6.2.1 A tedious digression

Before we go into any discussion of customising plots, we need a little more background. The important thing to note when using the plot() function, is that it’s another example of a generic function (Section 4.11, much like print() and summary(), and so its behaviour changes depending on what kind of input you give it. However, the plot() function is somewhat fancier than the other two, and its behaviour depends on two arguments, x (the first input, which is required) and y (which is optional). This makes it (a) extremely powerful once you get the hang of it, and (b) hilariously unpredictable, when you’re not sure what you’re doing. As much as possible, I’ll try to make clear what type of inputs produce what kinds of outputs. For now, however, it’s enough to note that I’m only doing very basic plotting, and as a consequence all of the work is being done by the plot.default() function.

What kinds of customisations might we be interested in? If you look at the help documentation for the default plotting method (i.e., type ?plot.default or help("plot.default")) you’ll see a very long list of arguments that you can specify to customise your plot. I’ll talk about several of them in a moment, but first I want to point out something that might seem quite wacky. When you look at all the different options that the help file talks about, you’ll notice that some of the options that it refers to are “proper” arguments to the plot.default() function, but it also goes on to mention a bunch of things that look like they’re supposed to be arguments, but they’re not listed in the “Usage” section of the file, and the documentation calls them graphical parameters instead. Even so, it’s usually possible to treat them as if they were arguments of the plotting function. Very odd. In order to stop my readers trying to find a brick and look up my home address, I’d better explain what’s going on; or at least give the basic gist behind it.

What exactly is a graphical parameter? Basically, the idea is that there are some characteristics of a plot which are pretty universal: for instance, regardless of what kind of graph you’re drawing, you probably need to specify what colour to use for the plot, right? So you’d expect there to be something like a col argument to every single graphics function in R? Well, sort of. In order to avoid having hundreds of arguments for every single function, what R does is refer to a bunch of these “graphical parameters” which are pretty general purpose. Graphical parameters can be changed directly by using the low-level par() function, which I discuss briefly in Section 6.7.1 though not in a lot of detail. If you look at the help files for graphical parameters (i.e., type ?par) you’ll see that there’s lots of them. Fortunately, (a) the default settings are generally pretty good so you can ignore the majority of the parameters, and (b) as you’ll see as we go through this chapter, you very rarely need to use par() directly, because you can “pretend” that graphical parameters are just additional arguments to your high-level function (e.g. plot.default()). In short… yes, R does have these wacky “graphical parameters” which can be quite confusing. But in most basic uses of the plotting functions, you can act as if they were just undocumented additional arguments to your function.

6.2.2 Customising the title and the axis labels

One of the first things that you’ll find yourself wanting to do when customising your plot is to label it better. You might want to specify more appropriate axis labels, add a title or add a subtitle. The arguments that you need to specify to make this happen are:

• main. A character string containing the title.
• sub. A character string containing the subtitle.
• xlab. A character string containing the x-axis label.
• ylab. A character string containing the y-axis label.

These aren’t graphical parameters, they’re arguments to the high-level function. However, because the high-level functions all rely on the same low-level function to do the drawing⁹¹ the names of these arguments are identical for pretty much every high-level function I’ve come across. Let’s have a look at what happens when we make use of all these arguments. Here’s the command. The picture that this draws is shown in Figure 6.3.

plot( x = Fibonacci,
               main = "You specify title using the 'main' argument",
               sub = "The subtitle appears here! (Use the 'sub' argument for this)",
               xlab = "The x-axis label is 'xlab'",
                ylab = "The y-axis label is 'ylab'" 
            )

Figure 6.3: How to add your own title, subtitle, x-axis label and y-axis label to the plot.

It’s more or less as you’d expect. The plot itself is identical to the one we drew in Figure 6.2, except for the fact that we’ve changed the axis labels, and added a title and a subtitle. Even so, there’s a couple of interesting features worth calling your attention to. Firstly, notice that the subtitle is drawn below the plot, which I personally find annoying; as a consequence I almost never use subtitles. You may have a different opinion, of course, but the important thing is that you remember where the subtitle actually goes. Secondly, notice that R has decided to use boldface text and a larger font size for the title. This is one of my most hated default settings in R graphics, since I feel that it draws too much attention to the title. Generally, while I do want my reader to look at the title, I find that the R defaults are a bit overpowering, so I often like to change the settings. To that end, there are a bunch of graphical parameters that you can use to customise the font style:

