Comparing Groups Script

In this movie, you'll learn how to use TinkerPlots features to make group comparisons.

We'll be looking at occupational data from 1985. We have information from 534 people, including their gender, education, and hourly wage.

Let's look at Wage, how much people make per hour. With Wage selected, drag a icon until the cases are fully separated.

Now each case appears over the Wage axis. Here's someone who is making 15 an hour, is a male who is 36 years old.

When we stack them up, we see that the distribution of wage is very skewed. There are a lot of people on the lower end earning 4,5 and 6 dollars an hour. As we move to higher hourly wages, 10 …… 20 and higher, we find fewer and fewer people. Recall that these data are from 1985. The minimum wage then was 3.50, which explains the pile of data here.

Let's see whether people in unions tend to make more than the people not in unions. Select that attribute, union, and make two groups by pulling up.

Some people might conclude from this graph that the non-union workers make more. Note that the highest wage here belongs to a non-union person. And if we look at those who make above 16, many more of them are non-union. Dividers are handy for comparing groups in this way. When we click on them, we get two dividers. If we now turn on counts, we can see the number of cases in each section.

Let's move this divider to just above 16. Go to the Dividers option, and uncheck Split Dividers. This makes one divider that goes across the two groups. Let's also move the right hand divider to the end of the data.

Now we see that 36 of the non-union workers earn more than about 16 compared to only 7 of the union members.

There's a problem with this argument, however. In this collection, there are many more non-union workers overall. We can use this button to display percents which take into account the different sizes of the groups. We see that the percents in each group are nearly equal, 8 vs. 7 percent.

Another way to compare groups is to see where they cluster. Let's split the dividers then adjust them. We might see the bulk of the non-union group as lying between, say 3.50 and 10 dollars an hour.

For the union group, we might locate the center clump between, say, 7 and 14. Note that the center clump of the union group is further to the right than the non-union group, suggesting that the union wages tend to be higher.

We can compare the medians of the two groups by clicking the median button. Again, the median of the union group is higher. If you'd like, you can display the values of the median right on the plot. We can now see that the median for union workers is about 3 dollars more than for the non-union workers.

Another useful tool for comparing groups is the hat plot. Let's make the plot icons smaller so we can better see the hats. Notice that the crowns of these hat plots are located roughly where we located the center clumps using the dividers. The brims of the hats extend out to the range of the data.

Right now the crown edges are set to contain about the middle 50% of the groups. But you can adjust these edges, or change the type of the hat. So it appears that union members make more on average than non-union members. But we should be careful how we interpret this difference.

First, notice how the union wages are distributed, fairly symmetrically. The non-union wages, however, are bunched up against this left wall, the minimum wage. This difference in shape is as important to consider as the difference in centers.

Second, the difference in wages might be due to differences in job type, education, or experience. We'll leave it up to you to explore these questions.