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I know I can't average percentages, but can I average percentage differences. For example, I've calculated the Mean Absolute Error (MAE) of two forecasts (same sample sizes) and the percentage difference between the MAEs. This is done for each month in the year.

Can I now calculate the average of the 12 percentage differences?

Here's an example of the results:

MAE (OSM) 0.59 0.30 0.47
MAE (DRP) 0.79 0.77 0.80 
Perc. Difference -30% -88% -53%

Would the average percentage difference of three results be -57%?

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  • $\begingroup$ You can average percentages. As Dilbert says, you can multiply them, too. Whether the results are useful is the question. Depending on what you are doing, averaging percentages can make sense. I don't think you have described the computation or objective well enough to answer. $\endgroup$ – Ross Millikan Dec 21 '18 at 15:47
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In your case, yes due to the sample sizes being the same, however I don't know how to interpret your percentages.

The reason you cannot use a straight average of percentages is because you are assuming an even weight on each percentage when in most cases the sample/population size in each percentage is not the same.

Let's say you're flipping a coin. Your first trial run is 10 flips and all heads. Your second trial run is 90 flips and 40 heads.

Averaging the percentages give (100%+44.44%)/2 = 72.22% when it is clearly 50% overall.

With the exact same logic, taking the average of difference of percentages makes no difference.

However if the sample/population size is the same then taking a straight average will give an accurate overall percentage.

Alternatively using a weighted average will give an accurate overall percentage no matter what.

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