R help - Feb 2003 - calculating mean direction (CircStats)

Hi,

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

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

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

I would be very happy if anybody has some hints concerning this problem.

Thanks a lot, Cordula Becker
--------------------------------------------------------
Cordula Becker

Ludwig-Maximilians-Universit?t M?nchen
Allgemeine und Experimentelle Psychologie

Leopoldstr.13
D-80802 M?nchen
Germany

Tel. +49 (89) 2180 6231
Fax. +49 (89) 2180 5211

>>>>> "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

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			<><