Box-Percentile Panel Function for Trellis

For all their good points, box plots have a high ink/information ratio in that they mainly display 3 quartiles. Many practitioners have found that the "outer values" are difficult to explain to non-statisticians and many feel that the notion of "outliers" is too dependent on (false) expectations that data distributions should be Gaussian.

panel.bpplot is a panel function for use with trellis, especially for bwplot. It draws box plots (without the whiskers) with any number of user-specified "corners" (corresponding to different quantiles), but it also draws box-percentile plots similar to those drawn by Jeffrey Banfield's ( bpplot function. To quote from Banfield, "box-percentile plots supply more information about the univariate distributions. At any height the width of the irregular 'box' is proportional to the percentile of that height, up to the 50th percentile, and above the 50th percentile the width is proportional to 100 minus the percentile. Thus, the width at any given height is proportional to the percent of observations that are more extreme in that direction. As in boxplots, the median, 25th and 75th percentiles are marked with line segments across the box."

panel.bpplot can also be used with base graphics to add extended box plots to an existing plot, by specifying nogrid=TRUE, height=....

panel.bpplot is a generalization of bpplot and panel.bwplot in that it works with trellis (making the plots horizontal so that category labels are more visable), it allows the user to specify the quantiles to connect and those for which to draw reference lines, and it displays means (by default using dots).

bpplt draws horizontal box-percentile plot much like those drawn by panel.bpplot but taking as the starting point a matrix containing quantiles summarizing the data. bpplt is primarily intended to be used internally by plot.summary.formula.reverse or plot.summaryM but when used with no arguments has a general purpose: to draw an annotated example box-percentile plot with the default quantiles used and with the mean drawn with a solid dot. This schematic plot is rendered nicely in postscript with an image height of 3.5 inches.

bppltp is like bpplt but for plotly graphics, and it does not draw an annotated extended box plot example.

bpplotM uses the lattice bwplot function to depict multiple numeric continuous variables with varying scales in a single lattice graph, after reshaping the dataset into a tall and thin format.

hplot, distribution, nonparametric
panel.bpplot(x, y, box.ratio=1, means=TRUE, qref=c(.5,.25,.75),
             probs=c(.05,.125,.25,.375), nout=0,
             nloc=c('right lower', 'right', 'left', 'none'), cex.n=.7,
             datadensity=FALSE, scat1d.opts=NULL,
             violin=FALSE, violin.opts=NULL,
             nogrid=NULL, height=NULL, …)

# E.g. bwplot(formula, panel=panel.bpplot, panel.bpplot.parameters)

bpplt(stats, xlim, xlab='', box.ratio = 1, means=TRUE, qref=c(.5,.25,.75), qomit=c(.025,.975), pch=16, cex.labels=par('cex'), cex.points=if(prototype)1 else 0.5, grid=FALSE)

bppltp(p=plotly::plot_ly(), stats, xlim, xlab='', box.ratio = 1, means=TRUE, qref=c(.5,.25,.75), qomit=c(.025,.975), teststat=NULL, showlegend=TRUE)

bpplotM(formula=NULL, groups=NULL, data=NULL, subset=NULL, na.action=NULL, qlim=0.01, xlim=NULL, nloc=c('right lower','right','left','none'), vnames=c('labels', 'names'), cex.n=.7, cex.strip=1, outerlabels=TRUE, …)


continuous variable whose distribution is to be examined


grouping variable


see panel.bwplot


set to FALSE to suppress drawing a character at the mean value


vector of quantiles for which to draw reference lines. These do not need to be included in probs.


vector of quantiles to display in the box plot. These should all be less than 0.5; the mirror-image quantiles are added automatically. By default, probs is set to c(.05,.125,.25,.375) so that intervals contain 0.9, 0.75, 0.5, and 0.25 of the data. To draw all 99 percentiles, i.e., to draw a box-percentile plot, set probs=seq(.01,.49,by=.01). To make a more traditional box plot, use probs=.25.


tells the function to use scat1d to draw tick marks showing the nout smallest and nout largest values if nout >= 1, or to show all values less than the nout quantile or greater than the 1-nout quantile if 0 < nout <= 0.5. If nout is a whole number, only the first n/2 observations are shown on either side of the median, where n is the total number of observations.


location to plot number of non-NA observations next to each box. Specify nloc='none' to suppress. For panel.bpplot, the default nloc is 'none' if nogrid=TRUE.


character size for nloc


set to TRUE to invoke scat1d to draw a data density (one-dimensional scatter diagram or rug plot) inside each box plot.


a list containing named arguments (without abbreviations) to pass to scat1d when datadensity=TRUE or nout > 0


set to TRUE to invoke panel.violin in addition to drawing box-percentile plots


a list of options to pass to panel.violin


character size for dots representing means


see panel.bwplot


set to TRUE to use in base graphics


if nogrid=TRUE, specifies the height of the box in user y units

arguments passed to points or panel.bpplot or bwplot


undocumented arguments to bpplt. For bpplotM, xlim is a list with elements named as the x-axis variables, to override the qlim calculations with user-specified x-axis limits for selected variables. Example: xlim=list(age=c(20,60)).


an already-started plotly object


an html expression containing a test statistic


set to TRUE to have plotly include a legend. Not recommended when plotting more than one variable.