• Font styles: font.main, font.sub, font.lab, font.axis. These four parameters control the font style used for the plot title (font.main), the subtitle (font.sub), the axis labels (font.lab: note that you can’t specify separate styles for the x-axis and y-axis without using low level commands), and the numbers next to the tick marks on the axis (font.axis). Somewhat irritatingly, these arguments are numbers instead of meaningful names: a value of 1 corresponds to plain text, 2 means boldface, 3 means italic and 4 means bold italic.
• Font colours: col.main, col.sub, col.lab, col.axis. These parameters do pretty much what the name says: each one specifies a colour in which to type each of the different bits of text. Conveniently, R has a very large number of named colours (type colours() to see a list of over 650 colour names that R knows), so you can use the English language name of the colour to select it.⁹² Thus, the parameter value here string like "red", "gray25" or "springgreen4" (yes, R really does recognise four different shades of “spring green”).
• Font size: cex.main, cex.sub, cex.lab, cex.axis. Font size is handled in a slightly curious way in R. The “cex” part here is short for “character expansion”, and it’s essentially a magnification value. By default, all of these are set to a value of 1, except for the font title: cex.main has a default magnification of 1.2, which is why the title font is 20% bigger than the others.
• Font family: family. This argument specifies a font family to use: the simplest way to use it is to set it to "sans", "serif", or "mono", corresponding to a san serif font, a serif font, or a monospaced font. If you want to, you can give the name of a specific font, but keep in mind that different operating systems use different fonts, so it’s probably safest to keep it simple. Better yet, unless you have some deep objections to the R defaults, just ignore this parameter entirely. That’s what I usually do.

To give you a sense of how you can use these parameters to customise your titles, the following command can be used to draw Figure 6.4:

plot( x = Fibonacci,                           # the data to plot
          main = "The first 7 Fibonacci numbers",  # the title
          xlab = "Position in the sequence",       # x-axis label
          ylab = "The Fibonacci number",           # y-axis 
          font.main = 1,
          cex.main = 1,
          font.axis = 2,
          col.lab = "gray50" )

Figure 6.4: How to customise the appearance of the titles and labels.

Although this command is quite long, it’s not complicated: all it does is override a bunch of the default parameter values. The only difficult aspect to this is that you have to remember what each of these parameters is called, and what all the different values are. And in practice I never remember: I have to look up the help documentation every time, or else look it up in this book.

6.2.3 Changing the plot type

Adding and customising the titles associated with the plot is one way in which you can play around with what your picture looks like. Another thing that you’ll want to do is customise the appearance of the actual plot! To start with, let’s look at the single most important options that the plot() function (or, recalling that we’re dealing with a generic function, in this case the plot.default() function, since that’s the one doing all the work) provides for you to use, which is the type argument. The type argument specifies the visual style of the plot. The possible values for this are:

• type = "p". Draw the points only.
• type = "l". Draw a line through the points.
• type = "o". Draw the line over the top of the points.
• type = "b". Draw both points and lines, but don’t overplot.
• type = "h". Draw “histogram-like” vertical bars.
• type = "s". Draw a staircase, going horizontally then vertically.
• type = "S". Draw a Staircase, going vertically then horizontally.
• type = "c". Draw only the connecting lines from the “b” version.
• type = "n". Draw nothing. (Apparently this is useful sometimes?)

The simplest way to illustrate what each of these really looks like is just to draw them. To that end, Figure 6.5 shows the same Fibonacci data, drawn using six different types of plot. As you can see, by altering the type argument you can get a qualitatively different appearance to your plot. In other words, as far as R is concerned, the only difference between a scatterplot (like the ones we drew in Section 5.7 and a line plot is that you draw a scatterplot by setting type = "p" and you draw a line plot by setting type = "l". However, that doesn’t imply that you should think of them as begin equivalent to each other. As you can see by looking at Figure 6.5, a line plot implies that there is some notion of continuity from one point to the next, whereas a scatterplot does not.

Figure 6.5: Changing the type of the plot.

6.2.4 Changing other features of the plot

In Section 6.2.2 we talked about a group of graphical parameters that are related to the formatting of titles, axis labels etc. The second group of parameters I want to discuss are those related to the formatting of the plot itself:

• Colour of the plot: col. As we saw with the previous colour-related parameters, the simplest way to specify this parameter is using a character string: e.g., col = "blue". It’s a pretty straightforward parameter to specify: the only real subtlety is that every high-level function tends to draw a different “thing” as it’s output, and so this parameter gets interpreted a little differently by different functions. However, for the plot.default() function it’s pretty simple: the col argument refers to the colour of the points and/or lines that get drawn!
• Character used to plot points: pch. The plot character parameter is a number, usually between 1 and 25. What it does is tell R what symbol to use to draw the points that it plots. The simplest way to illustrate what the different values do is with a picture. Figure 6.6 shows the first 25 plotting characters. The default plotting character is a hollow circle (i.e., pch = 1).

Figure 6.6: Changing the plotted characters

• Plot size: cex. This parameter describes a character expansion factor (i.e., magnification) for the plotted characters. By default cex=1, but if you want bigger symbols in your graph you should specify a larger value.
• Line type: lty. The line type parameter describes the kind of line that R draws. It has seven values which you can specify using a number between 0 and 7, or using a meaningful character string: "blank", "solid", "dashed", "dotted", "dotdash", "longdash", or "twodash". Note that the “blank” version (value 0) just means that R doesn’t draw the lines at all. The other six versions are shown in Figure 6.7.

