Heterogeneous Subsamples of Data

This applet allows you to look at the relationship between X and Y for a combined data set or for individual subsamples of data

The first applet follows:

This applet illustrates one form of what is called Simpson's Paradox, which is a set of data that shows one kind of a relationship when you look at separate subsets of the data, but quite a different form when you look at the combined data.

Notice how the data within each set have a distinctly negative relationship. Then look at the combined data and note the strong positive relationship.

• How would you report such a result if these were your data?
• Notice that the first subset is distinctly to the left of the observations in the second subset. They are also lower, but not by much. What would happen if we eliniated the difference between the two sets along the X axis? To see what would happen, I created another data set in which I have added 12 points to the X values for the first subset, thus displacing them to the right. Make a guess what you think will happen, and then click here .to see the new graph

The next applet is shown below. These are the data that you saw in Figure 9.8 on the relationship between height and weight in males and females.

• What would you conclude about the slopes in the two situations?
• I would argue that differences in intercepts are more interesting here. Why might I think that?

Comments to: Gary.McClelland@Colorado.edu

Return to index