>
|
||
Numeric summaries</h1>
|
||
<p>Just using the counts, means, and sums that we’ve introduced already can get you a long way, but R provides many other useful summary functions. Here are a selection that you might find useful.</p>
|
||
|
||
<section id="center" data-type="sect2">
|
||
<h2>
|
||
Center</h2>
|
||
<p>So far, we’ve mostly used <code><a href="https://rdrr.io/r/base/mean.html">mean()</a></code> to summarize the center of a vector of values. Because the mean is the sum divided by the count, it is sensitive to even just a few unusually high or low values. An alternative is to use the <code><a href="https://rdrr.io/r/stats/median.html">median()</a></code>, which finds a value that lies in the “middle” of the vector, i.e. 50% of the values is above it and 50% are below it. Depending on the shape of the distribution of the variable you’re interested in, mean or median might be a better measure of center. For example, for symmetric distributions we generally report the mean while for skewed distributions we usually report the median.</p>
|
||
<p><a href="#fig-mean-vs-median" data-type="xref">#fig-mean-vs-median</a> compares the mean vs the median when looking at the hourly vs median departure delay. The median delay is always smaller than the mean delay because because flights sometimes leave multiple hours late, but never leave multiple hours early.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
mean = mean(dep_delay, na.rm = TRUE),
|
||
median = median(dep_delay, na.rm = TRUE),
|
||
n = n(),
|
||
.groups = "drop"
|
||
) |>
|
||
ggplot(aes(mean, median)) +
|
||
geom_abline(slope = 1, intercept = 0, color = "white", size = 2) +
|
||
geom_point()
|
||
#> Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
|
||
#> ℹ Please use `linewidth` instead.</pre>
|
||
<div class="cell-output-display">
|
||
|
||
<figure id="fig-mean-vs-median"><p><img src="numbers_files/figure-html/fig-mean-vs-median-1.png" alt="All points fall below a 45° line, meaning that the median delay is always less than the mean delay. Most points are clustered in a dense region of mean [0, 20] and median [0, 5]. As the mean delay increases, the spread of the median also increases. There are two outlying points with mean ~60, median ~50, and mean ~85, median ~55." width="576"/></p>
|
||
<figcaption>A scatterplot showing the differences of summarising hourly depature delay with median instead of mean.</figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
<p>You might also wonder about the <strong>mode</strong>, or the most common value. This is a summary that only works well for very simple cases (which is why you might have learned about it in high school), but it doesn’t work well for many real datasets. If the data is discrete, there may be multiple most common values, and if the data is continuous, there might be no most common value because every value is ever so slightly different. For these reasons, the mode tends not to be used by statisticians and there’s no mode function included in base R<span data-type="footnote">The <code><a href="https://rdrr.io/r/base/mode.html">mode()</a></code> function does something quite different!</span>.</p>
|
||
</section>
|
||
|
||
<section id="sec-min-max-summary" data-type="sect2">
|
||
<h2>
|
||
Minimum, maximum, and quantiles</h2>
|
||
<p>What if you’re interested in locations other than the center? <code><a href="https://rdrr.io/r/base/Extremes.html">min()</a></code> and <code><a href="https://rdrr.io/r/base/Extremes.html">max()</a></code> will give you the largest and smallest values. Another powerful tool is <code><a href="https://rdrr.io/r/stats/quantile.html">quantile()</a></code> which is a generalization of the median: <code>quantile(x, 0.25)</code> will find the value of <code>x</code> that is greater than 25% of the values, <code>quantile(x, 0.5)</code> is equivalent to the median, and <code>quantile(x, 0.95)</code> will find a value that’s greater than 95% of the values.</p>
|
||