Figure 6.7: Line types

• Line width: lwd. The last graphical parameter in this category that I want to mention is the line width parameter, which is just a number specifying the width of the line. The default value is 1. Not surprisingly, larger values produce thicker lines and smaller values produce thinner lines. Try playing around with different values of lwd to see what happens.

To illustrate what you can do by altering these parameters, let’s try the following command, the output is shown in Figure 6.8.

plot( x = Fibonacci,
         type = "b",
         col = "blue",
         pch = 19,
         cex=5,
         lty=2,
         lwd=4)

Figure 6.8: Customising various aspects to the plot itself.

6.2.5 Changing the appearance of the axes

There are several other possibilities worth discussing. Ignoring graphical parameters for the moment, there’s a few other arguments to the plot.default() function that you might want to use. As before, many of these are standard arguments that are used by a lot of high level graphics functions:

• Changing the axis scales: xlim, ylim. Generally R does a pretty good job of figuring out where to set the edges of the plot. However, you can override its choices by setting the xlim and ylim arguments. For instance, if I decide I want the vertical scale of the plot to run from 0 to 100, then I’d set ylim = c(0, 100).
• Suppress labelling: ann. This is a logical-valued argument that you can use if you don’t want R to include any text for a title, subtitle or axis label. To do so, set ann = FALSE. This will stop R from including any text that would normally appear in those places. Note that this will override any of your manual titles. For example, if you try to add a title using the main argument, but you also specify ann = FALSE, no title will appear.
• Suppress axis drawing: axes. Again, this is a logical valued argument. Suppose you don’t want R to draw any axes at all. To suppress the axes, all you have to do is add axes = FALSE. This will remove the axes and the numbering, but not the axis labels (i.e. the xlab and ylab text). Note that you can get finer grain control over this by specifying the xaxt and yaxt graphical parameters instead (see below).
• Include a framing box: frame.plot. Suppose you’ve removed the axes by setting axes = FALSE, but you still want to have a simple box drawn around the plot; that is, you only wanted to get rid of the numbering and the tick marks, but you want to keep the box. To do that, you set frame.plot = TRUE.

Note that this list isn’t exhaustive. There are a few other arguments to the plot.default function that you can play with if you want to, but those are the ones you are probably most likely to want to use. As always, however, if these aren’t enough options for you, there’s also a number of other graphical parameters that you might want to play with as well. That’s the focus of the next section. In the meantime, here’s a command that makes use of all these different options. The output is shown in Figure 6.9, and it’s pretty much exactly as you’d expect. The axis scales on both the horizontal and vertical dimensions have been expanded, the axes have been suppressed as have the annotations, but I’ve kept a box around the plot.

plot( x = Fibonacci,       # the data
       xlim = c(0, 15),     # expand the x-scale
       ylim = c(0, 15),     # expand the y-scale
       ann = FALSE,         # delete all annotations
       axes = FALSE,        # delete the axes
       frame.plot = TRUE    # but include a framing box
 )

Figure 6.9: Altering the scale and appearance of the plot axes.

Before moving on, I should point out that there are several graphical parameters relating to the axes, the box, and the general appearance of the plot which allow finer grain control over the appearance of the axes and the annotations.

• Suppressing the axes individually: xaxt, yaxt. These graphical parameters are basically just fancier versions of the axes argument we discussed earlier. If you want to stop R from drawing the vertical axis but you’d like it to keep the horizontal axis, set yaxt = "n". I trust that you can figure out how to keep the vertical axis and suppress the horizontal one!
• Box type: bty. In the same way that xaxt, yaxt are just fancy versions of axes, the box type parameter is really just a fancier version of the frame.plot argument, allowing you to specify exactly which out of the four borders you want to keep. The way we specify this parameter is a bit stupid, in my opinion: the possible values are "o" (the default), "l", "7", "c", "u", or "]", each of which will draw only those edges that the corresponding character suggests. That is, the letter "c" has a top, a bottom and a left, but is blank on the right hand side, whereas "7" has a top and a right, but is blank on the left and the bottom. Alternatively a value of "n" means that no box will be drawn.
• Orientation of the axis labels las. I presume that the name of this parameter is an acronym of label style or something along those lines; but what it actually does is govern the orientation of the text used to label the individual tick marks (i.e., the numbering, not the xlab and ylab axis labels). There are four possible values for las: A value of 0 means that the labels of both axes are printed parallel to the axis itself (the default). A value of 1 means that the text is always horizontal. A value of 2 means that the labelling text is printed at right angles to the axis. Finally, a value of 3 means that the text is always vertical.

