I see a lot of financial charts cited on many websites. They have a common flaw. Here is an example:

Do you see the arithmetic flaw?

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In financial charts, the percentage gain matters, and not the absolute gain. The y-axis should be a log scale and not a linear scale. Given exponential growth over time (due to inflation), a linear scale exaggerates recent changes and makes old changes seem small.

Here's the same data copied from Wikipedia.

Here's the same information on a log-scale.

See! The log-scale makes a big difference! On the linear scale, the "national debt increase rate" is dramatically accelerating. On the log scale, the "rate of national debt increase" seems constant.

By default, Yahoo finance uses a logarithmic y-axis, which is correct. Compare a 20 year dow chart or S&P chart with and without a log-scale y-axis. (you have to go to the page and edit the settings) It makes a big difference! Yahoo Finance uses the correct y-axis scale (logarithmic) by default.

When viewing a financial chart over a 1+ year period, the y-axis should *ALWAYS* be a log-scale. If you have a linear y-axis, you're distorting the magnitude of recent changes. In financial analysis, you usually care about % gain or loss and not absolute gain or loss. Therefore, the y-axis of financial charts should be a log-scale.

It is offensive that I see this common basic math error. When viewing financial data over many years, the y-axis should be a log-scale and not linear-scale. If you use a linear scale, you're exaggerating recent changes and diminishing older changes.

## Thursday, February 3, 2011

### Chart Innumeracy

Posted by FSK at 12:00 PM

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## 1 comment:

Are you implying that promotion of the linear y-axis chart is just an evil fnord to help the state justify cutting aid to blood sucking leaches?

"Look at this chart. It is going up. We must cut aid to XXXX or we will be broke."

That would be a clever tactical use of charts.

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