I’m always on the lookout for statistical news, so I was excited by the recent Matt Phillips article on Quartz titled Painfully, American families are learning the difference between median and mean. Phillips' allegory about Warren Buffet walking into a skid row bar makes a nice illustration of the statistical question about how outliers affect the mean. (If you want more on the mean and median, we showed you how to spot when the mean can mislead with Michael Jordan in 2012.)
Rather than do more on the mean and the median, I’m going to explore the income trends that Phillips graphs to illustrate ways that you can edit scatterplots in Minitab. Graphs are powerful tools for explaining the data, and the graphs that Minitab produces by default are usually excellent. However, the duty of the analyst is to make sure that graphs help people make the best decisions possible. Minitab provides numerous tools that make it fast and easy for you to clarify the meaning in your data.
The data that Phillips uses are from the Federal Reserve’s 2013 Survey of Consumer Finances. All amounts have been converted to 2013 dollars so that changes are not due to inflation.
What makes this graph painful
The first graph that Phillips shows in the article displays the trend in what’s happening to the mean household income and the median household income over time. When I recreate it from the tables the Federal Reserve published in an Excel file, it looks like this:
Phillips echoes the same point that the authors of the Federal Reserve’s report do. The growth in average income since the 2010 survey is largely due to increases in the highest 10 percent of incomes. The decline in the median at the same time suggests that typical Americans are not doing as well.
Easing the pain
If all we wanted to do was make the situation look less dire on a graph, Minitab provides some easy-to-use features that can change the message of this graph.
Edit the scale
- Double-click the numbers on the y-scale
- In Scale Range, Uncheck Auto.
- Enter new values.
By default, Minitab does a good job of editing your scales to contain your data, but sometimes different values can be meaningful. For example, you can change the y-scale so that it contains 0—the lowest income that someone can have. The change in scale has two pronounced effects on the graph. Let’s look at them side-by-side to make the comparison easier.
The median wage looks higher.
The first thing you probably notice in the new graph is that the median wage is shown much higher on the figure. On the original graph, the median was about as low as you could get, but the message of the new graph is that the median is in the middle. The vertical lines illustrate the distance from the bottom of the graph to the median.
The difference between the mean and the median looks smaller.
Take a look at the length of the line between the points in 2013. With the extra space at the bottom of the graph, the mean and median are a lot closer together on the graph than they were before. The vertical lines here illustrate the distance between the mean and the median.
Add a reference line.
Choose Editor > Add > Reference Lines.
The economist and philosopher John Stuart Mill is credited with the saying: “Men do not desire to be rich, but to be richer than other men.” Thus, when we compare the mean to the median, the median looks low. Changing the point of comparison can make the median look higher. For example, we can add to the plot the 2014 guideline for a family of 4 to qualify for Medicaid and CHIP in the 48 contiguous U.S. states and the District of Columbia.
With the median now in the middle of two points of comparison, we reinforce the visual impression that the median is not low.
Add a regression fit.
Choose Editor > Add > Regression Fit.
Phillips and the report from the federal reserve note that median wages were lower in 2010 than in 2007 and lower in 2013 than in 2010. But the data on the graph go back to the Survey of Consumer Finances from 1989. Display the least-squares regression line on this graph and the overall trend suggests that median wages have been (ever so slightly) increasing since 1989.
To communicate your message most effectively, you have to think about how to make the message of a graph as clear as possible. Minitab Statistical Software makes it easy to rescale, add lines, and add shapes so that your graphs are the best representation of the data possible. When the message of the data is clear, then you can make good decisions.
Ready for more? Check out even more of the graph options you can use to get your point across.