45 Comparing categories

How do many categories compare, and how did their order change over time? Many groups splits one plot by a few groups, with color or with panels. This chapter compares one value for each of many categories. A ranked bar chart answers the first question, and the chapter starts from that chart and changes a few atoms at a time. Each change draws a chart that has a name of its own: the Cleveland dot plot, the lollipop chart, the dumbbell chart, the slope chart and the bump chart. All of them show twelve countries of East, Southeast and South Asia, and how long their people lived, from the gapminder data.

45.1 Which country lives longest?

The question is which of the twelve countries had the longest life expectancy in 2007. The ranked bar chart is the usual answer, and Which group is biggest? shows how order() sorts the bars. gm_twelve_2007 holds the twelve countries’ life expectancy in 2007, one row per country:

`gm_twelve_2007`: first 5 of 12 rows
country	life
Japan	82.603
Hong Kong, China	82.208
Singapore	79.972
Korea, Rep.	78.623
Taiwan	78.400

data(gm_twelve_2007) + bar + y(country) + x(life) + order(life, desc = TRUE) +
  title("Life expectancy in 2007")

(data(gm_twelve_2007) + bar + y(col.country) + x(col.life) + order(col.life, desc = True) +
  title("Life expectancy in 2007"))

data(gm_twelve_2007) + bar + y(:country) + x(:life) +
  order(:life, desc = true) + title("Life expectancy in 2007")

plot(data(gm_twelve_2007), bar, y(col.country), x(col.life),
  order(col.life, { desc: true }), title("Life expectancy in 2007"))

“Given the gapminder twelve in 2007: bars, y is country, x is life, ordered by life, largest first.”

Japan is first, at 82.6 years, and India is last, at 64.7. The country names are long, so they go on y, where each one is written in full on one line. Every bar starts at zero, because a bar shows its value by its length. So all twelve bars end in the right part of the panel, between 64 and 83 years.

45.2 What if the differences are small?

In the bar chart, most of the twelve values are between 70 and 80 years. When every bar is more than 60 years long, a difference of one or two years is hard to see. A Cleveland dot plot puts one point at each value instead. It is named after the statistician William Cleveland, who recommended it (Cleveland, 1984). Write point in place of bar (Point):

data(gm_twelve_2007) + point + y(country) + x(life) + order(life, desc = TRUE) +
  title("The same values as dots")

(data(gm_twelve_2007) + point + y(col.country) + x(col.life) + order(col.life, desc = True) +
  title("The same values as dots"))

data(gm_twelve_2007) + point + y(:country) + x(:life) +
  order(:life, desc = true) + title("The same values as dots")

plot(data(gm_twelve_2007), point, y(col.country), x(col.life),
  order(col.life, { desc: true }), title("The same values as dots"))

“Given the gapminder twelve in 2007: points, y is country, x is life, ordered by life, largest first.”

A point shows its value by its position, not by a length, so the axis does not need to start at zero. It now covers only the values, from about 65 to 83 years, and the twelve points spread across the whole panel. China and Malaysia differ by 1.3 years, and the gap between their points is now easy to see.

45.3 What if the length matters too?

A bar’s length says how large a value is, not only where it ranks. The Cleveland dot plot shows each value by a position only, with no length. A lollipop chart shows both: a thin stem from zero to the value, and a dot at the value. Add one layer to the Cleveland dot plot’s sentence: interval * bounds(zero, life) draws each stem as an interval between two columns (Interval). The table has no column of zeros, so add one before you draw:

gm_twelve_2007$zero <- 0

data(gm_twelve_2007) + y(country) + x(life) + order(life, desc = TRUE) +
  interval * bounds(zero, life) + style(caps = FALSE) + point +
  title("A stem from zero, and a dot")

gm_twelve_2007["zero"] = [0] * len(gm_twelve_2007["life"])

(data(gm_twelve_2007) + y(col.country) + x(col.life) + order(col.life, desc = True) +
  interval * bounds(col.zero, col.life) + style(caps = False) + point +
  title("A stem from zero, and a dot"))

gm_twelve_2007["zero"] = zeros(length(gm_twelve_2007["life"]))

data(gm_twelve_2007) + y(:country) + x(:life) + order(:life, desc = true) +
  interval * bounds(:zero, :life) + style(caps = false) + point +
  title("A stem from zero, and a dot")

gm_twelve_2007.zero = gm_twelve_2007.life.map(() => 0);

plot(data(gm_twelve_2007), y(col.country), x(col.life),
  order(col.life, { desc: true }),
  layer(interval, bounds(col.zero, col.life)), style({ caps: false }),
  point, title("A stem from zero, and a dot"));

“Given the gapminder twelve in 2007: y is country, x is life, ordered by life, largest first, intervals from zero to life, and also points.”

The stems start at zero, as the bars did, and the dots mark the values. An interval draws a short crossbar, its cap, at each end, and style(caps = FALSE) leaves both out, so each stem is a plain line. The axis starts at zero again, so the 1.3 years between China and Malaysia are as hard to see as in the bar chart. Use the lollipop chart when the size of each value matters more than the small gaps between values.

