I was preparing some teaching material recently and wanted to show how two samples distributions overlapped. This meant I needed to work out how to plot two histograms on one axis and also to make the colors transparent, so that they could both be discerned.

For my teaching example I wanted to make some normally distributed data and show how the overlap changes as the means and variance of the samples alters. However, being able to plot two sample distributions on a single chart is a generally useful thing so I wrote some code to take two samples and do just that.

The first step is to make transparent colors; then any overlapping bars will remain visible. The key command is rgb() but you need to get R G and B values first.

Select a color that you want to make transparent. Then use the col2rgb() command to get the red, green and blue values you need for the rgb() command e.g.:

> col2rgb("lightblue")
      [,1]
red    173
green  216
blue   230

This gives you a matrix with three rows (red, blue, green). This means you can get values for several colors at once:

> col2rgb(c("lightblue", "lightgreen", "pink"))
      [,1] [,2] [,3]
red    173  144  255
green  216  238  192
blue   230  144  203

The rgb() command defines a color: you define a new color using numerical values (0–255) for red, green and blue. In addition, you set an alpha value (also 0–255), which sets the transparency (0 being fully transparent and 255 being “solid”).

You also need to set the maximum color value, so that the command can relate your alpha value to a level of transparency. In practice setting max = 255 works well (since RGB colors are usually defined in the range 0–255).

The following example takes the standard blue and makes it transparent (~50%):

> mycol <- rgb(0, 0, 255, max = 255, alpha = 125, names = "blue50")

Note that the names parameter sets a name attribute for your color. You cannot use the name directly but it can be useful to see a name. You can call your colors anything of course, here they are simply named c1 and c2:

> c1 <- rgb(173,216,230,max = 255, alpha = 80, names = "lt.blue")
> c2 <- rgb(255,192,203, max = 255, alpha = 80, names = "lt.pink")

Note that the second breakpoint is the right edge of the first histogram bar. In the previous example the pretty() command was used to set the breaks. This command splits up a range of values into a tidy set of values, and is generally used internally by graphics commands to set axes.

The limits of the x-axis are set by the breakpoints but you can over-ride them as you need. There are two ways you can control the width, either way will permit you to make the space for two histograms on the one axis:

• Use the xlim parameter: you can set the axis width to cover the range of the combined samples.
• Use the breaks parameter: you can set the breaks to cover the range of the combined sample.

In the previous example you can see that the x-axis is not quite large enough to accommodate the entire range of the histogram. If you save the histogram to a named object you can see the data:

> hgB <- hist(B, plot = FALSE)

> hgB
$breaks
[1] 25 30 35 40 45 50

$counts
[1] 3 7 10 4 1

$density
[1] 0.024 0.056 0.080 0.032 0.008

$mids
[1] 27.5 32.5 37.5 42.5 47.5

$xname
[1] "B"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"

So, if you want to use xlim to set the axis limits you should use the histogram $breaks data, rather than the original sample data.

The pretty() command is useful to set your x-axis limits because it moves the breakpoints about and makes tidy intervals. For example:

> range(c(A,B))
[1] 16 46

> pretty(16:46)
[1] 15 20 25 30 35 40 45 50

If you used this method your x-axis would encompass the entire histogram range.

You can set the “desired” number of breaks in the pretty() command:

> pretty(16:46)
[1] 15 20 25 30 35 40 45 50

> pretty(16:46, n = 10)
[1] 15 20 25 30 35 40 45 50

> pretty(16:46, n = 12)
[1] 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46

You set n = your desired optimal number and the command does its best to create approximately that number of intervals.

Using the pretty() command has an additional benefit: the interval will be the same for both histograms so that when plotted the bars will be the same width.

In order to plot two histograms on one plot you need a way to add the second sample to an existing plot. You cannot do this directly via the hist() command.

You need to save your histogram as a named object without plotting it. To do this you specify plot = FALSE as a parameter. If you save the histogram to a named object you can plot it later. Actually you can save the histogram data and plot it at the same time but you cannot add to an existing plot in this way.

> A
[1] 17 26 28 27 29 28 25 26 34 32 23 29 24 21 26 31 31 22 26 19 36 23 21 16 30

> hgA <- hist(A)
> hgA
$breaks
[1] 15 20 25 30 35 40

$counts
[1] 3 7 10 4 1

$density
[1] 0.024 0.056 0.080 0.032 0.008

$mids
[1] 17.5 22.5 27.5 32.5 37.5

$xname
[1] "A"

$equidist
[1] TRUE

attr(,"class")
[1] "histogram"

You can see that the data are stored in $ components and that you can access the frequency or density data. The breakpoints are set at this time and you cannot alter them unless you re-run the command and specify different values.

In order to plot a histogram object you simply use plot(). You can specify add = TRUE to plot a second histogram in the same plot window.

If you have a histogram object, all the data you need is contained in that object. Using plot() will simply plot the histogram as if you’d typed hist() from the start. However, you can now use add = TRUE as a parameter, which allows a second histogram to be plotted on the same chart/axis.

To make sure that both histograms fit on the same x-axis you’ll need to specify the appropriate xlim() command to set the x-axis limits. Alternatively, (and probably better) is to set the breakpoints for both histograms to cover the combined range of the samples.

Inevitably some bars will overlap, which is where the transparent colors come in useful. The following steps illustrate the process using the data examples you’ve already seen.

In this example the y-axis is sufficient to cover both samples but if your data contain quite different frequencies you can use the ylim parameter to set the appropriate size for the y-axis.

