47 Above and below a reference

How far is each value from a reference, and is it above or below? Comparing categories ranks twelve countries by how long their people lived. This chapter measures each one against a reference instead: the world median. The chapter starts from the Cleveland dot plot and changes a few atoms at a time. Each change adds a reference line or draws a chart that has a name of its own: the diverging lollipop chart, the diverging bar chart and the back-to-back bar chart. Every section but one uses the same twelve countries of East, Southeast and South Asia, from the gapminder data. The back-to-back bar chart uses the Titanic.

47.1 Which countries live longer than the world median?

In 2007, half of the 142 countries in the gapminder data had a life expectancy above 71.94 years, and half had one below it. That number is the world median. 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

A reference is a single number, so give it a table with a single row. A rule draws one line for each row of its own table, on the axis whose column that table holds (A line at a threshold). Here the table holds life, the plot’s x, so the line runs up the panel:

reference <- data.frame(life = 71.94)

data(gm_twelve_2007) + y(country) + x(life) + order(life, desc = TRUE) +
  point + data(reference) + rule + style(pattern = "dashed") +
  title("The world median as a line")

reference = {"life": [71.94]}
(data(gm_twelve_2007) + y(col.country) + x(col.life) + order(col.life, desc = True) +
  point + data(reference) + rule + style(pattern = "dashed") +
  title("The world median as a line"))

reference = (life = [71.94],)
data(gm_twelve_2007) + y(:country) + x(:life) +
  order(:life, desc = true) + point + data(reference) + rule +
  style(pattern = "dashed") + title("The world median as a line")

const reference = { life: [71.94] };
plot(data(gm_twelve_2007), y(col.country), x(col.life),
  order(col.life, { desc: true }), point, data(reference), rule,
  style({ pattern: "dashed" }), title("The world median as a line"))

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

This is the Cleveland dot plot with one layer added, a reference line. The eight countries from Japan to China are to the right of the line, so their people lived longer than the median. The Philippines, Indonesia, Thailand and India are to its left. The line is dashed so that it does not read as a country’s value.

47.2 How far is each country from the median?

The reference line shows the side of each country, but the reader has to judge each distance from the line. The lollipop chart draws a stem from zero to each value. Start each stem at the median instead, and its length is the distance from the reference. That is the diverging lollipop chart. interval * bounds(world, life) draws each stem between two columns, so the table needs a column world that holds the median in every row. Add it, and a column side that says on which side of the median each country falls:

gm_twelve_2007$world <- 71.94
gm_twelve_2007$side <- ifelse(gm_twelve_2007$life >= 71.94, "Above", "Below")

data(gm_twelve_2007) + y(country) + x(life) + order(life, desc = TRUE) +
  interval * bounds(world, life) + style(caps = FALSE) +
  point + color(side) +
  title("A stem from the median to each value")

gm_twelve_2007["world"] = [71.94] * len(gm_twelve_2007["life"])
gm_twelve_2007["side"] = ["Above" if v >= 71.94 else "Below"
                          for v in gm_twelve_2007["life"]]

(data(gm_twelve_2007) + y(col.country) + x(col.life) + order(col.life, desc = True) +
  interval * bounds(col.world, col.life) + style(caps = False) +
  point + color(col.side) +
  title("A stem from the median to each value"))

gm_twelve_2007["world"] = fill(71.94, length(gm_twelve_2007["life"]))
gm_twelve_2007["side"] = [v >= 71.94 ? "Above" : "Below" for v in gm_twelve_2007["life"]]

data(gm_twelve_2007) + y(:country) + x(:life) + order(:life, desc = true) +
  interval * bounds(:world, :life) + style(caps = false) +
  point + color(:side) + title("A stem from the median to each value")

gm_twelve_2007.world = gm_twelve_2007.life.map(() => 71.94);
gm_twelve_2007.side = gm_twelve_2007.life.map((v) => (v >= 71.94 ? "Above" : "Below"));

plot(data(gm_twelve_2007), y(col.country), x(col.life),
  order(col.life, { desc: true }),
  layer(interval, bounds(col.world, col.life)), style({ caps: false }),
  point, color(col.side), title("A stem from the median to each value"));

