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I'm comparing wind direction distributions using Python's scipy.stats.circmean and scipy.stats.circstd, and I encountered some unexpected results.

As illustrated for example in this answer, for 'normal' (non-circular) data, the mean of the difference between two samples is equivalent to the difference between their means. I blindly assumed this would be the same for circular statistics, but I'm getting different results and I'm suspecting that for circular statistics, things might be different. I just can't wrap my head around why this would be the case.

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    $\begingroup$ It depends on you definition of "mean": if it's the usual arithmetic mean of the data, then the answer is mathematically trivial:yes. But the fact you're asking this suggests you might have something else in mind, such as estimates of the means or possibly a different kind of mean. Could you clarify? (I did look up the docs for those Python procedures but the ones I found are useless, so I must presume you understand what your chosen tools do.) $\endgroup$
    – whuber ♦
    Commented May 8, 2019 at 18:21
  • $\begingroup$ The docs are useless indeed, but they link to the source code, which is quite simple. It appears to be an implementation of the first expression on wikipedia. $\endgroup$
    – Peter9192
    Commented May 8, 2019 at 18:56
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    $\begingroup$ And that brings me to the answer I was looking for! Quoting from wikipedia: "This computation produces a different result than the arithmetic mean, with the difference being greater when the angles are widely distributed." $\endgroup$
    – Peter9192
    Commented May 8, 2019 at 18:58

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