<p>For the <code>flights</code> data, you might want to look at the 95% quantile of delays rather than the maximum, because it will ignore the 5% of most delayed flights which can be quite extreme.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
max = max(dep_delay, na.rm = TRUE),
|
||
q95 = quantile(dep_delay, 0.95, na.rm = TRUE),
|
||
.groups = "drop"
|
||
)
|
||
#> # A tibble: 365 × 5
|
||
#> year month day max q95
|
||
#> <int> <int> <int> <dbl> <dbl>
|
||
#> 1 2013 1 1 853 70.1
|
||
#> 2 2013 1 2 379 85
|
||
#> 3 2013 1 3 291 68
|
||
#> 4 2013 1 4 288 60
|
||
#> 5 2013 1 5 327 41
|
||
#> 6 2013 1 6 202 51
|
||
#> # … with 359 more rows</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="spread" data-type="sect2">
|
||
<h2>
|
||
Spread</h2>
|
||
<p>Sometimes you’re not so interested in where the bulk of the data lies, but in how it is spread out. Two commonly used summaries are the standard deviation, <code>sd(x)</code>, and the inter-quartile range, <code><a href="https://rdrr.io/r/stats/IQR.html">IQR()</a></code>. We won’t explain <code><a href="https://rdrr.io/r/stats/sd.html">sd()</a></code> here since you’re probably already familiar with it, but <code><a href="https://rdrr.io/r/stats/IQR.html">IQR()</a></code> might be new — it’s <code>quantile(x, 0.75) - quantile(x, 0.25)</code> and gives you the range that contains the middle 50% of the data.</p>
|
||
<p>We can use this to reveal a small oddity in the <code>flights</code> data. You might expect the spread of the distance between origin and destination to be zero, since airports are always in the same place. But the code below makes it looks like one airport, <a href="https://en.wikipedia.org/wiki/Eagle_County_Regional_Airport">EGE</a>, might have moved.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
group_by(origin, dest) |>
|
||
summarise(
|
||
distance_sd = IQR(distance),
|
||
n = n(),
|
||
.groups = "drop"
|
||
) |>
|
||
filter(distance_sd > 0)
|
||
#> # A tibble: 2 × 4
|
||
#> origin dest distance_sd n
|
||
#> <chr> <chr> <dbl> <int>
|
||
#> 1 EWR EGE 1 110
|
||
#> 2 JFK EGE 1 103</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="distributions" data-type="sect2">
|
||
<h2>
|
||
Distributions</h2>
|
||
<p>It’s worth remembering that all of the summary statistics described above are a way of reducing the distribution down to a single number. This means that they’re fundamentally reductive, and if you pick the wrong summary, you can easily miss important differences between groups. That’s why it’s always a good idea to visualize the distribution before committing to your summary statistics.</p>
|
||
<p><a href="#fig-flights-dist" data-type="xref">#fig-flights-dist</a> shows the overall distribution of departure delays. The distribution is so skewed that we have to zoom in to see the bulk of the data. This suggests that the mean is unlikely to be a good summary and we might prefer the median instead.</p>
|
||
<div>
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
ggplot(aes(dep_delay)) +
|
||
geom_histogram(binwidth = 15)
|
||
#> Warning: Removed 8255 rows containing non-finite values (`stat_bin()`).
|
||
|
||
flights |>
|
||
filter(dep_delay < 120) |>
|
||
ggplot(aes(dep_delay)) +
|
||
geom_histogram(binwidth = 5)</pre>
|
||
<div id="fig-flights-dist" class="cell quarto-layout-panel">
|
||
<figure class="figure"><div class="quarto-layout-row quarto-layout-valign-top">
|
||
<div class="cell-output-display quarto-layout-cell quarto-layout-cell-subref" style="flex-basis: 50.0%;justify-content: center;">
|
||
|
||
<figure id="fig-flights-dist-1"><p><img src="numbers_files/figure-html/fig-flights-dist-1.png" alt="Two histograms of `dep_delay`. On the left, it's very hard to see any pattern except that there's a very large spike around zero, the bars rapidly decay in height, and for most of the plot, you can't see any bars because they are too short to see. On the right, where we've discarded delays of greater than two hours, we can see that the spike occurs slightly below zero (i.e. most flights leave a couple of minutes early), but there's still a very steep decay after that. " data-ref-parent="fig-flights-dist" width="384"/></p>
