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Friday Function: nclass

When you draw a histogram, an important question is “how many bar should I draw?”. This should inspire an indignant response. You didn’t become a programmer to answer questions, did you? No. The whole point of programming is to let your computer do your thinking for you, giving you more time to watch videos of fluffy kittens.

Fortunately, R contains three functions to automate the answer, namely nclass.Sturges, nclass.scott and nclass.FD. (FD is short for Freedman-Diaconis; watch out for the fact that scott isn’t capitalised.)

The differences depend upon length and spread of data. For longer vectors, Scott and Freedman-Diaconis tend to give bigger answers.

short_normal <- rnorm(1e2) 
nclass.Sturges(short_normal)      #8
nclass.scott(short_normal)        #8
nclass.FD(short_normal)           #12
long_normal <- rnorm(1e5) 
nclass.Sturges(long_normal)       #18
nclass.scott(long_normal)         #111
nclass.FD(long_normal)            #144

For strongly skewed data, you are best to use some sort of transformation before you draw a histogram, but for the record, Freedman-Diaconis again gives bigger answers for highly skewed (and thus wider) vectors.

short_lognormal <- rlnorm(1e2) 
nclass.Sturges(short_lognormal)   #8
nclass.scott(short_lognormal)     #9
nclass.FD(short_lognormal)        #20
long_lognormal <- rlnorm(1e5) 
nclass.Sturges(long_lognormal)    #18
nclass.scott(long_lognormal)      #443
nclass.FD(long_lognormal)         #1134

My feeling is that since each of the three algorithms is rather dumb, it is safest to calculate all three, then pick the middle one.

nclass.all <- function(x, fun = median)
{
  fun(c(
    nclass.Sturges(x), 
    nclass.scott(x),
    nclass.FD(x)
  ))
}

log_islands 
hist(log_islands, breaks = nclass.all(log_islands))

I also wrote a MATLAB implementation of this a couple of years ago.

It is worth noting that ggplot2 doesn’t accept a number-of-bins argument to geom_histogram, because

In practice, you will need to use multiple bin widths to
discover all the signal in the data, and having bins with
meaningful widths (rather than some arbitrary fraction of the
range of the data) is more interpretable.

That’s fine if you are interactively exploring the data, but if you want a purely automated solution, then you need to make up a number of bins.

calc_bin_width <- function(x, ...)
{
  rangex <- range(x, na.rm = TRUE)
  (rangex[2] - rangex[1]) / nclass.all(x, ...)
}

p <- ggplot(movies, aes(x = votes)) +
  geom_histogram(binwidth = calc_bin_width(log10(movies$votes))) + 
  scale_x_log10()
p
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  1. Martin Maechler
    7th May, 2011 at 21:17 pm

    you are right that one should explore ..
    but then you really should upgrade from histograms to density plots.
    The exploration is much more fun there, and is continuous.
    There even GUI’s for exploration there, e.g., tkdensity() in CRAN package sfsmisc,
    but also something (I think) in the “TeachingDemos” package.

    • 8th May, 2011 at 11:16 am

      Thanks for the heads up about the functions.

      I agree that density plots are superior in most cases, but histograms seem to be less scary for non-statisticians, so they still have a use.

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