Again, these aren’t the only possibilities. There are a few other graphical parameters that I haven’t mentioned that you could use to customise the appearance of the axes,⁹³ but that’s probably enough (or more than enough) for now. To give a sense of how you could use these parameters, let’s try the following command. The output is shown in Figure 6.10. As you can see, this isn’t a very useful plot at all. However, it does illustrate the graphical parameters we’re talking about, so I suppose it serves its purpose.

    plot( x = Fibonacci, # the data
         xaxt = "n",       # don't draw the x-axis  
         bty = "]",        # keep bottom, right and top of box only
         las = 1 )         # rotate the text

Figure 6.10: Other ways to customise the axes

6.2.6 Don’t panic

At this point, a lot of readers will be probably be thinking something along the lines of, “if there’s this much detail just for drawing a simple plot, how horrible is it going to get when we start looking at more complicated things?” Perhaps, contrary to my earlier pleas for mercy, you’ve found a brick to hurl and are right now leafing through an Adelaide phone book trying to find my address. Well, fear not! And please, put the brick down. In a lot of ways, we’ve gone through the hardest part: we’ve already covered vast majority of the plot customisations that you might want to do. As you’ll see, each of the other high level plotting commands we’ll talk about will only have a smallish number of additional options. Better yet, even though I’ve told you about a billion different ways of tweaking your plot, you don’t usually need them. So in practice, now that you’ve read over it once to get the gist, the majority of the content of this section is stuff you can safely forget: just remember to come back to this section later on when you want to tweak your plot.

6.3.1 Visual style of your histogram

Okay, so at this point we can draw a basic histogram, and we can alter the number and even the location of the breaks. However, the visual style of the histograms shown in Figures 6.11, 6.12, and 6.13 could stand to be improved. We can fix this by making use of some of the other arguments to the hist() function. Most of the things you might want to try doing have already been covered in Section 6.2, but there’s a few new things:

• Shading lines: density, angle. You can add diagonal lines to shade the bars: the density value is a number indicating how many lines per inch R should draw (the default value of NULL means no lines), and the angle is a number indicating how many degrees from horizontal the lines should be drawn at (default is angle = 45 degrees).
• Specifics regarding colours: col, border. You can also change the colours: in this instance the col parameter sets the colour of the shading (either the shading lines if there are any, or else the colour of the interior of the bars if there are not), and the border argument sets the colour of the edges of the bars.
• Labelling the bars: labels. You can also attach labels to each of the bars using the labels argument. The simplest way to do this is to set labels = TRUE, in which case R will add a number just above each bar, that number being the exact number of observations in the bin. Alternatively, you can choose the labels yourself, by inputting a vector of strings, e.g., labels = c("label 1","label 2","etc")

Not surprisingly, this doesn’t exhaust the possibilities. If you type help("hist") or ?hist and have a look at the help documentation for histograms, you’ll see a few more options. A histogram that makes use of the histogram-specific customisations as well as several of the options we discussed in Section 6.2 is shown in Figure 6.14. The R command that I used to draw it is this:

hist( x = afl.margins, 
      main = "2010 AFL margins", # title of the plot
      xlab = "Margin",           # set the x-axis label
      density = 10,              # draw shading lines: 10 per inch
      angle = 40,                # set the angle of the shading lines is 40 degrees
      border = "gray20",         # set the colour of the borders of the bars
      col = "gray80",            # set the colour of the shading lines
      labels = TRUE,             # add frequency labels to each bar
      ylim = c(0,40)             # change the scale of the y-axis
)

Figure 6.14: A histogram with histogram specific customisations

Overall, this is a much nicer histogram than the default ones.

6.5.1 Visual style of your boxplot

I’ll talk a little more about the relationship between boxplots and outliers in the Section 6.5.2, but before I do let’s take the time to clean this figure up. Boxplots in R are extremely customisable. In addition to the usual range of graphical parameters that you can tweak to make the plot look nice, you can also exercise nearly complete control over every element to the plot. Consider the boxplot in Figure 6.18: in this version of the plot, not only have I added labels (xlab, ylab) and removed the stupid border (frame.plot), I’ve also dimmed all of the graphical elements of the boxplot except the central bar that plots the median (border) so as to draw more attention to the median rather than the rest of the boxplot.

Figure 6.18: A boxplot with boxplot specific customisations

You’ve seen all these options in previous sections in this chapter, so hopefully those customisations won’t need any further explanation. However, I’ve done two new things as well: I’ve deleted the cross-bars at the top and bottom of the whiskers (known as the “staples” of the plot), and converted the whiskers themselves to solid lines. The arguments that I used to do this are called by the ridiculous names of staplewex and whisklty,⁹⁵ and I’ll explain these in a moment.

But first, here’s the actual command I used to draw this figure:

boxplot( x = afl.margins,           # the data
          xlab = "AFL games, 2010",  # x-axis label
          ylab = "Winning Margin",   # y-axis label
          border = "grey50",         # dim the border of the box
          frame.plot = FALSE,        # don't draw a frame
          staplewex = 0,             # don't draw staples
          whisklty = 1               # solid line for whisker 
 )

Overall, I think the resulting boxplot is a huge improvement in visual design over the default version. In my opinion at least, there’s a fairly minimalist aesthetic that governs good statistical graphics. Ideally, every visual element that you add to a plot should convey part of the message. If your plot includes things that don’t actually help the reader learn anything new, you should consider removing them. Personally, I can’t see the point of the cross-bars on a standard boxplot, so I’ve deleted them.