|
||
<figcaption>(a) Histogram shows the full range of delays.</figcaption>
|
||
</figure>
|
||
</div>
|
||
<div class="cell-output-display quarto-layout-cell quarto-layout-cell-subref" style="flex-basis: 50.0%;justify-content: center;">
|
||
|
||
<figure id="fig-flights-dist-2"><p><img src="numbers_files/figure-html/fig-flights-dist-2.png" alt="Two histograms of `dep_delay`. On the left, it's very hard to see any pattern except that there's a very large spike around zero, the bars rapidly decay in height, and for most of the plot, you can't see any bars because they are too short to see. On the right, where we've discarded delays of greater than two hours, we can see that the spike occurs slightly below zero (i.e. most flights leave a couple of minutes early), but there's still a very steep decay after that. " data-ref-parent="fig-flights-dist" width="384"/></p>
|
||
<figcaption>(b) Histogram is zoomed in to show delays less than 2 hours.</figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
<p/><figcaption class="figure-caption">Figure 13.3: The distribution of <code>dep_delay</code> appears highly skewed to the right in both histograms.</figcaption><p/>
|
||
</figure></div>
|
||
</div>
|
||
<p>It’s also a good idea to check that distributions for subgroups resemble the whole. <a href="#fig-flights-dist-daily" data-type="xref">#fig-flights-dist-daily</a> overlays a frequency polygon for each day. The distributions seem to follow a common pattern, suggesting it’s fine to use the same summary for each day.</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
filter(dep_delay < 120) |>
|
||
ggplot(aes(dep_delay, group = interaction(day, month))) +
|
||
geom_freqpoly(binwidth = 5, alpha = 1/5)</pre>
|
||
<div class="cell-output-display">
|
||
|
||
<figure id="fig-flights-dist-daily"><p><img src="numbers_files/figure-html/fig-flights-dist-daily-1.png" alt="The distribution of `dep_delay` is highly right skewed with a strong peak slightly less than 0. The 365 frequency polygons are mostly overlapping forming a thick black bland." width="576"/></p>
|
||
<figcaption>365 frequency polygons of <code>dep_delay</code>, one for each day. The frequency polygons appear to have the same shape, suggesting that it’s reasonable to compare days by looking at just a few summary statistics.</figcaption>
|
||
</figure>
|
||
</div>
|
||
</div>
|
||
<p>Don’t be afraid to explore your own custom summaries specifically tailored for the data that you’re working with. In this case, that might mean separately summarizing the flights that left early vs the flights that left late, or given that the values are so heavily skewed, you might try a log-transformation. Finally, don’t forget what you learned in <a href="#sec-sample-size" data-type="xref">#sec-sample-size</a>: whenever creating numerical summaries, it’s a good idea to include the number of observations in each group.</p>
|
||
</section>
|
||
|
||
<section id="positions" data-type="sect2">
|
||
<h2>
|
||
Positions</h2>
|
||
<p>There’s one final type of summary that’s useful for numeric vectors, but also works with every other type of value: extracting a value at specific position. You can do this with the base R <code>[</code> function, but we’re not going to cover it in detail until <a href="#sec-subset-many" data-type="xref">#sec-subset-many</a>, because it’s a very powerful and general function. For now we’ll introduce three specialized functions that you can use to extract values at a specified position: <code>first(x)</code>, <code>last(x)</code>, and <code>nth(x, n)</code>.</p>
|
||
<p>For example, we can find the first and last departure for each day:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
group_by(year, month, day) |>
|
||
summarise(
|
||
first_dep = first(dep_time),
|
||
fifth_dep = nth(dep_time, 5),
|
||
last_dep = last(dep_time)
|
||
)
|
||
#> `summarise()` has grouped output by 'year', 'month'. You can override using
|
||
#> the `.groups` argument.
