Where is the Money that can be Taxed?

From an interesting post by Brendan Nyhan on his blog. He takes issue with a WSJ editorial which uses the following graph which suggests the only place to get money to reduce the budget deficit is by taxing the middle class:

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When it would prehaps be more meaningful to use this graph which seems to indicate that if you want to tax people with money available for taxing you need to look at the super rich:

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Both are accurate, but they look at the data in different ways which can mislead. Here is Nyhan's comment on the top chart and how the same data can be reorganized to get the bottom chart:

... this chart is a textbook example of how to lie with statistics. It's unfortunate that the Wall Street Journal chose to undermine the rest of its editorial by including such a breathtakingly misleading image.

It purports to show visually that the majority of taxable income in this country is made by those in the middle class—after all, the highest bar is for people making $100-$200K, which is in the middle of the graph! However, the heights of the bars depend as much on the width of your "bins" as on the actual statistic the bars measure. Look more closely: the bar immediately previous to this one is for the income range of $75K to $100K—an income range only one-quarter the size. Of course you're going to get a higher bar when you quadruple the income range it measures. The point here is that you can finagle the ranges for the bars any way you want, and get vastly different charts.

Go read the whole post.

If you want to mislead, there is no better technique than statistics. Sadly most people don't realize what a wonderfully "flexible" tool statistics can be so they fall prey to its misuse. I remember as a young kid the book How to Lie with Statistics:

The book is a brief, breezy, illustrated volume outlining common errors, both intentional and unintentional, associated with the interpretation of statistics, and how these errors can lead to inaccurate conclusions. It has become one of the best-selling statistics books in history, with over one and a half million copies sold in the English-language edition, even though the monetary examples have become dated because of inflation.

I seems that some lessons require more than a little beating to get it into the public mind. Half a century, and the lesson has not yet been learned. Patience. Maybe in another millennium and people will know that pretty pictures and nice statistical statements can misrepresent when used by a master propagandist or clever deceiver.