Summary statistics by two or more factor variables?

Question

This is best illustrated with an example

str(mtcars)
mtcars$gear <- factor(mtcars$gear, labels=c("three","four","five"))
mtcars$cyl <- factor(mtcars$cyl, labels=c("four","six","eight"))
mtcars$am <- factor(mtcars$am, labels=c("manual","auto")
str(mtcars)
tapply(mtcars$mpg, mtcars$gear, sum)

That gives me the summed mpg per gear. But say I wanted a 3x3 table with gear across the top and cyl down the side, and 9 cells with the bivariate sums in, how would I get that 'smartly'.

I could go.

tapply(mtcars$mpg[mtcars$cyl=="four"], mtcars$gear[mtcars$cyl=="four"], sum)
tapply(mtcars$mpg[mtcars$cyl=="six"], mtcars$gear[mtcars$cyl=="six"], sum)
tapply(mtcars$mpg[mtcars$cyl=="eight"], mtcars$gear[mtcars$cyl=="eight"], sum)

This seems cumbersome.

Then how would I bring a 3rd variable in the mix?

This is somewhat in the space I'm thinking about. Summary statistics using ddply

update This gets me there, but it's not pretty.

aggregate(mpg ~ am+cyl+gear, mtcars,sum)

Cheers

Answer 1

How about this, still using tapply()? It's more versatile than you knew!

with(mtcars, tapply(mpg, list(cyl, gear), sum))
#       three  four five
# four   21.5 215.4 56.4
# six    39.5  79.0 19.7
# eight 180.6    NA 30.8

Or, if you'd like the printed output to be a bit more interpretable:

with(mtcars, tapply(mpg, list("Cylinder#"=cyl, "Gear#"=gear), sum))

---

If you want to use more than two cross-classifying variables, the idea's exactly the same. The results will then be returned in a 3-or-more-dimensional array:

A <- with(mtcars, tapply(mpg, list(cyl, gear, carb), sum))

dim(A)
# [1] 3 3 6
lapply(1:6, function(i) A[,,i]) # To convert results to a list of matrices

# But eventually, the curse of dimensionality will begin to kick in...
table(is.na(A))
# FALSE  TRUE 
#    12    42 

Answer 2

I think the answers already on this question are fantastic options, but I wanted to share an additional option based on the dplyr package (this came up for me because I'm teaching a class right now where we use dplyr for data manipulation, so I wanted to avoid introducing students to specialized base R functions like tapply or aggregate).

You can group on as many variables as you want using the group_by function and then summarize information from these groups with summarize. I think this code is more readable to an R newcomer than the formula-based interface of aggregate, yielding identical results:

library(dplyr)
mtcars %>%
  group_by(am, cyl, gear) %>%
  summarize(mpg=sum(mpg))
#       am   cyl  gear   mpg
#    (dbl) (dbl) (dbl) (dbl)
# 1      0     4     3  21.5
# 2      0     4     4  47.2
# 3      0     6     3  39.5
# 4      0     6     4  37.0
# 5      0     8     3 180.6
# 6      1     4     4 168.2
# 7      1     4     5  56.4
# 8      1     6     4  42.0
# 9      1     6     5  19.7
# 10     1     8     5  30.8

With two variables, you can summarize with one variable on the rows and the other on the columns by adding a call to the spread function from the tidyr package:

library(dplyr)
library(tidyr)
mtcars %>%
  group_by(cyl, gear) %>%
  summarize(mpg=sum(mpg)) %>%
  spread(gear, mpg)
#     cyl     3     4     5
#   (dbl) (dbl) (dbl) (dbl)
# 1     4  21.5 215.4  56.4
# 2     6  39.5  79.0  19.7
# 3     8 180.6    NA  30.8