If you want to plot the densities instead of the frequencies you can use freq = FALSE as you would when using the hist() command. This means you could also add the density lines to your plots as well as the histograms. Note that you cannot set the breaks in this manner.

In the previous example both xlim and ylim parameters needed to be altered. Note that although the xlim parameter set the minimum to 16, the axis ended up with a minimum of 15. This is because the plot() command has used pretty() internally to “neaten” the axis intervals.

You only need to alter the xlim and ylim parameters for the first plot because the plot dimensions are already set by the time you add the second histogram.

You can easily make transparent colors using R and the rgb() command. These colors can be useful for charts and graphics with overlapping elements.

The rgb() command is the key: you define a new color using numerical values (0–255) for red, green and blue. In addition, you set an alpha value (also 0–255), which sets the transparency (0 being fully transparent and 255 being “solid”).

You also need to set the maximum color value, so that the command can relate your alpha value to a level of transparency. In practice setting max = 255 works well (since RGB colors are usually defined in the range 0–255).

The following example takes the standard blue and makes it transparent (~50%):

mycol <- rgb(0, 0, 255, max = 255, alpha = 125, names = "blue50")

Note that the names parameter sets a name attribute for your color. You cannot use the name directly but it can be useful to see a name, e.g.

> mycol
     blue50
"#0000FF7D"

Use the col2rgb() command to get the red, green and blue values you need for the rgb() command e.g.:

> col2rgb("lightblue")
      [,1]
red    173
green  216
blue   230

This gives you a matrix with three rows (red, blue, green). This means you can get values for several colors at once:

> col2rgb(c("lightblue", "lightgreen", "pink"))
      [,1] [,2] [,3]
red    173  144  255
green  216  238  192
blue   230  144  203

It is fairly easy to make a custom function that takes a named color and makes a transparent version. Here is some code that makes a single color. It could be extended to make a matrix of several colors quite easily:

## Transparent colors
## Mark Gardener 2015
## www.dataanalytics.org.uk

t_col <- function(color, percent = 50, name = NULL) {
  #      color = color name
  #    percent = % transparency
  #       name = an optional name for the color

## Get RGB values for named color
rgb.val <- col2rgb(color)

## Make new color using input color as base and alpha set by transparency
t.col <- rgb(rgb.val[1], rgb.val[2], rgb.val[3],
             max = 255,
             alpha = (100 - percent) * 255 / 100,
             names = name)

## Save the color
invisible(t.col)
}
## END

Sometimes you want to get the results of an analysis from your R console to a word processor. Copy and paste does not work well unless you are prepared to use fixed width font in the target document. The trick is to send the output to a disk file using the sink() command first.

The sink() command allows you to send anything that would have gone to the console (your screen) to a disk file instead.

sink(file = NULL, append = FALSE, split = FALSE)

You need to supply the filename, setting file = NULL closes the connection and stops sink()ing. To add to an existing file use append = TRUE. If you set split = TRUE the output goes to the console and the file you specified.

When you issue the command a file is created, ready to accept the output. If you set append = FALSE and the file already exists, it will be overwritten. If you set file = TRUE a connection is opened and subsequent output goes to the file.

# Send output to screen and file
> sink(file = "Out1.txt", split = TRUE, append = FALSE)

> summary(lm(Fertility ~ . , data = swiss))

Call:
lm(formula = Fertility ~ ., data = swiss)
Residuals:
     Min       1Q   Median       3Q      Max
-15.2743  -5.2617   0.5032   4.1198  15.3213

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)
(Intercept)      66.91518   10.70604   6.250 1.91e-07 ***
Agriculture      -0.17211    0.07030  -2.448  0.01873 *
Examination      -0.25801    0.25388  -1.016  0.31546
Education        -0.87094    0.18303  -4.758 2.43e-05 ***
Catholic          0.10412    0.03526   2.953  0.00519 **
Infant.Mortality  1.07705    0.38172   2.822  0.00734 **
—
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1

Residual standard error: 7.165 on 41 degrees of freedom
Multiple R-squared:  0.7067,     Adjusted R-squared:  0.671
F-statistic: 19.76 on 5 and 41 DF,  p-value: 5.594e-10

# Stop sending output to file
> sink(file = NULL)

Note that even if you set append = FALSE subsequent output is appended to the file. Once you issue the command sink(file = NULL) output stops and you can see your file using any kind of text editor.

If you only want to send a single “result” to a disk file you can use the capture.output() command instead.

capture.output(..., file = NULL, append = FALSE)

You provide the commands that will produce the output and the filename. If you set append = TRUE and the target file exists, the output will be added to the file. If you set append = FALSE (the default) the file will be “blanked” and the output will therefore overwrite the original contents.

Note that there is no equivalent of the split argument, all output goes to the file and cannot be “mirrored” to the console. You can supply several commands, separated by commas.

> capture.output(ls(), search(), file = "Out1.txt")

This example sent the ls() command followed by search(), with the results being output to the disk file.

Once you have your output in a text file you can transfer it to your word processor with a little pre-processing via Excel.

You can also use Paste Special and select the RTF format option, which takes Excel cells and transfers them as table cells in Word.

If you have other elements to transfer, you can deal with them separately. This is not an ideal method but the amount of user intervention is fairly minimal. You might also try opening the file in Word to start with and replacing spaces with Tab characters. You want to keep single spaces as spaces so start by replacing 3-space with 2-space until there are no more double spaces left. Then replace 2-space with Tab (^t in the Word replace box). You’ll need to do some manual editing as this will not produce a perfect result but it will do most of the work automatically. Then save the file and use Excel again, setting the delimiter to Tab.