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So I need a way of ruling out outliers and "the ice skater method" has been suggested. The person who suggested it has a good deal of experience of doing the task I am doing, so I am certainly compelled to use it! However, I can't find anything about anyone else using/testing it...

The figure skating method: in figure skating competitions, there are five judges and after a routine you get 5 scores ("five samples from a 1D distribution"). To calculate your final score they discard the highest and lowest individual score(the outliers) then average the three scores in the middle.

To me it is a vaguely intuitively appealing method of getting an average that is not biased by outliers. To scale it to an average coming from more than 5 values you could either discard the top and bottom 20% or just the top and bottom datapoints. At this point I guess I could describe the data we're measuring and argue that it's a good fit (it feels like it is!), but that's not exactly my question...

...what worries me is that from googling is that I haven't found any mention of it. Is it at all a formalized idea, perhaps by another name? Is it widely used? Have its properties been studied/is there literature on when it might/might not be a good idea?

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    $\begingroup$ Looks similar to a trimmed mean. I would not call this a "good" option, you are throwing away possibly good information. $\endgroup$ – user2974951 Sep 10 '19 at 11:15
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    $\begingroup$ Discarding data requires a good reason. Just because a point is different from the rest does NOT make it invalid. $\endgroup$ – mkt - Reinstate Monica Sep 10 '19 at 11:55
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    $\begingroup$ This sounds more like a resistant estimator of a mean than "ruling out outliers." Could you elaborate on how you intend to use or interpret the result? $\endgroup$ – whuber Sep 10 '19 at 12:52
  • $\begingroup$ Why do you need a method of excluding outliers? Perhaps you really do, but probably not. And this method does not exclude outliers. It is the trimmed mean. That automatically excludes a certain proportion of values, regardless of whether they are outliers or not. In figure skating, they are almost never outliers. $\endgroup$ – Peter Flom - Reinstate Monica Sep 11 '19 at 11:44
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"Trimmed mean" appears to be what we're talking about here! https://en.wikipedia.org/wiki/Truncated_mean apparently this is sometimes called the "Olympic average".

Agree that discarding loads of data is not ideal. In this context data is cheap... but I am thinking of using the mode instead of a trimmed mean now. Thank you!

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