X: Univariate and Grouped Displays for a Continuous Variable

In lessR: Less Code with More Comprehensive Results

Univariate and Grouped Displays for a Continuous Variable

Description

lessR introduces the concept of a data view visualization function, in which the choice of visualization function directly reflects the structure of the data and the analyst's goal for understanding the data. The function X() visualizes the distribution of a continuous variable along with associated summary statistics. The specific representation is selected with the type argument:

• Histogram with type = "histogram" (default)

• Density plot with type = "density"

• Box plot with type = "box"

• Violin plot with type = "violin"

• Strip (one-dimensional scatter) plot with type = "strip"

• Integrated violin-box-strip (VBS) plot with type = "vbs"

• Two-dimensional scatter plot for a by variable with type = "scatter"

Stratification divides the distribution into groups. Use by to overlay the groups within a single panel, or facet to display each group, or combination of groups, in separate panels.

When running in RStudio, static displays appear in the Plots window, while histograms and density plots also appear as interactive Plotly visualizations in the Viewer window.

Usage

X(

    # ----------------------------------------------
    # Data from which to construct the visualization
    x=NULL, by=NULL, facet=NULL, data=d, filter=NULL,

    # ------------------------------------------
    # Type of plot for the continuous variable x
    type = c("histogram", "freq_poly", "density", "scatter",
             "violin", "box", "strip", "bs", "vbs"), # violin, box, strip
    stat=c("count", "proportion", "density"),

    n_row=NULL, n_col=NULL, aspect="fill",

    # -----------------------------------------------------------------
    # Analogy of physical Marks on paper that create the bars and labels
    theme=getOption("theme"),
    fill=getOption("bar_fill_cont"),
    color=getOption("bar_color_cont"),
    transparency=getOption("trans_bar_fill"),

    # -----------------------------------------------------
    # Form of the histogram - bin the continuous variable x
    counts=FALSE, 
    bin_start=NULL, bin_width=NULL, bin_end=NULL, breaks="Sturges",
    cumulate=c("off", "on", "both"), reg="snow2",  # Cumulative histogram

    # -----------------------------------------------------
    # Density (smooth curve) plot
    show_histogram=TRUE,
    bandwidth=NULL, kind=c("general", "normal", "both"),
    fill_normal=NULL, fill_hist=getOption("se_fill"), 
    color_normal="gray20", line_width=NULL,
    x_pt=NULL, y_axis=FALSE,
    rug=FALSE, color_rug="black", size_rug=0.5,

    # -------------------------------------------------
    # Integrated violin/box/scatter plot
    vbs_plot="vbs", vbs_ratio=0.9, bw=NULL, bw_iter=10,
    violin_fill=getOption("violin_fill"),
    box_fill=getOption("box_fill"),
    pt_size=NULL,
    vbs_pt_fill="black",
    vbs_mean=FALSE, fences=FALSE, n_min_pivot=1,
    k=1.5, box_adj=FALSE, a=-4, b=3,

    ID="row.name", ID_size=0.60,
    MD_cut=0, out_cut=0, out_shape="circle", out_size=1,

    # -----------------------------------------------------------------
    # Labels for axes, values, and legend if x and by variables, margins
    xlab=NULL, ylab=NULL, main=NULL, sub=NULL,
    lab_adjust=c(0,0), margin_adjust=c(0,0,0,0),

    rotate_x=getOption("rotate_x"), rotate_y=getOption("rotate_y"),
    offset=getOption("offset"),
    scale_x=NULL,
    axis_fmt=c("K", ",", ".", ""), axis_x_pre="", axis_y_pre="",

    # ----------------------------------------------------------------------
    # Draw one or more objects, text, or geometric figures, on the histogram
    add=NULL, x1=NULL, y1=NULL, x2=NULL, y2=NULL,

    # ---------------------------------------
    # Output: turn off, chart to PDF file, decimal digits, markdown file
    quiet=getOption("quiet"), do_plot=TRUE,
    use_plotly=getOption("lessR.use_plotly"),
    pdf_file=NULL, width=6.5, height=6, digits_d=NULL, Rmd=NULL,

