
COMPARISON PLOT 

The COMPARISON PLOT uses what is usually known as a Quantile-Quantile plot (QQ-Plot) to aid you in comparing the distributions of two numeric variables. In the QQ-plot, the quantiles of two variables are plotted against each other, forming the jagged blue line. This line represents the relationship between the two distributions. Since, for these data, the two variables have the same number of observations,the jagged blue line is  simply a plot of one sorted variable against the other sorted variable.

The blue line on the QQ-Plot tells us whether the two variables have distributions that have the same shape. If the line is roughly straight, the two variables have roughly the same shape. This is important to know, since many analyses assume that the variables are "identically" distributed, which means they have the same shape. When two variables are normally distributed, for example, they have the same shape.

CENTER AND SPREAD:
The straight dashed black line represents two identically distributed variables (this line does not appear when the centers of the two variables are very different). The straight red line represents two variables whose distributions are the same shape and which have measures of center and spread which are like those of the observed variables. Such distributions are geometrically "similar", since they have the same shape.

When the dashed and red lines are parallel but not near each other, the measures of spread of the observed distributions are about the same, but the centers are different. The the two lines are near each other but not parallel, then the observed distributions have roughly the same centers, but different spreads.

The measures of center and spread that are compared in this plot are the mean and variance of the quantiles. If the jagged blue line is systematically different from a straight line the distributions of the two variables do not have the same shape, and are not geometrically similar. Outliers appear as large deviations from the straight line.

If the jagged blue line is roughly straight, the two variables have aproximately the same shaped distributions. If the blue line approximately follows the dashed line, then the two distributions are roughly identical. If it approximately follows the red line, but not the dashed line, the two distributions are "similar", but have different centers and spreads.

When you click on the X or Y buttons at the top of the graph you will be presented with a list of variables to display. Clicking on a variable will change the plot to display the variable on the X or Y axis. 
