A reader responds to yesterday's graph:

Yesterday's Chart Of The Day should be on a log scale for that kind of data. Gives it a different feel (and prompts other questions). Red is linear and on the left axis, blue is log and on the right. The Motley Fool has some good text, but I like pictures, so here’s how I look at it.

The data should drive the charts. The key difference is that a linear chart plots values while a log chart plots the percentage change in those values. They are easily and often abused.

If you are looking at data that moves in uniform units, then you want a linear chart that plots the data as values. For instance, global temperatures go up and down in regular units. So do Katie Couric’s ratings on the news and my speedometer on the freeway. All of these are candidates for a linear chart.

If you are looking at data that moves in percentages, then you want a log chart that tracks the change in the data’s rate of growth. For instance, back in 1901, the entire economy’s output was about 22 billion dollars. Today, we spend more than that just on shoes. In this case, the units are not at all uniform, partly because there are more people making things, partly because of inflation and productivity. Regardless, a linear chart would quickly become nonsensical since a billion dollars just isn’t the same as what it used to be. What really matters is the percentage change. Because a log chart moves up and down in powers of 10, an increase of 10 percent a hundred years ago will look just the same today.

Now, back to that chart of the day on owners’ equity in real estate, which measures the sum total of everyone’s real estate holdings minus how much they owe on their mortgages. In the raw data, that value was $5 trillion back in 1997 then soared to more than $12 trillion at the peak in 2005, a record-busting surge of over $7 trillion. However, in percentage terms, it’s a different story. During the surge, owner’s equity went up 150%, a huge number to be sure, but not without precedent. Over a similar time-frame between 1972 and 1980, for instance, owner’s equity went up by 172%. And here’s the kicker: there was no collapse. In fact, values just kept on going up for years to come. The story implied by the chart is that there was a bubble that had to pop. Perhaps so. But this data doesn’t really show it. If anything, the log chart (in blue, right-hand scale) suggests that we’re back near the long-term trends. (There is a story in that data, I think, but that’s another story.)

Here’s the bottom line: log data on a linear chart will always look like a bubble that is ready to pop. One last example. the stock market in the US. Take a few random decades and plot the data on a linear chart and it almost always looks like we’re headed for trouble. But on a log chart, which gives equal weight to percentage change over time, the trends are remarkably steady.

Always beware of pundits bearing linear charts. Indeed, the abuses can go both ways: plot global warming on a log chart and the problem disappears. That’s if you’re happy to know the rate of change is slowing. Well, maybe we should stick to the linear chart.

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