Okay, what commands can we use to customise the boxplot? If you type ?boxplot and flick through the help documentation, you’ll notice that it does mention staplewex as an argument, but there’s no mention of whisklty. The reason for this is that the function that handles the drawing is called bxp(), so if you type ?bxp all the gory details appear. Here’s the short summary. In order to understand why these arguments have such stupid names, you need to recognise that they’re put together from two components. The first part of the argument name specifies one part of the box plot: staple refers to the staples of the plot (i.e., the cross-bars), and whisk refers to the whiskers. The second part of the name specifies a graphical parameter: wex is a width parameter, and lty is a line type parameter. The parts of the plot you can customise are:

• box. The box that covers the interquartile range.
• med. The line used to show the median.
• whisk. The vertical lines used to draw the whiskers.
• staple. The cross bars at the ends of the whiskers.
• out. The points used to show the outliers.

The actual graphical parameters that you might want to specify are slightly different for each visual element, just because they’re different shapes from each other. As a consequence, the following options are available:

• Width expansion: boxwex, staplewex, outwex. These are scaling factors that govern the width of various parts of the plot. The default scaling factor is (usually) 0.8 for the box, and 0.5 for the other two. Note that in the case of the outliers this parameter is meaningless unless you decide to draw lines plotting the outliers rather than use points.
• Line type: boxlty, medlty, whisklty, staplelty, outlty. These govern the line type for the relevant elements. The values for this are exactly the same as those used for the regular lty parameter, with two exceptions. There’s an additional option where you can set medlty = "blank" to suppress the median line completely (useful if you want to draw a point for the median rather than plot a line). Similarly, by default the outlier line type is set to outlty = "blank", because the default behaviour is to draw outliers as points instead of lines.
• Line width: boxlwd, medlwd, whisklwd, staplelwd, outlwd. These govern the line widths for the relevant elements, and behave the same way as the regular lwd parameter. The only thing to note is that the default value for medlwd value is three times the value of the others.
• Line colour: boxcol, medcol, whiskcol, staplecol, outcol. These govern the colour of the lines used to draw the relevant elements. Specify a colour in the same way that you usually do.
• Fill colour: boxfill. What colour should we use to fill the box?
• Point character: medpch, outpch. These behave like the regular pch parameter used to select the plot character. Note that you can set outpch = NA to stop R from plotting the outliers at all, and you can also set medpch = NA to stop it from drawing a character for the median (this is the default!)
• Point expansion: medcex, outcex. Size parameters for the points used to plot medians and outliers. These are only meaningful if the corresponding points are actually plotted. So for the default boxplot, which includes outlier points but uses a line rather than a point to draw the median, only the outcex parameter is meaningful.
• Background colours: medbg, outbg. Again, the background colours are only meaningful if the points are actually plotted.

Taken as a group, these parameters allow you almost complete freedom to select the graphical style for your boxplot that you feel is most appropriate to the data set you’re trying to describe. That said, when you’re first starting out there’s no shame in using the default settings! But if you want to master the art of designing beautiful figures, it helps to try playing around with these parameters to see what works and what doesn’t. Finally, I should mention a few other arguments that you might want to make use of:

• horizontal. Set this to TRUE to display the plot horizontally rather than vertically.
• varwidth. Set this to TRUE to get R to scale the width of each box so that the areas are proportional to the number of observations that contribute to the boxplot. This is only useful if you’re drawing multiple boxplots at once (see Section 6.5.3.
• show.names. Set this to TRUE to get R to attach labels to the boxplots.
• notch. If you set notch = TRUE, R will draw little notches in the sides of each box. If the notches of two boxplots don’t overlap, then there is a “statistically significant” difference between the corresponding medians. If you haven’t read Chapter 11, ignore this argument – we haven’t discussed statistical significance, so this doesn’t mean much to you. I’m mentioning it only because you might want to come back to the topic later on. (see also the notch.frac option when you type ?bxp).

6.5.2 Using box plots to detect outliers

Because the boxplot automatically (unless you change the range argument) separates out those observations that lie within a certain range, people often use them as an informal method for detecting outliers: observations that are “suspiciously” distant from the rest of the data. Here’s an example. Suppose that I’d drawn the boxplot for the AFL margins data, and it came up looking like Figure 6.19.

Figure 6.19: A boxplot showing one very suspicious outlier! I’ve drawn this plot in a similar, minimalist style to the one in Figure 6.18, but I’ve used the horizontal argument to draw it sideways in order to save space.