    # --------------------------------------
    # Deprecated, removed in future versions
    n_cat=getOption("n_cat"), 
    rows=NULL, facet1=NULL, facet2=NULL,

    # ---------------------------------
    # Other
    eval_df=NULL, fun_call=NULL, ...)

Arguments

x	Variable(s) to analyze. May be a single numeric variable, a vector in the workspace, multiple variables combined with c, or an entire data frame. If omitted, defaults to all numeric variables in the data frame d.
by	A categorical grouping variable. When supplied, overlapping histograms or other distributional displays are drawn on the same coordinate system.
facet	A categorical conditioning variable, or a vector of two such variables, that activates Trellis (lattice) graphics to produce separate panels for each level or combination of levels.
data	Optional data frame that contains the variables of interest. Default is d.
filter	Logical expression or integer index vector identifying the rows to retain for analysis.

type

Type of univariate display. Default is "histogram". Additional options include: "freq_poly" (frequency polygon), "density" (kernel density curve), "violin", "strip" (one-dimensional scatter plot), "scatter" (two-dimensional scatter plot with one panel per by), and "vbs" (combined violin-box-strip display). When using "vbs", the vbs_plot parameter may specify a subset such as "bs" for a box-strip display.

stat

Specifies the vertical axis content. Default is "count". Use "proportion" for relative frequencies, or "density" for density scaling in histogram mode.

n_row	Optional number of rows for multi-panel displays created by facet.
n_col	Optional number of columns for multi-panel displays. If n_col = 1, facet strips appear at the left rather than top.
aspect	Aspect ratio of lattice panels (height/width). Default "fill" expands panels to available space. Use 1 for square panels or "xy" for banking to 45 degrees.
theme	Color theme. Use style to set persistent defaults.
fill	Fill color for bars or density regions. May be a single color, named palette ("grays", "hcl", "blues", "reds", "greens"), or custom vector.
color	Border color for bars or density curves. May be a vector. Default follows style.
transparency	Transparency of filled areas. Default from style.

counts	If TRUE, display counts for each bin on the histogram.
bin_start	Optional starting value of the first bin.
bin_width	Optional bin width, with or without a specified bin start.
bin_end	Optional value that must fall inside the final bin.
breaks	Method used to compute bins or an explicit set of breakpoints. Default is "Sturges"; options include "Scott" and "FD".

cumulate	Produces a cumulative histogram when set to "on". Use "both" to superimpose the standard histogram.
reg	Color of the regular histogram when cumulate="both".
show_histogram	When plotting a density curve, optionally draw a histogram behind it.
bandwidth	Bandwidth for kernel density estimation. Default begins with bw.nrd0 but may be iteratively increased for smoother curves.
kind	Determines whether to display the general density curve, the normal density curve, or both.
fill_normal	Fill color used for the normal density curve.
fill_hist	Fill color for histograms under density curves.
color_normal	Border color for the normal density curve.
line_width	Line width of density curves.
x_pt	Value on the x-axis from which to illustrate a unit interval of density area. Applies when kind = "general".
y_axis	If TRUE, display the density axis.
rug	If TRUE, draw a rug plot beneath the density curve.
color_rug	Color of rug ticks.
size_rug	Line width of rug ticks.

vbs_plot	Controls which components of the violin-box-strip display appear. Characters "v", "b", and "s" indicate violin, box, and strip components. Upper/lower case permitted. Adjust colors with style parameters such as violin_fill, box_fill, out_fill, etc.
vbs_ratio	Relative height of the violin (and box) component.
bw	Bandwidth for violins; larger values yield smoother shapes.
bw_iter	Number of iterations for modifying the bandwidth to produce smoother violins.
violin_fill	Fill color for violins.
box_fill	Fill color for box plots.
pt_size	Size of points in strip plots.
vbs_pt_fill	Point color in the strip component of the VBS display. Default is black.
vbs_mean	If TRUE, show the mean in box plots.
fences	If TRUE, draw Tukey inner fences.
n_min_pivot	Minimum sample size required for a group to appear in a VBS pivot table (default 1).
k	IQR multiplier for determining whisker length.
box_adj	If TRUE, adjust box plot for skewness using medcouple.
a, b	Scaling factors for adjusted boxplot whiskers.