a formula with continuous numeric analysis variables on the left hand side and stratification variables on the right. The first variable on the right is the one that will vary the fastest, forming the y-axis. formula may be omitted, in which case all numeric variables with more than 5 unique values in data will be analyzed. Or formula may be a vector of variable names in data to analyze. In the latter two cases (and only those cases), groups must be given, representing a character vector with names of stratification variables.


see above


an optional data frame


an optional subsetting expression or logical vector


specifies a function to possibly subset the data according to NAs (default is no such subsetting).


the outer quantiles to use for scaling each panel in bpplotM


default is to use variable label attributes when they exist, or use variable names otherwise. Specify vnames='names' to always use variable names for panel labels in bpplotM


character size for panel strip labels


if TRUE, pass the lattice graphics through the latticeExtra package's useOuterStrips function if there are two conditioning (paneling) variables, to put panel labels in outer margins.


Esty WW, Banfield J: The box-percentile plot. J Statistical Software 8 No. 17, 2003.

See Also

bpplot, panel.bwplot, scat1d, quantile, Ecdf, summaryP, useOuterStrips

  • panel.bpplot
  • bpplotM
  • bpplt
  • bppltp
x <- rnorm(1000)
g <- sample(1:6, 1000, replace=TRUE)
x[g==1][1:20] <- rnorm(20)+3   # contaminate 20 x's for group 1

# default trellis box plot
bwplot(g ~ x)

# box-percentile plot with data density (rug plot)
bwplot(g ~ x, panel=panel.bpplot, probs=seq(.01,.49,by=.01), datadensity=TRUE)
# add ,scat1d.opts=list(tfrac=1) to make all tick marks the same size
# when a group has > 125 observations

# small dot for means, show only .05,.125,.25,.375,.625,.75,.875,.95 quantiles
bwplot(g ~ x, panel=panel.bpplot, cex.means=.3)

# suppress means and reference lines for lower and upper quartiles
bwplot(g ~ x, panel=panel.bpplot, probs=c(.025,.1,.25), means=FALSE, qref=FALSE)

# continuous plot up until quartiles ("Tootsie Roll plot")
bwplot(g ~ x, panel=panel.bpplot, probs=seq(.01,.25,by=.01))

# start at quartiles then make it continuous ("coffin plot")
bwplot(g ~ x, panel=panel.bpplot, probs=seq(.25,.49,by=.01))

# same as previous but add a spike to give 0.95 interval
bwplot(g ~ x, panel=panel.bpplot, probs=c(.025,seq(.25,.49,by=.01)))

# decile plot with reference lines at outer quintiles and median
bwplot(g ~ x, panel=panel.bpplot, probs=c(.1,.2,.3,.4), qref=c(.5,.2,.8))

# default plot with tick marks showing all observations outside the outer
# box (.05 and .95 quantiles), with very small ticks
bwplot(g ~ x, panel=panel.bpplot, nout=.05, scat1d.opts=list(frac=.01))

# show 5 smallest and 5 largest observations
bwplot(g ~ x, panel=panel.bpplot, nout=5)

# Use a scat1d option (preserve=TRUE) to ensure that the right peak extends 
# to the same position as the extreme scat1d
bwplot(~x , panel=panel.bpplot, probs=seq(.00,.5,by=.001), 
       datadensity=TRUE, scat1d.opt=list(preserve=TRUE))

# Add an extended box plot to an existing base graphics plot
plot(x, 1:length(x))
panel.bpplot(x, 1070, nogrid=TRUE, pch=19, height=15, cex.means=.5)

# Draw a prototype showing how to interpret the plots

# Example for bpplotM
n <- 800
d <- data.frame(treatment=sample(c('a','b'), n, TRUE),
                sex=sample(c('female','male'), n, TRUE),
                age=rnorm(n, 40, 10),
                bp =rnorm(n, 120, 12),
                wt =rnorm(n, 190, 30))
label(d$bp) <- 'Systolic Blood Pressure'
units(d$bp) <- 'mmHg'
bpplotM(age + bp + wt ~ treatment, data=d)
bpplotM(age + bp + wt ~ treatment * sex, data=d, cex.strip=.8)
bpplotM(age + bp + wt ~ treatment*sex, data=d,
        violin.opts=list(col=adjustcolor('blue', alpha.f=.15),

bpplotM(c('age', 'bp', 'wt'), groups='treatment', data=d)
# Can use Hmisc Cs function, e.g. Cs(age, bp, wt)
bpplotM(age + bp + wt ~ treatment, data=d, nloc='left')

# Without treatment: bpplotM(age + bp + wt ~ 1, data=d)

# }
# Automatically find all variables that appear to be continuous
bpplotM(data=support, group='dzgroup',
        cex.strip=.4, cex.means=.3, cex.n=.45)

# Separate displays for categorical vs. continuous baseline variables
pbc <- upData(pbc, moveUnits=TRUE)

s <- summaryM(stage + sex + spiders ~ drug, data=pbc)
Key(0, .5)
s <- summaryP(stage + sex + spiders ~ drug, data=pbc)
plot(s, val ~ freq | var, groups='drug', pch=1:3, col=1:3,
     key=list(x=.6, y=.8))

bpplotM(bili + albumin + protime + age ~ drug, data=pbc)
# }
Documentation reproduced from package Hmisc, version 4.0-3, License: GPL (>= 2)

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