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In forecasting, there is a very common point forecast accuracy measure, the Mean Absolute Error (MAE) or Mean Absolute Deviation (MAD), which simply calculates the mean absolute difference between point forecasts and the corresponding actuals.

However, the term "MAD" is also used in non-forecasting statistics, specifically in descriptive statistics, to denote the spread of a distribution by calculating the Mean Absolute Deviation between the distribution and (say) its median.

I have just created an tag, put in a tag wiki & excerpt, and edited the tag, suggesting that posters use if they are asking about the point forecast accuracy measure. I have also started to retag a few questions and will retag some more over the next days, to avoid bump-flooding the landing page.

No, there is no question as such here - this is more of a public service announcement (plus an attempt to raise awareness about the different tags, and an explanation we can send people to who wonder about the two similar tags in the future).


This is part of my little project of improving forecast accuracy related tags. So far, I have also created a tag, and I will look at whether a tag makes sense in a few days.

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    $\begingroup$ MAD is often used to denote median absolute deviation from the median. In literature I see, that's more common than your usage. In fact I see sometimes mean absolute deviation from the mean but not IIRC the mean absolute deviation from the median. Yet further, there are some conventions to apply multiplicative factors to make estimates comparable with SDs (the multiplier coming from the normal distribution) and these factors are sometimes not even mentioned in reports! So, I tend to trust no one on MAD unless I can see their precise definition or their code. $\endgroup$ – Nick Cox Apr 12 '16 at 7:16
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    $\begingroup$ Note also a long-standing idea of "probable error", now generally superseded by standard deviation or standard error, depending on what is fed to it. $\endgroup$ – Nick Cox Apr 12 '16 at 8:48
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    $\begingroup$ It's cool that you are doing that but what is the question?.. $\endgroup$ – amoeba Apr 12 '16 at 10:27
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    $\begingroup$ Indeed, cleaning up tags is much valued. (It's perhaps fortunate that the question "Who wrote that?" is not, so far as I know, answerable.) $\endgroup$ – Nick Cox Apr 12 '16 at 10:33
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    $\begingroup$ @NickCox: you are completely right about MAD usually standing for a median absolute deviation. (It was early, and I had to catch a train.) In forecasting accuracy measurements, "MAD" invariably stands for the mean absolute deviation. Yet another potential source of confusion. $\endgroup$ – Stephan Kolassa Apr 12 '16 at 10:43
  • $\begingroup$ @amoeba: you have a point. I have edited my post to say that there is indeed no question here, more a PSA. $\endgroup$ – Stephan Kolassa Apr 12 '16 at 10:45
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    $\begingroup$ Okay. Consider "answering" this "question" in some way yourself and perhaps accepting your answer too -- to mark this thread as resolved, both visually and formally. $\endgroup$ – amoeba Apr 12 '16 at 10:57
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Self-answered to mark this as resolved - no action required from anyone (apart from eagerly using the new tag, and referring anyone confused about and here).

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