ID	Variable supplying labels for selected points (outlier identification). Defaults to row names.
ID_size	Point label text size.
MD_cut	Mahalanobis distance cutoff for outliers in 2-variable plots.
out_cut	Number or proportion of extreme points to label. Interpreted differently for univariate vs. bivariate displays.
out_shape	Plotting symbol for outliers.
out_size	Point size for labeled outliers.

xlab	X-axis label. Defaults to variable name or label.
ylab	Y-axis label. Defaults to "Frequency" or "Proportion".
main	Main title for the plot.
sub	Subtitle (not yet implemented).
lab_adjust	Two-element vector adjusting axis-label positions.
margin_adjust	Four-element vector adjusting plot margins.

rotate_x	Rotation (in degrees) of x-axis tick labels.
rotate_y	Rotation (in degrees) of y-axis tick labels.
offset	Distance between tick labels and axis.
scale_x	Vector specifying start, end, and number of intervals for the x-axis.
axis_fmt	Formatting of axis numbers ("K", ",", ".", or "").
axis_x_pre	Prefix for x-axis labels (e.g., "$").
axis_y_pre	Prefix for y-axis labels.

add	Add text or geometric objects (rectangles, lines, arrows, horizontal/vertical lines, etc.) to the plot.
x1	First x-coordinate for added objects.
y1	First y-coordinate.
x2	Second x-coordinate (for applicable object types).
y2	Second y-coordinate.

quiet	If TRUE, suppress textual output.
do_plot	If TRUE, generate the plot.
use_plotly	If TRUE (default), draw a Plotly interactive version in addition to the static plot.
pdf_file	Optional file name to direct static graphics output to PDF.
width	Width of plot window (inches).
height	Height of plot window (inches).
digits_d	Digits of precision for printed statistics.
Rmd	Name of an R Markdown file to generate containing the analysis.

n_cat	Maximum number of unique integer values to treat as categorical. Deprecated.
rows	Deprecated; use filter.
facet1	Deprecated; use facet.
facet2	Deprecated; use a two-element vector in facet.

eval_df	If TRUE, checks that variables exist in the supplied data frame. Must be FALSE in Shiny or pipe workflows.
fun_call	Function call used internally for knitr compatibility.

...	Additional graphics parameters passed to hist, par, and related functions (e.g., xlim, ylim, cex.main, col.main, cex, col.lab).

Details

OVERVIEW

X() implements the univariate, distributional view for numeric variables. Internally it still relies on the base R hist function for histogram binning when type = "histogram", but extends that core infrastructure to a larger family of displays including frequency polygons, kernel density estimates, violin plots, strip plots, and the integrated violin-box-strip (VBS) display. For histogram-based displays, the freq option of hist is always set to FALSE, so counts, proportions, or densities are controlled through the lessR arguments (stat and type) rather than directly through hist.

For plotting densities, the recommended approach is to use type = "density", which computes and displays a kernel density estimate. The older usage of stat = "density" is maintained for backward compatibility but is not recommended for new code.

VARIABLES AND TRELLIS PLOTS

At a minimum there is one primary numeric variable, x, which results in a single univariate display (histogram, density, VBS, etc.). Facet graphics (also called Trellis graphics), from Deepayan Sarkar's lattice package, may be requested by supplying one or two categorical conditioning variables to the facet argument. A single facet variable produces one panel per level of that variable; a two-element vector in facet produces a panel for each combination of levels of the two facet variables.