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

Every stem starts at 71.94, and each dot is at the country’s own value. Japan’s stem is the longest above the median, and India’s is the longest below it. The Philippines is only 0.25 years below the median, so its stem is very short. color(side) comes after point, so it colors only the points, and the stems stay gray (Encoding scope). As in the lollipop chart, style(caps = FALSE) leaves out the short crossbar that an interval draws at each end.

47.3 What if only the distance matters?

The axis of the diverging lollipop chart still shows life expectancy, from about 65 to 83 years. When the distance itself is the answer, subtract the median from every value. The median then becomes zero. A bar runs from zero to its value, on whichever side of zero the value is. So a country above the median gets a bar to the right of zero, and a country below it gets a bar to the left. That is the diverging bar chart. Add the difference as a column, gap:

gm_twelve_2007$gap <- gm_twelve_2007$life - 71.94

data(gm_twelve_2007) + bar + y(country) + x(gap) + order(gap, desc = TRUE) +
  color(side) + title("Years above or below the world median")

gm_twelve_2007["gap"] = [v - 71.94 for v in gm_twelve_2007["life"]]

(data(gm_twelve_2007) + bar + y(col.country) + x(col.gap) + order(col.gap, desc = True) +
  color(col.side) + title("Years above or below the world median"))

gm_twelve_2007["gap"] = gm_twelve_2007["life"] .- 71.94

data(gm_twelve_2007) + bar + y(:country) + x(:gap) + order(:gap, desc = true) +
  color(:side) + title("Years above or below the world median")

gm_twelve_2007.gap = gm_twelve_2007.life.map((v) => v - 71.94);

plot(data(gm_twelve_2007), bar, y(col.country), x(col.gap),
  order(col.gap, { desc: true }), color(col.side),
  title("Years above or below the world median"));

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

The axis now measures years from the median. Japan is 10.66 years above it and India 7.24 years below. The bars of Vietnam and Malaysia are nearly the same length, 2.31 and 2.30 years, and so are the bars of Indonesia and Thailand, 1.29 and 1.32. Bars on both sides of zero need no new atom, only negative values.

47.4 How did the distance change over the years?

The world median rose in every five-year step, from 45.14 years in 1952 to 71.94 in 2007. So each year needs a reference of its own. gm_twelve_gap holds the twelve countries in every year, with that year’s median in world, the difference in gap, and side. Each year’s median comes from all 142 countries, not from these twelve, so the table’s file already holds world and gap:

`gm_twelve_gap`: first 5 of 144 rows
country	year	life	world	gap	side
Japan	1952	63.03	45.14	17.89	Above
Japan	1957	65.50	48.36	17.14	Above
Japan	1962	68.73	50.88	17.85	Above
Japan	1967	71.43	53.83	17.60	Above
Japan	1972	73.42	56.53	16.89	Above

The diverging bar chart for one year becomes one panel for each country, with the years on x and the gap on y. | facet(country, wrap = 4) draws the panels in rows of four (Faceting):

data(gm_twelve_gap) + bar + x(year) + y(gap) + color(side) +
  title("Each year's gap from the world median") | facet(country, wrap = 4)

(data(gm_twelve_gap) + bar + x(col.year) + y(col.gap) + color(col.side) +
  title("Each year's gap from the world median") | facet(col.country, wrap = 4))

data(gm_twelve_gap) + bar + x(:year) + y(:gap) + color(:side) +
  title("Each year's gap from the world median") |
  facet(:country, wrap = 4)

plot(data(gm_twelve_gap), bar, x(col.year), y(col.gap), color(col.side),
  title("Each year's gap from the world median"),
  across(col.country, { wrap: 4 }))

“Given the gapminder twelve’s gaps: bars, x is year, y is gap, color by side, split into panel columns by country, wrapped at 4.”

