Question

How does the formula in the first parameter of boxplot in the following code make the correct correspondence between b and a after a has been reordered.

a <- as.factor(c("TX", "NY", "WA"))
levels(a)
b <- c(5, 3, 2)
boxplot(b ~ a)
# Order the levels of a according to their value in b
a_reordered <- reorder(a, b)
levels(a_reordered)
boxplot(b ~ a_reordered)

Why doesn’t b need to be reordered as well?

edit: I replaced my example with the concrete example of @Marius

Answer 1

In your boxplot(quantity ~ bymedian) call, the order of states on the x-axis is determined by the order of levels for the bymedian factor. Compare levels(x$State) to levels(bymedian), and you’ll see why the two variables behave differently when used in a plot. Note that the data itself in bymedian hasn’t changed order.

A quick example:

a <- as.factor(c("TX", "NY", "WA"))
levels(a)
b <- c(5, 3, 2)
boxplot(b ~ a)
# Order the levels of a according to their value in b
a_reordered <- reorder(a, b)
levels(a_reordered)
boxplot(b ~ a_reordered)

And just to make it clear what it means to say that the actual data hasn’t changed:

> a
[1] TX NY WA
Levels: NY TX WA
> a_reordered
[1] TX NY WA
# Don't be confused by this extra attr(, "scores") bit: the line
# above is the actual data stored in the vector
#attr(,"scores")
#NY TX WA 
# 3  5  2 
Levels: WA NY TX
> b
[1] 5 3 2