In each panel, the same numeric primary variable x is displayed, conditioning on the facet levels. The combination of x with facet thus yields a grid of small multiples that share scales and styling, facilitating comparisons across subgroups without changing the underlying analysis.

BOXPLOTS AND THE VBS DISPLAY

For a single variable, the preferred summary display is often the integrated violin-box-strip (VBS) plot, requested with type = "vbs". Only the violin or only the box portion can be obtained either via the corresponding aliases or by setting vbs_plot to "v" or "b". To view a boxplot of a continuous variable across the levels of a categorical variable, either as part of the full VBS plot or alone, there are two primary styles:
1. X(x, by = g, type = "box")
2. X(x, facet = f, type = "box")

Both styles convey the same information about numeric-by-category distributions. The difference is visual: with by, multiple boxplots appear in a single panel using the qualitative color palette from getColors, with all hues chosen to be comparable in perceived saturation and brightness. With facet, a separate panel is drawn for each group, typically using a single hue. The same default qualitative colors are used throughout lessR, including in Chart.

DATA

The data may be supplied as a vector from the global environment (user workspace), as one or more variables within a data frame, or as an entire data frame. The default input data frame is d. A different source data frame may be specified with the data argument. When multiple variables are listed, only those of numeric type are analyzed by X().

Variables in a data frame are referenced directly by their names; there is no need to use d$name, with, or attach. If a name exists both as a vector in the global environment and as a variable in the specified data frame, the vector in the global environment takes precedence.

To obtain a histogram (or other univariate display) for each numeric variable in the default data frame d, call X() without specifying x. For a different data frame, set the data argument accordingly. To restrict analysis to a subset of variables, specify them with : or c, such as m01:m03 or c(m01, m02, m03).

The filter parameter subsets rows (cases) of the input data frame according to either (a) a logical expression or (b) a vector of integer row indices. Logical expressions use standard R logical operators as described in Logic (e.g., \& for "and", | for "or", ! for "not") and relational operators as described in Comparison (e.g., == for equality, != for inequality, > for "greater than"). A vector of integers can be created with standard R syntax; see the Examples section for illustrations.

COLORS

Colors for individual elements of the plot can be controlled directly through arguments such as fill (for areas) and color (for borders), or indirectly through the global style system. The style function allows selection of a color theme for the entire analysis. The default theme is "lightbronze", with additional themes such as "gray" for grayscale and several color-emphasis themes (e.g., "red", "green").

For black backgrounds and partially transparent colors, use style(sub_theme = "black"). For all color options, including fill, a setting of "off" is equivalent to "transparent".

For fill, you may specify a single color, a vector of colors, or a color range. Besides standard color names, lessR provides multiple hue-balanced palettes, including "hues", as well as pre-specified ranges "blues", "reds", and "greens". Standard R palettes "rainbow", "terrain", and "heat" are also available. Custom ranges can be generated via getColors.

HISTOGRAMS AND RELATED OUTPUT

When type = "histogram", the output includes a frequency histogram with lessR's default background and grid styling, along with optional relative frequency and/or cumulative histograms. Summary statistics and a table of bin information (bin boundaries, midpoints, counts, proportions, cumulative counts, and cumulative proportions) are provided as part of the returned object.

Bin construction can follow the default Sturges rule or be customized via bin_width, bin_start, and bin_end, or via the breaks argument (which can accept numeric vectors or named rules such as "Scott" or "FD" as in hist). lessR adds more informative error checking and guidance when user-specified bins do not fully span the data or otherwise lead to problematic binning.

If multiple variables are supplied (including a complete data frame), X() analyzes each numeric variable in turn. The related CountAll function performs a similar role across mixed types, producing bar charts for categorical variables and histograms for numeric variables. Faceting via facet can be combined with X() to create trellised displays across conditioning variables.

VARIABLE LABELS

If variable labels exist (e.g., created by Read), they are used by default for the horizontal axis label and in the text output. Variable names are still available, but labels provide more descriptive and publication-ready annotations.

