[R] calculating mean direction (CircStats)

Martin Maechler maechler at stat.math.ethz.ch
Mon Feb 24 17:32:52 CET 2003

>>>>> "Cordula" == Cordula Becker <cbecker at psy.uni-muenchen.de>
>>>>>     on Fri, 21 Feb 2003 20:39:00 +0100 writes:

    Cordula> Hi, I've currently to work with some circular
    Cordula> data. Unfortunately I'm not very familiar with
    Cordula> circular statistics and would really appreciate if
    Cordula> I could get some help concerning the CircStats
    Cordula> package this way.

    Cordula> My data lies in the range 0 to 2*pi, and is
    Cordula> transformed to radians (as expected by the
    Cordula> CircStats methods). Calculating the mean direction
    Cordula> (circ.mean) results for some datasets in a negative
    Cordula> mean direction like -0.8309982. I think that this
    Cordula> might be wrong. If it is correct, what is the
    Cordula> meaning of a negative mean direction?

It's in  (-pi, pi]  which is as valid as (0, 2*pi].

As a matter of fact, any angle is valid; it's just they are
periodic, i.e.,  phi + 2*k*pi is equivalent to phi for any
k in Z = { .... -1,0,1,.... }p.

    Cordula> I also read that some transformation of the data
    Cordula> might be necessary to get the correct mean
    Cordula> direction (multiplying all angles by two and taking
    Cordula> the modulus of these angles and 360°). I manage to
    Cordula> do so, but I'm not sure about how to back-transfer
    Cordula> the mean direction I'm getting as a result to the
    Cordula> angles of my original data.

I don't think that the CircStats package has any of those
restrictions for input.
It *is* important to use "radians", not "degrees" though
(I say this, since you mention 360° above).

I hope this helps,

Martin Maechler <maechler at stat.math.ethz.ch>	http://stat.ethz.ch/~maechler/
Seminar fuer Statistik, ETH-Zentrum  LEO C16	Leonhardstr. 27
ETH (Federal Inst. Technology)	8092 Zurich	SWITZERLAND
phone: x-41-1-632-3408		fax: ...-1228			<><

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