More polishing
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Hadley Wickham
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logicals.Rmd
161
logicals.Rmd
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@ -198,15 +198,15 @@ Figure \@ref(fig:bool-ops) shows the complete set of Boolean operations and how
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#| echo: false
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#| out.width: NULL
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#| fig.cap: >
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#| Complete set of boolean operations. `x` is the left-hand
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#| The complete set of boolean operations. `x` is the left-hand
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#| circle, `y` is the right-hand circle, and the shaded region show
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#| which parts each operator selects."
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#| which parts each operator selects.
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#| fig.alt: >
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#| Six Venn diagrams, each explaining a given logical operator. The
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#| circles (sets) in each of the Venn diagrams represent x and y. 1. y &
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#| !x is y but none of x, x & y is the intersection of x and y, x & !y is
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#| x but none of y, x is all of x none of y, xor(x, y) is everything
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#| except the intersection of x and y, y is all of y none of x, and
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#| !x is y but none of x; x & y is the intersection of x and y; x & !y is
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#| x but none of y; x is all of x none of y; xor(x, y) is everything
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#| except the intersection of x and y; y is all of y and none of x; and
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#| x | y is everything.
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knitr::include_graphics("diagrams/transform.png", dpi = 270)
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```
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@ -216,50 +216,6 @@ Don't use them in dplyr functions!
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These are called short-circuiting operators and only ever return a single `TRUE` or `FALSE`.
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They're important for programming and you'll learn more about them in Section \@ref(conditional-execution).
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The following code finds all flights that departed in November or December:
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```{r, eval = FALSE}
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flights |>
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filter(month == 11 | month == 12)
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```
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Note that the order of operations doesn't work like English.
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You can't think "find all flights that departed in November or December" and write `flights |> filter(month == 11 | 12)`.
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This code will not error, but it will do something rather confusing.
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First R evaluates `11 | 12` which is equivalent to `TRUE | TRUE`, which returns `TRUE`.
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Then it evaluates `month == TRUE`.
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Since month is numeric, this is equivalent to `month == 1`, so `flights |> filter(month == 11 | 12)` returns all flights in January!
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### `%in%`
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An easy way to avoid this issue is to use `%in%`.
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`x %in% y` returns a logical vector the same length as `x` that is `TRUE` whenever a value in `x` is anywhere in `y` .
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```{r}
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letters[1:10] %in% c("a", "e", "i", "o", "u")
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```
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So we could instead write:
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```{r, eval = FALSE}
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flights |>
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filter(month %in% c(11, 12))
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```
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Note that `%in%` obeys different rules for `NA` to `==`.
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```{r}
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c(1, 2, NA) == NA
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c(1, 2, NA) %in% NA
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```
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This can make for a useful shortcut:
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```{r}
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flights |>
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filter(dep_time %in% c(NA, 0800))
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```
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### Missing values {#na-boolean}
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The rules for missing values in Boolean algebra are a little tricky to explain because they seem inconsistent at first glance:
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@ -279,6 +235,69 @@ A missing value in a logical vector means that the value could either be `TRUE`
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`TRUE | TRUE` and `FALSE | TRUE` are both `TRUE`, so `NA | TRUE` must also be `TRUE`.
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Similar reasoning applies with `NA & FALSE`.
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### Order of operations
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Note that the order of operations doesn't work like English.
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Take the following code finds all flights that departed in November or December:
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```{r, eval = FALSE}
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flights |>
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filter(month == 11 | month == 12)
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```
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You might be tempted to write it like you'd say in English: "find all flights that departed in November or December":
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```{r}
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flights |>
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filter(month == 11 | 12)
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```
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This code doesn't error but it also doesn't seem to have worked.
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What's going on?
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Here R first evaluates `month == 11` creating a logical vector, which I'll call `nov`.
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It computes `nov | 12`.
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When you use a number with a logical operator it converts everything apart from 0 to TRUE, so this is equivalent to `nov | TRUE` which will always be `TRUE`, so every row will be selected:
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```{r}
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flights |>
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mutate(
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nov = month == 11,
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final = nov | 12,
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.keep = "used"
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)
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```
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### `%in%`
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An easy way to avoid the problem of getting your `==`s and `|`s in the right order is to use `%in%`.
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`x %in% y` returns a logical vector the same length as `x` that is `TRUE` whenever a value in `x` is anywhere in `y` .
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```{r}
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1:12 %in% c(1, 5, 11)
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letters[1:10] %in% c("a", "e", "i", "o", "u")
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```
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So to find all flights in November and December we could write:
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```{r, eval = FALSE}
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flights |>
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filter(month %in% c(11, 12))
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```
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Note that `%in%` obeys different rules for `NA` to `==`, as `NA %in% NA` is `TRUE`.