ONLY VARIABLES ARE REFERENCED

In lessR functions, the primary argument x (and any other variable arguments) must be specified as variable names, not expressions. The variables must exist either in the referenced data frame (such as the default d) or in the global environment. Direct expressions are not evaluated. For example:

> X(rnorm(50)) # does NOT work

Instead, assign the expression to a named object and then reference that name:

    > Y <- rnorm(50)  # create vector Y in user workspace
    > X(Y)            # directly reference Y

ERROR DETECTION

A common error for beginning users of hist is to specify a sequence of break points that does not fully span the data, often constructed with seq. Base R then produces a cryptic error. In contrast, X() (and the Histogram() alias) checks for this problem before calling hist and, if detected, issues a more informative message along with guidance on how to correct the specification.

In addition, full control of the binning is available via bin_width and bin_start. If bin_start is specified without bin_width, the bin width is determined by the default Sturges rule.

PDF OUTPUT

To obtain PDF output directly, use the pdf_file argument, optionally with width and height to control the device size in inches. The resulting files are written to the current working directory, which can be set explicitly via setwd. This mechanism facilitates high-quality, publication-ready graphics saved directly from X().

Value

The output may be assigned to an R object; otherwise it is printed directly to the console. The returned object contains two types of components:

• Readable output: character strings such as tables and summaries, formatted for display.

• Statistics: numerical values suitable for further computation or inclusion in dynamic documents.

These components are designed to support R Markdown workflows. Any element of the saved object can be inserted into an R Markdown document by referencing its name, preceded by the object name and the $ operator (see examples). Only elements relevant to the requested analysis are returned. For example, bin proportions appear only when a histogram is requested.

To save the results, assign the output to an object, such as h <- Histogram(Salary). Use names(h) to view the available components, and display any one by typing, for example, h$out_freq. Output can be viewed interactively at the console or embedded in R Markdown documents along with narrative interpretation.

READABLE OUTPUT
out_suggest: Suggestions for other similar analyses
out_summary: Summary statistics
out_freq: Frequency distribution
out_outliers: Outlier analysis

STATISTICS
bin_width: Bin width
n_bins: Number of bins
breaks: Breaks of the bins
mids: Bin midpoints
counts: Bin counts
prop: Bin proportions
cumulate: Bin cumulative counts
cprop: Bin cumulative proportions

Author(s)

David W. Gerbing (Portland State University; [e-mail])

References

Gerbing, D. W. (2023). R Data Analysis without Programming: Explanation and Interpretation, 2nd edition, Chapter 5, NY: Routledge.

Gerbing, D. W. (2020). R Visualizations: Derive Meaning from Data, Chapter 4, NY: CRC Press.

Gerbing, D. W. (2021). Enhancement of the Command-Line Environment for use in the Introductory Statistics Course and Beyond, Journal of Statistics and Data Science Education, 29(3), 251-266.

Hubert, M. and Vandervieren, E. (2008). An adjusted boxplot for skewed distributions, Computational Statistics and Data Analysis 52, 51865201.

Sarkar, D. (2008). Lattice: Multivariate Data Visualization with R. Springer.

Sievert, C. (2020). Interactive Web-Based Data Visualization with R, plotly, and shiny. Chapman and Hall/CRC. URL: https://plotly.com/r/

See Also

XY, Chart, getColors, style.

Examples

# get the data
d <- rd("Employee")

# make sure default style is active
style()

# --------------------
# different histograms
# --------------------

# histogram with all defaults
X(Salary, type="histogram")
# with deprecated alias
Histogram(Salary)

# output saved for later analysis into object h
h <- hs(Salary)
# view full text output
h
# view just the outlier analysis
h$out_outliers
# list the names of all the components
names(h)

# histogram with no borders for the bars
X(Salary, color="off")

# just males employed more than 5 years
X(Salary, filter=(Gender=="M" & Years > 5))

# histogram with red bars, black background, and black border
style(panel_fill="black", fill="red", panel_color="black")
X(Salary)
# or use a lessR pre-defined sequential color palette
#   with some transparency
X(Salary, fill="rusts", color="brown", transparency=.1)

