“I’m not a statistician, but . . .”

Alex Lamb writes:

I’m not a statistician, but one thing I’ve noticed is that most (or all?) of the percentage change plots that I’ve seen don’t use a logarithmic scale. I think the logarithmic scale would be better, since most people are better at mentally performing addition operations, and the cumulative effect of percent-changes is multiplicative.

The log-scale would reflect this, by making the cumulative effects over many time steps additive with respect to the scale of the plot.

For example, it seems like it would make a lot of these plots easier to interpret.

I replied that I agree, but it’s controversial, and I pointed to Jessica’s recent post on the topic.

Lamb responded:

I was specifically thinking about percentage growth rates, for example GDP growth per year like: 5%, 10%, -10%, …, 1%. One thing I noticed is that if you compare countries which have had really good economic growth like Malaysia or China vs. unstable countries with low growth, the unstable country’s growth plot often has a higher net area under the curve in total, since it’s a mix of years with very high positive growth and negative growth. The negative growth years actually count for much more due to the multiplicative interaction. If you plot on the log scale, then net area under the curve actually is a correct measure for total growth.

For absolute measures like how many people have gotten coronavirus, it’s less obvious to me if log scale is the right choice. I think log scale makes it easier to discriminate between different exponential growth rates, but makes it much harder to discriminate between exponential and non-exponential growth rates.

Uh oh, don’t talk about Malaysia, it will bring the racists out of the woodwork!

2 thoughts on ““I’m not a statistician, but . . .”

    • So the problem that log changes are asymmetric around the mean are solved by redefining the mean? Yeah, that’ll be intuitive to people…

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