|
||
#> # A tibble: 365 × 6
|
||
#> # Groups: year, month [12]
|
||
#> year month day first_dep fifth_dep last_dep
|
||
#> <int> <int> <int> <int> <int> <int>
|
||
#> 1 2013 1 1 517 554 NA
|
||
#> 2 2013 1 2 42 535 NA
|
||
#> 3 2013 1 3 32 520 NA
|
||
#> 4 2013 1 4 25 531 NA
|
||
#> 5 2013 1 5 14 534 NA
|
||
#> 6 2013 1 6 16 555 NA
|
||
#> # … with 359 more rows</pre>
|
||
</div>
|
||
<p>(These functions currently lack an <code>na.rm</code> argument but will hopefully be fixed by the time you read this book: <a href="https://github.com/tidyverse/dplyr/issues/6242" class="uri">https://github.com/tidyverse/dplyr/issues/6242</a>).</p>
|
||
<p>If you’re familiar with <code>[</code>, you might wonder if you ever need these functions. There are two main reasons: the <code>default</code> argument and the <code>order_by</code> argument. <code>default</code> allows you to set a default value that’s used if the requested position doesn’t exist, e.g. you’re trying to get the 3rd element from a two element group. <code>order_by</code> lets you locally override the existing ordering of the rows, so you can get the element at the position in the ordering by <code><a href="https://dplyr.tidyverse.org/reference/order_by.html">order_by()</a></code>.</p>
|
||
<p>Extracting values at positions is complementary to filtering on ranks. Filtering gives you all variables, with each observation in a separate row:</p>
|
||
<div class="cell">
|
||
<pre data-type="programlisting" data-code-language="downlit">flights |>
|
||
group_by(year, month, day) |>
|
||
mutate(r = min_rank(desc(sched_dep_time))) |>
|
||
filter(r %in% c(1, max(r)))
|
||
#> # A tibble: 1,195 × 20
|
||
#> # Groups: year, month, day [365]
|
||
#> 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 1 517 515 2 830 819 11 UA
|
||
#> 2 2013 1 1 2353 2359 -6 425 445 -20 B6
|
||
#> 3 2013 1 1 2353 2359 -6 418 442 -24 B6
|
||
#> 4 2013 1 1 2356 2359 -3 425 437 -12 B6
|
||
#> 5 2013 1 2 42 2359 43 518 442 36 B6
|
||
#> 6 2013 1 2 458 500 -2 703 650 13 US
|
||
#> # … with 1,189 more rows, 10 more variables: flight <int>, tailnum <chr>,
|
||
#> # origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>, hour <dbl>,
|
||
#> # minute <dbl>, time_hour <dttm>, r <int>, and abbreviated variable names
|
||
#> # ¹sched_dep_time, ²dep_delay, ³arr_time, ⁴sched_arr_time, ⁵arr_delay</pre>
|
||
</div>
|
||
</section>
|
||
|
||
<section id="with-mutate" data-type="sect2">
|
||
<h2>
|
||
With<code>mutate()</code>
|
||
</h2>
|
||
<p>As the names suggest, the summary functions are typically paired with <code><a href="https://dplyr.tidyverse.org/reference/summarise.html">summarise()</a></code>. However, because of the recycling rules we discussed in <a href="#sec-recycling" data-type="xref">#sec-recycling</a> they can also be usefully paired with <code><a href="https://dplyr.tidyverse.org/reference/mutate.html">mutate()</a></code>, particularly when you want do some sort of group standardization. For example:</p>
|
||
<ul><li>
|
||
<code>x / sum(x)</code> calculates the proportion of a total.</li>
|
||
<li>
|
||
<code>(x - mean(x)) / sd(x)</code> computes a Z-score (standardized to mean 0 and sd 1).</li>
|
||
<li>
|
||
<code>x / first(x)</code> computes an index based on the first observation.</li>
|
||
</ul></section>
|
||
|
||
<section id="exercises-3" data-type="sect2">
|
||
<h2>
|
||
Exercises</h2>
|
||
<ol type="1"><li>
|
||
<p>Brainstorm at least 5 different ways to assess the typical delay characteristics of a group of flights. Consider the following scenarios:</p>
|
||
<ul><li>A flight is 15 minutes early 50% of the time, and 15 minutes late 50% of the time.</li>
|
||
<li>A flight is always 10 minutes late.</li>
|
||
<li>A flight is 30 minutes early 50% of the time, and 30 minutes late 50% of the time.</li>
|
||
<li>99% of the time a flight is on time. 1% of the time it’s 2 hours late.</li>
|
||
</ul><p>Which do you think is more important: arrival delay or departure delay?</p>
|
||
</li>
|
||
<li><p>Which destinations show the greatest variation in air speed?</p></li>
|
||
<li><p>Create a plot to further explore the adventures of EGE. Can you find any evidence that the airport moved locations?</p></li>
|
||
</ol></section>
|
||
</section>
|
||
|
||
<section id="summary" data-type="sect1">
|
||
<h1>
|
||
Summary</h1>
|
||
<p>You’re already familiar with many tools for working with numbers, and after reading this chapter you now know how to use them in R. You’ve also learned a handful of useful general transformations that are commonly, but not exclusively, applied to numeric vectors like ranks and offsets. Finally, you worked through a number of numeric summaries, and discussed a few of the statistical challenges that you should consider.</p>
|
||
<p>Over the next two chapters, we’ll dive into working with strings with the stringr package. Strings are a big topic so they get two chapters, one on the fundamentals of strings and one on regular expressions.</p>
|
||
|
||
|
||
</section>
|
||
</section>
|