Circular statistics

[Michael Doube-2]

Dear list,

I've been measuring the orientations of marrow spaces in images of bone
samples from exercised and non-exercised horses, using Analyze Particles.

Which software tools do people use to analyse circular data like these
angles? A quick look on Wikipedia indicates that tests based on assuming
a Normal distribution are not valid for circular data, and it appears
that SPSS v. 11.0.0 has no circular statistical ability. Is it time to
grow up and use SAS??

All comments welcome,

Mike

--
Michael Doube  BPhil BVSc MRCVS
PhD Student
Dental Institute
Queen Mary, University of London
New Rd
London  E1 1BB
United Kingdom

Phone [phone] ext 2681

[David Pettigrew-2]

>Which software tools do people use to analyse circular data like these
>angles?

I don't know of any software tools that implement circular statistics.  Most
circular statistical methods are simple enough to easily implement using an
Excel spreadsheet or even by hand.  The reference I use is Circular Statistics in
Biology by Edward Batschelet.

>A quick look on Wikipedia indicates that tests based on assuming
>a Normal distribution are not valid for circular data,

The homologue of the normal distribution for circular data is the von Mises
distribution, which looks like a normal curve with tails that wrap around and
meet 180 degrees from the mean.
______________________________________
David B. Pettigrew, Ph.D.
Postdoctoral Fellow
Dept. of Neurosurgery
Univ. of Cincinnati
_______________________________________

[Gerhard-5]

Michael Doube wrote:

> Dear list,
>
> I've been measuring the orientations of marrow spaces in images of
> bone samples from exercised and non-exercised horses, using Analyze
> Particles.
>
> Which software tools do people use to analyse circular data like these
> angles? A quick look on Wikipedia indicates that tests based on
> assuming a Normal distribution are not valid for circular data, and it
> appears that SPSS v. 11.0.0 has no circular statistical ability. Is it
> time to grow up and use SAS??
>
> All comments welcome,
>
> Mike
>

You can try R
http://www.r-project.org/
its a very powerful tool for Statistical Computing and is free

It has an module for circular statistics see
http://seldon.it.northwestern.edu/sscc/R/library/circular/html/00Index.html

[Dr Gareth Rees]

Hi Mike,

I don't know which stats packages can deal with circular statistics,
but I think the standard way of treating them is partly described in
Wikipedia at http://en.wikipedia.org/wiki/Directional_statistics. For a
set of angles theta, calculate S as the mean value of sin(theta) and C
as the mean value of cos(theta). You can then take arctan(S, C) as the
mean value of theta (this is in the Wikipedia article) and 1-S^2-C^2 as
the variance (this is not in the article). This function behaves just
as you'd expect it to for angles that are tightly distributed about the
mean (the variance will be in square radians not square degrees), but
obviously the variance in the case of randomly distributed angles
cannot exceed 1.

Hope this helps

Gareth


On Wednesday, October 25, 2006, at 02:51  pm, Michael Doube wrote:

> Dear list,
>
> I've been measuring the orientations of marrow spaces in images of
> bone samples from exercised and non-exercised horses, using Analyze
> Particles.
>
> Which software tools do people use to analyse circular data like these
> angles? A quick look on Wikipedia indicates that tests based on
> assuming a Normal distribution are not valid for circular data, and it
> appears that SPSS v. 11.0.0 has no circular statistical ability. Is it
> time to grow up and use SAS??
>
> All comments welcome,
>
> Mike
>
> --
> Michael Doube  BPhil BVSc MRCVS
> PhD Student
> Dental Institute
> Queen Mary, University of London
> New Rd
> London  E1 1BB
> United Kingdom
>
> Phone [phone] ext 2681
>
>

Dr W Gareth Rees                                                      
Tel [phone]
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