It’s pretty clear that something funny is going on with one of the observations. Apparently, there was one game in which the margin was over 300 points! That doesn’t sound right to me. Now that I’ve become suspicious, it’s time to look a bit more closely at the data. One function that can be handy for this is the which() function; it takes as input a vector of logicals, and outputs the indices of the TRUE cases. This is particularly useful in the current context because it lets me do this:

suspicious.cases <- afl.margins > 300
which( suspicious.cases )

## [1] 137

although in real life I probably wouldn’t bother creating the suspicious.cases variable: I’d just cut out the middle man and use a command like which( afl.margins > 300 ). In any case, what this has done is shown me that the outlier corresponds to game 137. Then, I find the recorded margin for that game:

afl.margins[137]

## [1] 333

Hm. That definitely doesn’t sound right. So then I go back to the original data source (the internet!) and I discover that the actual margin of that game was 33 points. Now it’s pretty clear what happened. Someone must have typed in the wrong number. Easily fixed, just by typing afl.margins[137] <- 33. While this might seem like a silly example, I should stress that this kind of thing actually happens a lot. Real world data sets are often riddled with stupid errors, especially when someone had to type something into a computer at some point. In fact, there’s actually a name for this phase of data analysis, since in practice it can waste a huge chunk of our time: data cleaning. It involves searching for typos, missing data and all sorts of other obnoxious errors in raw data files.⁹⁶

What about the real data? Does the value of 116 constitute a funny observation not? Possibly. As it turns out the game in question was Fremantle v Hawthorn, and was played in round 21 (the second last home and away round of the season). Fremantle had already qualified for the final series and for them the outcome of the game was irrelevant; and the team decided to rest several of their star players. As a consequence, Fremantle went into the game severely underpowered. In contrast, Hawthorn had started the season very poorly but had ended on a massive winning streak, and for them a win could secure a place in the finals. With the game played on Hawthorn’s home turf⁹⁷ and with so many unusual factors at play, it is perhaps no surprise that Hawthorn annihilated Fremantle by 116 points. Two weeks later, however, the two teams met again in an elimination final on Fremantle’s home ground, and Fremantle won comfortably by 30 points.⁹⁸

So, should we exclude the game from subsequent analyses? If this were a psychology experiment rather than an AFL season, I’d be quite tempted to exclude it because there’s pretty strong evidence that Fremantle weren’t really trying very hard: and to the extent that my research question is based on an assumption that participants are genuinely trying to do the task. On the other hand, in a lot of studies we’re actually interested in seeing the full range of possible behaviour, and that includes situations where people decide not to try very hard: so excluding that observation would be a bad idea. In the context of the AFL data, a similar distinction applies. If I’d been trying to make tips about who would perform well in the finals, I would have (and in fact did) disregard the Round 21 massacre, because it’s way too misleading. On the other hand, if my interest is solely in the home and away season itself, I think it would be a shame to throw away information pertaining to one of the most distinctive (if boring) games of the year. In other words, the decision about whether to include outliers or exclude them depends heavily on why you think the data look they way they do, and what you want to use the data for. Statistical tools can provide an automatic method for suggesting candidates for deletion, but you really need to exercise good judgment here. As I’ve said before, R is a mindless automaton. It doesn’t watch the footy, so it lacks the broader context to make an informed decision. You are not a mindless automaton, so you should exercise judgment: if the outlier looks legitimate to you, then keep it. In any case, I’ll return to the topic again in Section 15.9, so let’s return to our discussion of how to draw boxplots.

6.5.3 Drawing multiple boxplots

One last thing. What if you want to draw multiple boxplots at once? Suppose, for instance, I wanted separate boxplots showing the AFL margins not just for 2010, but for every year between 1987 and 2010. To do that, the first thing we’ll have to do is find the data. These are stored in the aflsmall2.Rdata file. So let’s load it and take a quick peek at what’s inside:

load( "aflsmall2.Rdata" )
who( TRUE )
#   -- Name --   -- Class --   -- Size --
#   afl2         data.frame    4296 x 2  
#    $margin     numeric       4296      
#    $year       numeric       4296     

Notice that afl2 data frame is pretty big. It contains 4296 games, which is far more than I want to see printed out on my computer screen. To that end, R provides you with a few useful functions to print out only a few of the row in the data frame. The first of these is head() which prints out the first 6 rows, of the data frame, like this:

head( afl2 )

##   margin year
## 1     33 1987
## 2     59 1987
## 3     45 1987
## 4     91 1987
## 5     39 1987
## 6      1 1987

You can also use the tail() function to print out the last 6 rows. The car package also provides a handy little function called some() which prints out a random subset of the rows.

