Graphs

Graphs play a major role in Statistics. Here are some of the commonly used graphs:

Boxplot

This is a graph for quantitative data. It shows the numbers from the 5-number summary:

Minimum | Q₁ | Median | Q₃ | Maximum

plus some rules for identifying observations that are shown as stars. The boxplot is done with the command bplot. The first argument has to be the quantitative variable and the second one (if needed) the categorical one.

Here are several examples:

plt1 <- bplot(Example1, return.graph = TRUE)
plt2 <- bplot(Example2, return.graph = TRUE)
plt3 <- bplot(x, y, label_x="Example3", label_y="", 
      return.graph = TRUE)
multiple.graphs(plt1, plt2, plt3)

note the use of the multiple.graphs command to combine several graphs into one. We also need the the additional argument return.graph = TRUE.

We use the boxplot mostly for these:

Are there any unusually large or small observations?

These appear as stars in the boxplot, compare the graph in the upper right corner with the one in the upper left corner.

Connected to this is the following question:

Do the observations come from a normal distribution?

Most of the methods discussed in this course require that the observations of a variable come from a normal distribution. Problems with this assumption can often be seen in the boxplot. If there are stars (far away) from the box the normal assumption is wrong.

We have observations from several groups, how do they compare?

check out graph in lower left corner

Scatterplot

This graph is for two quantitative variables. It is just a Cartesion coordinate system with the observations plotted as points. We have the command splot(y, x) to do the graph. Here y is the variable that goes on the y axis.

Normal Plot

This is a graph specifically designed to check whether the observations follow a normal distribution. If this is true the dots should (roughly) be on a line:

we have the command nplot to do the graph.

Normal Assumption is correct:

Normal Assumption is wrong:

Case Study: Euro Coins

The data were collected by Herman Callaert at Hasselt University in Belgium. The euro coins were “borrowed” at a local bank. Two assistants, Sofie Bogaerts and Saskia Litiere weighted the coins one by one, in laboratory conditions on a weighing scale of the type Sartorius BP 310s.

Here is the boxplot and the normal plot of the weights:

attach(euros)
head(euros)

##   Weight Roll
## 1  7.512    1
## 2  7.502    1
## 3  7.461    1
## 4  7.562    1
## 5  7.528    1
## 6  7.459    1

bplot(Weight)

nplot(Weight)

It appears that the weights do not come from a normal distribution.

Marginal Plot

There is a nice graph that combines a scatterplot and boxplots called the marginal plot. We can do it with the mplot(y, x) command:

mplot(y, x)