Using the R cut function - how do the breaks and labels options work

Question

I was looking for an clear explanation of the 'labels are constructed using "(a,b]" interval notation' - as described in the cut help file, which seemed to lack an explanation.

Answer 1

So I tested cut on some simple examples as follows:

df <- data.frame(c(1,2,3,4,5,6,7,99))
names(df) <- 'x'
df$cut <- cut(df[ ,1], breaks = c(2,4,6,8), right = TRUE)
df
       x cut
#      1  <NA>
#      2  <NA>
#      3 (2,4]
#      4 (2,4]
#      5 (4,6]
#      6 (4,6]
#      7 (6,8]
#     99  <NA>

So the '(' means x>break on the left and '[' means <= (next) break on the right and if a value is lower than the lowest break it is flagged as NA, similarly if a value exceed the highest break it is also flagged as NA.

Next testing the option include.lowest = TRUE

df$cut <- cut(df[ ,1], breaks = c(2,4,6,8), right = TRUE, include.lowest = TRUE)
df
  x   cut
# 1  <NA>
# 2 [2,4]
# 3 [2,4]
# 4 [2,4]
# 5 (4,6]
# 6 (4,6]
# 7 (6,8]

So here for the first bin between the first two breaks, the '[' on left means >=(first break) and the ']' means <=(second) break. Subsequent breaks are treated as above.

Next the NA values can be addressed by using -Inf and/or +Inf in the breaks as follows:

df$cut <- cut(df[ ,1], breaks = c(-Inf,2,4,6,8,+Inf), right = TRUE, include.lowest = TRUE)
df

   x      cut
#  1 [-Inf,2]
#  2 [-Inf,2]
#  3    (2,4]
#  4    (2,4]
#  5    (4,6]
#  6    (4,6]
#  7    (6,8]
# 99 (8, Inf]

Setting the right = FALSE option swaps around the sense of the thresholds as per the example below:

df$cut <- cut(df[ ,1], breaks = c(-Inf,2,4,6,8,+Inf), right = FALSE)
df
#   x      cut
#  1 [-Inf,2)
#  2    [2,4)
#  3    [2,4)
#  4    [4,6)
#  5    [4,6)
#  6    [6,8)
#  7    [6,8)
# 99    [8, Inf)

Finally the labels option allows custom names for the thresholds should you so wish ...

lbls <- c('x<=2','2<x<=4','4<x<=6','6<x<=8','x>8')
df$cut <- cut(df[ ,1], breaks = c(-Inf,2,4,6,8,+Inf), right = TRUE, include.lowest = TRUE, labels = lbls)
df
   x    cut
#  1   x<=2
#  2   x<=2
#  3 2<x<=4
#  4 2<x<=4
#  5 4<x<=6
#  6 4<x<=6
#  7 6<x<=8
# 99    x>8