The panels follow the order of 2007, because the table lists the countries in that order. Japan, Hong Kong and Singapore stayed far above the median, but their gaps became smaller, because the median rose faster than their life expectancy. Japan’s fell from 17.89 years in 1952 to 10.66 in 2007. Three countries moved to the other side of the median and stayed there. Vietnam was below the median until 1992 and above it from 1997. The Philippines moved below it in 1982, and Thailand in 1992. China was below the median in 1952 and 1962 and above it in every other year. India and Indonesia were below it in every year.

47.5 What if zero separates two groups?

So far the reference has been a median, computed from the data. It does not have to be. In a back-to-back bar chart, zero separates two groups: the bars of one group run to the right, and the bars of the other run to the left. titanic holds the passengers and crew of the Titanic, the ship that sank in 1912, as 32 groups, one for each combination of class, sex, age and survived. n is the number of people in each group:

`titanic`: first 5 of 32 rows
class	sex	age	survived	n
1st	Male	Adult	Yes	57
1st	Male	Adult	No	118
1st	Male	Child	Yes	5
1st	Male	Child	No	0
1st	Female	Adult	Yes	140

Make the counts of the people who died negative, and their bars run left of zero, while the bars of the survivors run right. Add the counts, with the deaths now negative, as a column, people:

titanic$people <- ifelse(titanic$survived == "No", -titanic$n, titanic$n)

data(titanic) + bar * sum + y(class) + x(people) + color(survived) +
  title("Who survived, and who died, in each class")

titanic["people"] = [-n if s == "No" else n
                     for n, s in zip(titanic["n"], titanic["survived"])]

(data(titanic) + bar * sum + y(col["class"]) + x(col.people) + color(col.survived) +
  title("Who survived, and who died, in each class"))

titanic["people"] = [s == "No" ? -n : n for (n, s) in zip(titanic["n"], titanic["survived"])]

data(titanic) + bar * sum + y(:class) + x(:people) + color(:survived) +
  title("Who survived, and who died, in each class")

titanic.people = titanic.n.map((n, i) => (titanic.survived[i] === "No" ? -n : n));

plot(data(titanic), layer(bar, sum), y(col.class), x(col.people),
  color(col.survived), title("Who survived, and who died, in each class"));

“Given titanic: bars derived by sum, y is class, x is people, color by survived.”

sum adds up the groups that share a class and a value of survived, so each class has one bar on each side. The crew had the most deaths, 673. First class is the only class in which more people survived than died: 203 survived and 122 died. The left half of the axis reads -600, -400 and -200, because those are counts of the dead, drawn as negative numbers. The population pyramid in Many groups is a back-to-back bar chart too, with age bands on y and the populations of two cities. It also says why gog keeps the minus sign on the axis.

47.6 What this section refuses

A diverging ramp colors each value by its distance from a center, so it might seem the natural way to color the diverging bar chart. On a bar, color takes only a categorical column, so the sentence with color(gap) is refused:

data(gm_twelve_2007) + bar + y(country) + x(gap) + color(gap) +
  palette("blue_red")

(data(gm_twelve_2007) + bar + y(col.country) + x(col.gap) + color(col.gap) +
  palette("blue_red"))

data(gm_twelve_2007) + bar + y(:country) + x(:gap) + color(:gap) +
  palette("blue_red")

plot(data(gm_twelve_2007), bar, y(col.country), x(col.gap),
  color(col.gap), palette("blue_red"))

Error:
! gog: `color(gap)` maps a continuous (numeric) column, but `color` on `bar` needs a categorical (text) column. Use `opacity` to show a numeric column.
gog: nothing was rendered. Fix the above, or set GOG_STRICT=0 to draw anyway.

The message says that color on a bar needs a categorical column, and that opacity can show a continuous one. That is why the diverging bar chart is colored by side, a categorical column, and not by gap.