Graphs play a major role in Statistics. Here are some of the commonly used graphs:
Boxplot
This is a graph for continuous 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 graph is done with the commands Graph > Boxplot > ...
We use the boxplot mostly for two reasons:
Are there unusually large or small observations in a variable?
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 of a variable 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 right corner
Scatterplot
This graph is for two continuous variables. It is just a Cartesion coordinate system with the observations plotted as points (upper left corner)
Often we add a line that in some way describes the relationship between the variables. If there is none the line should be flat. (upper right corner vs. lower left corner)
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:
Normal Assumption is ok:
Normal Assumption is wrong:
Example Consider the data on Euro coins. Here is the boxplot and the normal plot of the weights:
It appears that the weights do not come from a normal distribution.
Marginal Plot
This is a combination of the boxplot and the scatterplot:
Graph Matrix
In some of the graphs above we have several graphs combined and laid out in a square. This is a nice thing to do, mostly to save space (and paper!) It is done as follows:
Step 1: generate the graphs you want to include
Step 2: Editor > Layout Tool