In any case, the important thing is that we have the afl2 data frame which contains the variables that we’re interested in. What we want to do is have R draw boxplots for the margin variable, plotted separately for each separate year. The way to do this using the boxplot() function is to input a formula rather than a variable as the input. In this case, the formula we want is margin ~ year. So our boxplot command now looks like this. The result is shown in Figure 6.20.⁹⁹

boxplot( formula = margin ~ year,
         data = afl2
)

Figure 6.20: Boxplots showing the AFL winning margins for the 24 years from 1987 to 2010 inclusive. This is the default plot created by R, with no annotations added and no changes to the visual design. It’s pretty readable, though at a minimum you’d want to include some basic annotations labelling the axes. Compare and contrast with Figure 6.21

Even this, the default version of the plot, gives a sense of why it’s sometimes useful to choose boxplots instead of histograms. Even before taking the time to turn this basic output into something more readable, it’s possible to get a good sense of what the data look like from year to year without getting overwhelmed with too much detail. Now imagine what would have happened if I’d tried to cram 24 histograms into this space: no chance at all that the reader is going to learn anything useful.

That being said, the default boxplot leaves a great deal to be desired in terms of visual clarity. The outliers are too visually prominent, the dotted lines look messy, and the interesting content (i.e., the behaviour of the median and the interquartile range across years) gets a little obscured. Fortunately, this is easy to fix, since we’ve already covered a lot of tools you can use to customise your output. After playing around with several different versions of the plot, the one I settled on is shown in Figure 6.21. The command I used to produce it is long, but not complicated:

boxplot( formula =  margin ~ year,   # the formula
           data = afl2,                # the data set
           xlab = "AFL season",        # x axis label
           ylab = "Winning Margin",    # y axis label
           frame.plot = FALSE,         # don't draw a frame
           staplewex = 0,              # don't draw staples
           staplecol = "white",        # (fixes a tiny display issue)
           boxwex = .75,               # narrow the boxes slightly
           boxfill = "grey80",         # lightly shade the boxes
           whisklty = 1,               # solid line for whiskers 
           whiskcol = "grey70",        # dim the whiskers
           boxcol = "grey70",          # dim the box borders
           outcol = "grey70",          # dim the outliers
           outpch = 20,                # outliers as solid dots
           outcex = .5,                # shrink the outliers
           medlty = "blank",           # no line for the medians
           medpch = 20,                # instead, draw solid dots
           medlwd = 1.5                # make them larger
 )

Figure 6.21: A cleaned up version of Figure 6.20. Notice that I’ve used a very minimalist design for the boxplots, so as to focus the eye on the medians. I’ve also converted the medians to solid dots, to convey a sense that year to year variation in the median should be thought of as a single coherent plot (similar to what we did when plotting the Fibonacci variable earlier). The size of outliers has been shrunk, because they aren’t actually very interesting. In contrast, I’ve added a fill colour to the boxes, to make it easier to look at the trend in the interquartile range across years.

Of course, given that the command is that long, you might have guessed that I didn’t spend ages typing all that rubbish in over and over again. Instead, I wrote a script, which I kept tweaking until it produced the figure that I wanted. We’ll talk about scripts later in Section 8.1, but given the length of the command I thought I’d remind you that there’s an easier way of trying out different commands than typing them all in over and over.

6.6.1 More elaborate options

Often you find yourself wanting to look at the relationships between several variables at once. One useful tool for doing so is to produce a scatterplot matrix, analogous to the correlation matrix.

cor( x = parenthood ) # calculate correlation matrix

##              dan.sleep  baby.sleep   dan.grump         day
## dan.sleep   1.00000000  0.62794934 -0.90338404 -0.09840768
## baby.sleep  0.62794934  1.00000000 -0.56596373 -0.01043394
## dan.grump  -0.90338404 -0.56596373  1.00000000  0.07647926
## day        -0.09840768 -0.01043394  0.07647926  1.00000000

We can get a the corresponding scatterplot matrix by using the pairs() function:¹⁰²

pairs( x = parenthood ) # draw corresponding scatterplot matrix  

Figure 6.25: A scatterplot matrix from the `pairs() function

The output of the pairs() command is shown in Figure 6.25. An alternative way of calling the pairs() function, which can be useful in some situations, is to specify the variables to include using a one-sided formula. For instance, this

pairs( formula = ~ dan.sleep + baby.sleep + dan.grump,
        data = parenthood
)

would produce a \(3 \times 3\) scatterplot matrix that only compare dan.sleep, dan.grump and baby.sleep. Obviously, the first version is much easier, but there are cases where you really only want to look at a few of the variables, so it’s nice to use the formula interface.

6.7.1 Changing global settings using par()

Altering the margins to the plot is actually a somewhat more complicated exercise than you might think. In principle it’s a very simple thing to do: the size of the margins is governed by a graphical parameter called mar, so all we need to do is alter this parameter. First, let’s look at what the mar argument specifies. The mar argument is a vector containing four numbers: specifying the amount of space at the bottom, the left, the top and then the right. The units are “number of ‘lines’”. The default value for mar is c(5.1, 4.1, 4.1, 2.1), meaning that R leaves 5.1 “lines” empty at the bottom, 4.1 lines on the left and the bottom, and only 2.1 lines on the right. In order to make more room at the bottom, what I need to do is change the first of these numbers. A value of 10.1 should do the trick.

