Box Plot Statistics
This function is typically called by another function to gather the statistics necessary for producing box plots, but may be invoked separately.
a numeric vector for which the boxplot will
be constructed (
this determines how far the plot ‘whiskers’ extend out
from the box. If
The two ‘hinges’ are versions of the first and third quartile,
i.e., close to
quantile(x, c(1,3)/4). The hinges equal
the quartiles for odd n (where
n <- length(x)) and
differ for even n. Whereas the quartiles only equal observations
n %% 4 == 1 (n = 1 mod 4),
the hinges do so additionally for
n %% 4 == 2
(n = 2 mod 4), and are in the middle of
two observations otherwise.
The notches (if requested) extend to
This seems to be based on the same calculations as the formula with 1.57 in
Chambers et al (1983, p.\sspace62), given in McGill et al
(1978, p.\sspace16). They are based on asymptotic normality of the median
and roughly equal sample sizes for the two medians being compared, and
are said to be rather insensitive to the underlying distributions of
the samples. The idea appears to be to give roughly a 95% confidence
interval for the difference in two medians.
List with named components as follows:
a vector of length 5, containing the extreme of the lower whisker, the lower ‘hinge’, the median, the upper ‘hinge’ and the extreme of the upper whisker.
the number of non-
the lower and upper extremes of the ‘notch’
the values of any data points which lie beyond the
extremes of the whiskers (
$conf are sorted in increasing
order, unlike S, and that
$out include any
+- Inf values.
Tukey, J. W. (1977) Exploratory Data Analysis. Section 2C.
McGill, R., Tukey, J. W. and Larsen, W. A. (1978) Variations of box plots. The American Statistician 32, 12–16.
Velleman, P. F. and Hoaglin, D. C. (1981) Applications, Basics and Computing of Exploratory Data Analysis. Duxbury Press.
Emerson, J. D and Strenio, J. (1983). Boxplots and batch comparison. Chapter 3 of Understanding Robust and Exploratory Data Analysis, eds. D. C. Hoaglin, F. Mosteller and J. W. Tukey. Wiley.
Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. A. (1983) Graphical Methods for Data Analysis. Wadsworth & Brooks/Cole.
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require(stats) x <- c(1:100, 1000) (b1 <- boxplot.stats(x)) (b2 <- boxplot.stats(x, do.conf = FALSE, do.out = FALSE)) stopifnot(b1 $ stats == b2 $ stats) # do.out = FALSE is still robust boxplot.stats(x, coef = 3, do.conf = FALSE) ## no outlier treatment: boxplot.stats(x, coef = 0) boxplot.stats(c(x, NA)) # slight change : n is 101 (r <- boxplot.stats(c(x, -1:1/0))) stopifnot(r$out == c(1000, -Inf, Inf))