Good Stats     Bad Stats

The Internal Revenue Service(IRS) recently released a preliminary report on the taxes and income for 2010. CNN took the data from this report in conjunction with the same report from the IRS for 2009 to analyze the growth in income inequality in a report titled “Income goes up…especially for the rich.”

The report contains statements such as “Taxpayers earning more than $250,000 saw their total adjusted gross incomes rise by 13.8%, while those bringing home between $200K and $250K enjoyed a 6.7% increase, according to a CNNMoney analysis.”

Unfortunately the analysis of the data is more complicated than just calculating the simple ratio of numbers like CNN did. In 2009 the adjusted gross income for those earning more than $250,000 did go up by 13.8%. However the number of returns with incomes above $250,000 went up 9.6%. Because of this the per return increase in income was only up 3.8%. That is a vastly different number and is the appropriate way to to analyze the data. It provides a much better indicator of what is happening in the economy. CNN goes on to cite an increase of 6.7% in the adjusted gross income for those making $200,000 to $250,000. But there was also an increase in the number of returns in that group as well. As a consequence the grown in the adjusted gross income for that group was only 0.1%.

Those numbers are not anywhere near the 13.8% and the the 6.7% numbers cited by CNN. The error is in oversimplifying the analysis and failing to consider the full situation reflecting both the growth in income and the growth in the population. The two must be taken as a pair in any analysis of this type.

There is a second significant problem with this type of analysis. The upper interval is open ended. Thus the growth in this interval is unconstrained. All the other intervals are what would be called a closed intervals. They have both a lower and an upper bound on income. With all there are people moving both into and out of the various cells. As the economy improves the upper income cell will tend, with a growing economy, to grow in the relative number of people in the cell and the income levels will grow as well pushing up the average income level in that cell. Thus the AGI per return will generally increase as the economy improves. In the middle income cells the predominant movement will be people lower income levels moving into the cell and others will move out of the cell as their income increases. But the overall average income will tend to be stable and move mostly as a result of the shift in the overall income distribution. This is because the income level for the cell is constrained at both ends. But even that is somewhat of a generalization because the true impact will depend on where on the income distribution the cell falls.

In my last post I talked about the report from the Partnership for Public Service. Today I want to look at just one of the data visualizations in the report as it is a textbook example of how not to present data. The report presents some of the data that I talked about in that last post in what look like a nice fancy graphic image. It shows only three number in what I would call a bubble chart. Each circle represents a separate number. The general rule in graphic visualization is that the area of the graph should be proportionate the to area shown. However in this figure the diameter of the circle was used instead. As result a number that is twice as big shows four times the area. As a result the data visualization is a misrepresentation of the true difference. I have redone the image using the area instead of the diameter of the circles to illustrate the differences. The original graph and the revised graph as shown side by side below.

However I do not like even the revised image as placement of each circle on top of the other hides the true proportions.

This is a case in which a simple old fashioned bar chart would be much more effect.