# qbxp.stats: Box Plot Statistics In MKmisc: Miscellaneous Functions from M. Kohl

## Description

This functions works identical to `boxplot.stats`. It is typically called by another function to gather the statistics necessary for producing box plots, but may be invoked separately.

## Usage

 `1` ```qbxp.stats(x, coef = 1.5, do.conf = TRUE, do.out = TRUE, type = 7) ```

## Arguments

 `x` a numeric vector for which the boxplot will be constructed (`NA`s and `NaN`s are allowed and omitted). `coef` it 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` logical; if `FALSE`, the `conf` component will be empty in the result. `do.out` logical; if `FALSE`, `out` component will be empty in the result. `type` an integer between 1 and 9 selecting one of nine quantile algorithms; for more details see `quantile`.

## Details

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 first quartile, the median, the third quartile and the extreme of the upper whisker. `n` the number of non-`NA` observations in the sample. `conf` the lower and upper extremes of the ‘notch’ (`if(do.conf)`). See the details. `out` 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.

## Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

## 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.

`quantile`, `boxplot.stats`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## adapted example from boxplot.stats x <- c(1:100, 1000) (b1 <- qbxp.stats(x)) (b2 <- qbxp.stats(x, do.conf=FALSE, do.out=FALSE)) stopifnot(b1\$stats == b2\$stats) # do.out=F is still robust qbxp.stats(x, coef = 3, do.conf=FALSE) ## no outlier treatment: qbxp.stats(x, coef = 0) qbxp.stats(c(x, NA)) # slight change : n is 101 (r <- qbxp.stats(c(x, -1:1/0))) stopifnot(r\$out == c(1000, -Inf, Inf)) ```