# Box Plot Statistics

### Description

This function is typically called by another function to gather the statistics necessary for producing box plots, but may be invoked separately.

### Usage

1 | ```
boxplot.stats(x, coef = 1.5, do.conf = TRUE, do.out = TRUE)
``` |

### Arguments

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

`coef` |
this determines how far the plot ‘whiskers’ extend out
from the box. If |

`do.conf, do.out` |
logicals; if |

### 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 = 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 `+/-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:

`stats` |
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. |

`n` |
the number of non- |

`conf` |
the lower and upper extremes of the ‘notch’
( |

`out` |
the values of any data points which lie beyond the
extremes of the whiskers ( |

Note that `$stats`

and `$conf`

are sorted in *in*creasing
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.

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

`fivenum`

, `boxplot`

, `bxp`

.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 | ```
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))
``` |