So far this doesn’t seem any different to the other graphical parameters that we’ve talked about. However, because of the way that the traditional graphics system in R works, you need to specify what the margins will be before calling your high-level plotting function. Unlike the other cases we’ve see, you can’t treat mar as if it were just another argument in your plotting function. Instead, you have to use the par() function to change the graphical parameters beforehand, and only then try to draw your figure. In other words, the first thing I would do is this:

par( mar = c( 10.1, 4.1, 4.1, 2.1) )

There’s no visible output here, but behind the scenes R has changed the graphical parameters associated with the current device (remember, in R terminology all graphics are drawn onto a “device”). Now that this is done, we could use the exact same command as before, but this time you’d see that the labels all fit, because R now leaves twice as much room for the labels at the bottom. However, since I’ve now figured out how to get the labels to display properly, I might as well play around with some of the other options, all of which are things you’ve seen before:

barplot( height = freq,
        names.arg = teams,
        las=2,
        ylab = "Number of Finals",
        main = "Finals Played, 1987-2010",  
        density = 10,
        angle = 20)

Figure 6.29: we fix this by expanding the margin at the bottom, and add several other customisations to make the chart a bit nicer

However, one thing to remember about the par() function is that it doesn’t just change the graphical parameters for the current plot. Rather, the changes pertain to any subsequent plot that you draw onto the same device. This might be exactly what you want, in which case there’s no problem. But if not, you need to reset the graphical parameters to their original settings. To do this, you can either close the device (e.g., close the window, or click the “Clear All” button in the Plots panel in Rstudio) or you can reset the graphical parameters to their original values, using a command like this:

par( mar = c(5.1, 4.1, 4.1, 2.1) )

6.8.1 The ugly details (advanced)

As I say, the menu-based options should be good enough for most people most of the time. However, one day you might want to be a bit more sophisticated, and make use of R’s image writing capabilities at a lower level. In this section I’ll give you a very basic introduction to this. In all honesty, this barely scratches the surface, but it will help a little bit in getting you started if you want to learn the details.

Okay, as I hinted earlier, whenever you’re drawing pictures in R you’re deemed to be drawing to a device of some kind. There are devices that correspond to a figure drawn on screen, and there are devices that correspond to graphics files that R will produce for you. For the purposes of this section I’ll assume that you’re using the default application in either Windows or Mac OS, not Rstudio. The reason for this is that my experience with the graphical device provided by Rstudio has led me to suspect that it still has a bunch on non-standard (or possibly just undocumented) features, and so I don’t quite trust that it always does what I expect. I’ve no doubt they’ll smooth it out later, but I can honestly say that I don’t quite get what’s going on with the RStudioGD device. In any case, we can ask R to list all of the graphics devices that currently exist, simply by using the command dev.list(). If there are no figure windows open, then you’ll see this:

dev.list()
# NULL

which just means that R doesn’t have any graphics devices open. However, suppose if you’ve just drawn a histogram and you type the same command, R will now give you a different answer. For instance, if you’re using Windows:

hist( afl.margins )
dev.list()
# windows 
#      2

What this means is that there is one graphics device (device 2) that is currently open, and it’s a figure window. If you did the same thing on a Mac, you get basically the same answer, except that the name of the device would be quartz rather than windows. If you had several graphics windows open (which, incidentally, you can do by using the dev.new() command) then you’d see something like this:

dev.list()
# windows windows windows  
#       2       3       4 

Okay, so that’s the basic idea behind graphics devices. The key idea here is that graphics files (like JPEG images etc) are also graphics devices as far as R is concerned. So what you want to do is to copy the contents of one graphics device to another one. There’s a command called dev.copy() that does this, but what I’ll explain to you is a simpler one called dev.print(). It’s pretty simple:

dev.print( device = jpeg,              # what are we printing to?
            filename = "thisfile.jpg",  # name of the image file
            width = 480,                # how many pixels wide should it be
            height = 300                # how many pixels high should it be
)

This takes the “active” figure window, copies it to a jpeg file (which R treats as a device) and then closes that device. The filename = "thisfile.jpg" part tells R what to name the graphics file, and the width = 480 and height = 300 arguments tell R to draw an image that is 300 pixels high and 480 pixels wide. If you want a different kind of file, just change the device argument from jpeg to something else. R has devices for png, tiff and bmp that all work in exactly the same way as the jpeg command, but produce different kinds of files. Actually, for simple cartoonish graphics like this histogram, you’d be better advised to use PNG or TIFF over JPEG. The JPEG format is very good for natural images, but is wasteful for simple line drawings. The information above probably covers most things you might want to. However, if you want more information about what kinds of options you can specify using R, have a look at the help documentation by typing ?jpeg or ?tiff or whatever.