# boxplot.stats

##### 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.

- Keywords
- dplot

##### Usage

`boxplot.stats(x, coef = 1.5, do.conf = TRUE, do.out = TRUE)`

##### Arguments

- x
a numeric vector for which the boxplot will be constructed (

`NA`

s and`NaN`

s are allowed and omitted).- coef
this determines how far the plot ‘whiskers’ extend out from the box. If

`coef`

is positive, the whiskers extend to the most extreme data point which is no more than`coef`

times the length of the box away from the box. A value of zero causes the whiskers to extend to the data extremes (and no outliers be returned).- do.conf, do.out
logicals; if

`FALSE`

, the`conf`

or`out`

component respectively will be empty in the result.

##### Details

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
for `n %% 4 == 1`

(\(n\equiv 1 \bmod 4\)),
the hinges do so *additionally* for `n %% 4 == 2`

(\(n\equiv 2 \bmod 4\)), and are in the middle of
two observations otherwise.

The notches (if requested) extend to `+/-1.58 IQR/sqrt(n)`

.
This seems to be based on the same calculations as the formula with 1.57 in
Chambers *et al* (1983, p.62), given in McGill *et al*
(1978, p.16). 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.

##### Value

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-`NA`

observations in the sample.

the lower and upper extremes of the ‘notch’
(`if(do.conf)`

). See the details.

the values of any data points which lie beyond the
extremes of the whiskers (`if(do.out)`

).

Note that $stats and $conf are sorted in increasing order, unlike S, and that $n and $out include any +- Inf values.

##### References

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.
10.2307/2683468.

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.

##### See Also

##### Examples

`library(grDevices)`

```
# NOT RUN {
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))
# }
# NOT RUN {
<!-- %% extended example (for the NG of Rdoc): -->
# }
# NOT RUN {
# }
```

*Documentation reproduced from package grDevices, version 3.6.2, License: Part of R 3.6.2*