Summaries: stat_summary

Mix.install([
  {:giggly, path: Path.join(__DIR__, "..")},
  {:kino, "~> 0.19"}
  ])

alias Giggly.Plot

diamonds = Giggly.Datasets.diamonds()

render = fn plot ->
  plot
  |> Giggly.to_svg()
  |> IO.iodata_to_binary()
  |> Kino.Image.new(:svg)
end

About this notebook

This notebook follows the examples on ggplot2's reference page for stat_summary(), which covers stat_summary_bin() too, in the order the page gives them. Each example shows ggplot2's code first and then Giggly's. An example Giggly cannot draw yet keeps its ggplot2 code and names what it is waiting for, so the page is also a list of what remains.

stat_summary() summarises the y values at each unique x, or the x values at each y, and stat_summary_bin() those in each bin of x: where stat_bin() only counts, they compute any summary. The summary is one function that returns a middle and the ends of a range (fun.data), or a function for each (fun, fun.min and fun.max); given neither, it is the mean and its standard error, mean_se(). Each summary is drawn as a point with a line through its range, geom_pointrange(), unless another geom is given. Giggly has none of it yet; the nearest it has is Giggly.Plot.geom_boxplot/3, which summarises the y values at each x in five numbers. A plot is described with Giggly.Plot and drawn with Giggly.to_svg/2, which returns an SVG document. The setup cell aliases Giggly.Plot, so the cells write Plot.new/2, and defines render, which draws a plot and shows it below the cell with Kino.Image. It binds ggplot2's diamonds, Giggly.Datasets.diamonds/0, to diamonds, ggplot2's name for it.

Means with bootstrapped intervals

d <- ggplot(mtcars, aes(cyl, mpg)) + geom_point()
d + stat_summary(fun.data = "mean_cl_boot", colour = "red", linewidth = 2, size = 3)

mean_cl_boot(), from the Hmisc package, gives the mean with a confidence interval found by resampling the data.

Not in Giggly yet: stat_summary() and the point ranges it draws, geom_pointrange(), and the Hmisc package's summaries, here mean_cl_boot().

Horizontal summaries

# Orientation follows the discrete axis
ggplot(mtcars, aes(mpg, factor(cyl))) +
  geom_point() +
  stat_summary(fun.data = "mean_cl_boot", colour = "red", linewidth = 2, size = 3)

Not in Giggly yet: stat_summary(), geom_pointrange() and mean_cl_boot().

One summary function

# You can supply individual functions to summarise the value at
# each x:
d + stat_summary(fun = "median", colour = "red", size = 2, geom = "point")
d + stat_summary(fun = "mean", colour = "red", size = 2, geom = "point")
d + aes(colour = factor(vs)) + stat_summary(fun = mean, geom="line")

The last plot adds a mapping to d with + aes(), and joins the means of each group with a line.

Not in Giggly yet: stat_summary() and its fun option, and adding a mapping with + aes().

A range from three functions

d + stat_summary(fun = mean, fun.min = min, fun.max = max, colour = "red")

Each point is the mean mpg of its cyl, and its line runs from the smallest mpg to the largest.

Not in Giggly yet: stat_summary() and its fun, fun.min and fun.max options, and geom_pointrange().

Summaries as bars

d <- ggplot(diamonds, aes(cut))
d + geom_bar()
d + stat_summary(aes(y = price), fun = "mean", geom = "bar")

The first plot counts the diamonds of each cut; the second draws the mean price of each cut as a bar. Giggly draws the first, the cuts from Fair to Ideal, the order of their levels.

diamonds
|> Plot.new(%{x: :cut})
|> Plot.geom_bar()
|> render.()

Not in Giggly yet: stat_summary() drawn as bars.

Summaries in bins

# Orientation of stat_summary_bin is ambiguous and must be specified directly
ggplot(diamonds, aes(carat, price)) +
  stat_summary_bin(fun = "mean", geom = "bar", orientation = 'y')

Not in Giggly yet: stat_summary_bin() and its orientation option.

Zooming in without losing data

# Don't use ylim to zoom into a summary plot - this throws the
# data away
p <- ggplot(mtcars, aes(cyl, mpg)) +
  stat_summary(fun = "mean", geom = "point")
p
p + ylim(15, 30)
# Instead use coord_cartesian
p + coord_cartesian(ylim = c(15, 30))

ylim() sets the limits of the y scale, which drops the rows outside them before the means are taken, and so changes the means; coord_cartesian() zooms in after the stat, leaving them as they were.

Not in Giggly yet: stat_summary() and its fun option, and coord_cartesian() and its ylim option.

Summary functions from Hmisc

# A set of useful summary functions is provided from the Hmisc package:
stat_sum_df <- function(fun, geom="crossbar", ...) {
  stat_summary(fun.data = fun, colour = "red", geom = geom, width = 0.2, ...)
}
d <- ggplot(mtcars, aes(cyl, mpg)) + geom_point()
# The crossbar geom needs grouping to be specified when used with
# a continuous x axis.
d + stat_sum_df("mean_cl_boot", mapping = aes(group = cyl))
d + stat_sum_df("mean_sdl", mapping = aes(group = cyl))
d + stat_sum_df("mean_sdl", fun.args = list(mult = 1), mapping = aes(group = cyl))
d + stat_sum_df("median_hilow", mapping = aes(group = cyl))

stat_sum_df() is a helper the example writes: a stat_summary() drawn as red crossbars. mean_sdl() is the mean give or take a multiple of the standard deviation, which mult = 1 sets to one, and median_hilow() the median with a range holding the middle of the data.

Not in Giggly yet: stat_summary() and its fun.args option, crossbars, geom_crossbar() and its width option, and the Hmisc package's summaries: mean_cl_boot(), mean_sdl() and median_hilow().

Skewed distributions

ggplot2's example takes a random sample of the movies dataset, from the ggplot2movies package, with R's set.seed(596), and runs only where that package is installed.

# An example with highly skewed distributions:
if (require("ggplot2movies")) {
set.seed(596)
mov <- movies[sample(nrow(movies), 1000), ]
 m2 <-
   ggplot(mov, aes(x = factor(round(rating)), y = votes)) +
   geom_point()
 m2 <-
   m2 +
   stat_summary(
     fun.data = "mean_cl_boot",
     geom = "crossbar",
     colour = "red", width = 0.3
   ) +
   xlab("rating")
m2
# Notice how the overplotting skews off visual perception of the mean
# supplementing the raw data with summary statistics is _very_ important

Not in Giggly yet: the movies dataset, stat_summary(), geom_crossbar() and its width option, mean_cl_boot(), and xlab().

A log scale before or after the stat

# Next, we'll look at votes on a log scale.

# Transforming the scale means the data are transformed
# first, after which statistics are computed:
m2 + scale_y_log10()
# Transforming the coordinate system occurs after the
# statistic has been computed. This means we're calculating the summary on the raw data
# and stretching the geoms onto the log scale.  Compare the widths of the
# standard errors.
m2 + coord_transform(y="log10")
}

Not in Giggly yet: coord_transform() and everything the plot above waits for.