# histogram with purple color theme, translucent gold bars
style("purple", sub_theme="black")
X(Salary)
# back to default color theme
style()

# histogram with specified bin width
# can also use bin_start
X(Salary, bin_width=12000)

# histogram with rotated axis values, offset more from axis
# suppress text output
style(rotate_x=45, offset=1)
X(Salary, quiet=TRUE)
style()

# histogram with specified bin width
X(Salary, bin_width=20000, xlab="My Variable")

# histogram with bins calculated with the Scott method and values displayed
X(Salary, breaks="Scott", counts=TRUE, quiet=TRUE)

# histogram with the number of suggested bins, with proportions
X(Salary, breaks=15, stat="proportion")

# histogram with non-default values for x- and y-axes
d[2,4] <- 45000
X(Salary, scale_x=c(20000,160000,8))

# ----------------
# Trellis graphics
# ----------------
Histogram(Salary, facet=Dept)

# ---------------------
# cumulative histograms
# ---------------------

# cumulative histogram with superimposed regular histogram, all defaults
X(Salary, cumulate="both")

# cumulative histogram plus regular histogram
X(Salary, cumulate="both", reg="mistyrose")

# -------------
# density plots
# -------------

# default density plot
X(Salary, type="density")

# normal curve and general density curves superimposed over histogram
# all defaults
X(Salary, type="density", kind="both")

# display only the general estimated density
#  so do not display the estimated normal curve
# specify the bandwidth for the general density curve
X(Salary, type="density", bandwidth=8000)

# display only the general estimated density and a corresponding
#  interval of unit width around x_pt
X(Salary, type="density", x_pt=40000)

# densities for all specified numeric variables in a list of variables
# e.g., use the combine or c function to specify a list of variables
X(c(Years, Salary), type="density")

# -------------------------------------------------
# histograms for data frames and multiple variables
# -------------------------------------------------

# create data frame, d, to mimic reading data with Read function
# d contains both numeric and non-numeric data
d <- data.frame(rnorm(50), rnorm(50), rnorm(50), rep(c("A","B"),25))
names(d) <- c("X","Y","Z","C")

# although data not attached, access the variable directly by its name
X(X)

# histograms for all numeric variables in data frame called d
# d is the default name, so does not need to be specified with data
X()

# histogram with specified options, including red axis labels
style(fill="palegreen1", panel_fill="ivory", axis_color="red") 
X(counts=TRUE)
style()  # reset

# histograms for all specified numeric variables
# use the combine or c function to specify a list of variables
X(c(X,Y))

# integrated violin/box/scatter plot (VBS)
d <- Read("Employee")
X(Salary, type="vbs")

X(Years, by=Gender, pt_size=1.25,
     fill=c("olivedrab3", "gold1"),
     color=c("darkgreen", "gold4"), type="vbs")



# by variable, different colors for different values of the variable
# two panels
X(Salary, facet=Dept)

# large sample size
x <- rnorm(10000)
X(x)

# custom colors for outliers, which might not appear in this subset data
style(out_fill="hotpink", out2_fill="purple")
X(Salary, type="vbs")
style()

# no violin plot or scatterplot, just a boxplot
X(Salary, type="box")

# -----------
# annotations
# -----------

d <- rd("Employee")

# Place a message in the top-right of the graph
# Use \n to indicate a new line
X(Salary, add="Salaries in our Company", x1=100000, y1=7)

# Use style to change some parameter values
style(add_trans=.8, add_fill="gold", add_color="gold4",
      add_lwd=0.5, add_cex=1.1)
# Add a rectangle around the message centered at <100000,7>
X(Salary, add=c("rect", "Salaries in our Company"),
      x1=c(82000, 100000), y1=c(7.7, 7), x2=118000, y2=6.2)

lessR documentation built on Dec. 11, 2025, 5:07 p.m.