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```{r}
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c(1, 2, NA) == NA
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c(1, 2, NA) %in% NA
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```
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This can make for a useful shortcut:
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```{r}
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flights |>
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filter(dep_time %in% c(NA, 0800))
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```
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### Exercises
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1. Find all flights where `arr_delay` is missing but `dep_delay` is not. Find all flights where neither `arr_time` nor `sched_arr_time` are missing, but `arr_delay` is.
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@ -288,26 +307,23 @@ Similar reasoning applies with `NA & FALSE`.
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## Summaries {#logical-summaries}
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The following sections describe some useful techniques for summarizing logical vectors.
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As you'll learn as well as functions that only work with logical vectors, you can also effectively use functions that work with numeric vectors.
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As well as functions that only work specifically with logical vectors, you can also use functions that work with numeric vectors.
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### Logical summaries
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There are two important logical summaries: `any()` and `all()`.
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There are two main logical summaries: `any()` and `all()`.
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`any(x)` is the equivalent of `|`; it'll return `TRUE` if there are any `TRUE`'s in `x`.
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`all(x)` is equivalent of `&`; it'll return `TRUE` only if all values of `x` are `TRUE`'s.
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Like all summary functions, they'll return `NA` if there are any missing values present, and like usual you can make the missing values go away with `na.rm = TRUE`.
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Like all summary functions, they'll return `NA` if there are any missing values present, and as usual you can make the missing values go away with `na.rm = TRUE`.
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For example, we could use `all()` to find out if there were days where every flight was delayed:
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```{r}
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not_cancelled <- flights |>
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filter(!is.na(dep_delay), !is.na(arr_delay))
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not_cancelled |>
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flights |>
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group_by(year, month, day) |>
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summarise(
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all_delayed = all(arr_delay >= 0),
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any_delayed = any(arr_delay >= 0),
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all_delayed = all(arr_delay >= 0, na.rm = TRUE),
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any_delayed = any(arr_delay >= 0, na.rm = TRUE),
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.groups = "drop"
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)
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```
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@ -318,27 +334,32 @@ That leads us to the numeric summaries.
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### Numeric summaries
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When you use a logical vector in a numeric context, `TRUE` becomes 1 and `FALSE` becomes 0.
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This makes `sum()` and `mean()` are particularly useful with logical vectors because `sum(x)` will give the number of `TRUE`s and `mean(x)` gives the proportion of `TRUE`s.
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That lets us see the distribution of delays across the days of the year:
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This makes `sum()` and `mean()` very useful with logical vectors because `sum(x)` will give the number of `TRUE`s and `mean(x)` the proportion of `TRUE`s.
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That lets us see the distribution of delays across the days of the year as shown in Figure \@ref(fig:prop-delayed-dist).
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```{r}
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not_cancelled |>
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```{r prop-delayed-dist}
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#| fig.cap: >
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#| A histogram showing the proportion of delayed flights each day.
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#| fig.alt: >
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#| The distribution is unimodal and mildly right skewed. The distribution
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#| peaks around 30% delayed flights.
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flights |>
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group_by(year, month, day) |>
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summarise(
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prop_delayed = mean(arr_delay > 0),
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prop_delayed = mean(arr_delay > 0, na.rm = TRUE),
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.groups = "drop"
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) |>
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ggplot(aes(prop_delayed)) +
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geom_histogram(binwidth = 0.05)
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```
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Or we could ask how many flights left before 5am, which usually are flights that were delayed from the previous day:
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Or we could ask how many flights left before 5am, which are often flights that were delayed from the previous day:
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```{r}
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not_cancelled |>
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flights |>
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group_by(year, month, day) |>
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summarise(
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n_early = sum(dep_time < 500),
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n_early = sum(dep_time < 500, na.rm = TRUE),
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.groups = "drop"
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) |>
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arrange(desc(n_early))
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@ -353,7 +374,7 @@ Imagine we wanted to look at the average delay just for flights that were actual
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One way to do so would be to first filter the flights:
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```{r}
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not_cancelled |>
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flights |>
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filter(arr_delay > 0) |>
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group_by(year, month, day) |>
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summarise(
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@ -372,11 +393,11 @@ Instead you could use `[` to perform an inline filtering: `arr_delay[arr_delay >
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This leads to:
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```{r}
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not_cancelled |>
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flights |>
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group_by(year, month, day) |>
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summarise(
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ahead = mean(arr_delay[arr_delay > 0]),
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behind = mean(arr_delay[arr_delay < 0]),
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ahead = mean(arr_delay[arr_delay > 0], na.rm = TRUE),
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behind = mean(arr_delay[arr_delay < 0], na.rm = TRUE),
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n = n(),
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.groups = "drop"
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)
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