45.4 How did each country change?

A ranking for one year does not show how each country’s value changed over time. gm_twelve_ends holds the same twelve countries in 1952 and in 2007, two rows each. Its year names the two ends of the period and measures nothing, so the table keeps it as text (Labels that look like numbers):

`gm_twelve_ends`: first 5 of 24 rows
country	year	life
Japan	1952	63.030
Hong Kong, China	1952	60.960
Singapore	1952	60.396
Taiwan	1952	58.500
Thailand	1952	50.848

A dumbbell chart joins each country’s two values with a line. It keeps the lollipop chart’s two layers and changes the stem’s transform. interval * range draws one line for each country, from its smaller value to its larger one. point + color(year) marks the two ends:

data(gm_twelve_ends) + y(country) + x(life) + order(life, desc = TRUE) +
  interval * range + style(caps = FALSE) +
  point + color(year) +
  title("1952 and 2007 on one line")

(data(gm_twelve_ends) + y(col.country) + x(col.life) + order(col.life, desc = True) +
  interval * range + style(caps = False) +
  point + color(col.year) +
  title("1952 and 2007 on one line"))

data(gm_twelve_ends) + y(:country) + x(:life) +
  order(:life, desc = true) + interval * range + style(caps = false) +
  point + color(:year) + title("1952 and 2007 on one line")

plot(data(gm_twelve_ends), y(col.country), x(col.life),
  order(col.life, { desc: true }), layer(interval, range),
  style({ caps: false }), point, color(col.year),
  title("1952 and 2007 on one line"))

“Given the gapminder twelve in 1952 and 2007: y is country, x is life, ordered by life, largest first, intervals derived by range, and also points colored by year.”

Every country lived longer in 2007 than in 1952, so every orange point is to the right of its blue one. The longest lines belong to the countries that gained the most: Vietnam gained 33.8 years, Indonesia 33.2 and Korea 31.2. Japan was already first in 1952 and gained 19.6. order(life, desc = TRUE) sorts the countries by their two values added together, which is why Korea is 5th here but 4th in 2007 alone.

color(year) comes after point, so it colors only the points (Encoding scope). Written before the marks, it would also split each country’s range by year. A range over a single value has no length, so the lines would disappear.

45.5 What if the change matters most?

The dumbbell chart shows each change as a length along one axis. A slope chart puts the two years on an axis of their own. Each change then becomes the slope of a line, and two lines that cross belong to two countries whose order changed. The same three columns move: year from color to x, life from x to y, and country from y to color (Line):

data(gm_twelve_ends) + x(year) + y(life) + color(country) + line + point +
  title("The two years as an axis")

(data(gm_twelve_ends) + x(col.year) + y(col.life) + color(col.country) + line + point +
  title("The two years as an axis"))

data(gm_twelve_ends) + x(:year) + y(:life) + color(:country) + line +
  point + title("The two years as an axis")

plot(data(gm_twelve_ends), x(col.year), y(col.life), color(col.country),
  line, point, title("The two years as an axis"))

“Given the gapminder twelve in 1952 and 2007: x is year, y is life, color by country, lines, and also points.”

year is text, so the axis has two slots, 1952 and 2007. color(country) gives each country its own line, which joins that country’s two values. Korea’s line crosses four others. Korea was 8th in 1952, below Taiwan, Thailand, Malaysia and the Philippines, and 4th in 2007, above all four.

45.6 How did the order change over the years?

A slope chart has two years. A bump chart follows the order through every year: it draws each country’s rank instead of its value. gm_twelve holds the twelve years from 1952 to 2007, five years apart, with each country’s rank in its year, from 1st to 12th:

`gm_twelve`: first 5 of 144 rows
country	year	life	rank
Japan	1952	63.030	1st
Hong Kong, China	1952	60.960	2nd
Singapore	1952	60.396	3rd
Taiwan	1952	58.500	4th
Thailand	1952	50.848	5th

The ranks were computed from life before the table was written. gog draws a rank, but it does not compute one, so you compute it in your host language. Here rank is text with a declared order, so its values are placed on a categorical axis with 1st at the top. The sentence is the slope chart’s, with gm_twelve as the table, rank in place of life and path in place of line. A path joins each country’s points in the order of the rows, and the table lists the years in order (Path):

data(gm_twelve) + x(year) + y(rank) + color(country) + path + point +
  title("Rank in every year")

(data(gm_twelve) + x(col.year) + y(col.rank) + color(col.country) + path + point +
  title("Rank in every year"))

data(gm_twelve) + x(:year) + y(:rank) + color(:country) + path + point +
  title("Rank in every year")

plot(data(gm_twelve), x(col.year), y(col.rank), color(col.country), path,
  point, title("Rank in every year"))

“Given the gapminder twelve: x is year, y is rank, color by country, paths, and also points.”

Japan is 1st and Hong Kong is 2nd in every year. Korea rises from 8th in 1952 to 4th in 2002 and stays there. China jumps from 10th in 1962 to 5th in 1972, and then drops to 8th by 1997. The countries take the same colors as in the slope chart, because both tables list them in the same order.

45.7 What this section refuses

A bump chart looks like a line chart, so line is the mark you might try first. A line needs a continuous y, and a rank stored as text is categorical, so the same sentence with line is refused:

data(gm_twelve) + x(year) + y(rank) + color(country) + line

data(gm_twelve) + x(col.year) + y(col.rank) + color(col.country) + line

data(gm_twelve) + x(:year) + y(:rank) + color(:country) + line

plot(data(gm_twelve), x(col.year), y(col.rank), color(col.country), line)

Error:
! gog: `y(rank)` maps a categorical (text) column, but `y` on `line` needs a continuous (numeric) column. On these marks `x` is the domain and `y` the measure, and a category is not a quantity to measure: a mean of category names is not a number, and a region has no categorical baseline to close on. Put the category on `x` instead — `line * mean + x(<category>) + y(<number>)` is the profile plot, and `area * mean` fills it. Unlike `bar`/`box`/`interval`, these marks do not read their orientation off the bindings, because their two axes do not have the same role.
gog: nothing was rendered. Fix the above, or set GOG_STRICT=0 to draw anyway.

The message says that y on a line needs a continuous (numeric) column. It suggests the profile plot, which puts the category on x, but a bump chart needs the rank on y. A path has no such rule: it joins its points in the order of the rows, whatever kind of column y is.