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03-16-2001, 09:04 AM
I'll continue on with Patrick Sparto's response to Gulshan Khanna's request
about circular statistics. I've used circular (and in 3-D, spherical)
statistics to analyze directional tuning of muscle activity. Another good text
(for multi-dimensional data) is Statistical Analysis of Spherical Data, by
Fisher, Lewis and Embleton (Cambridge University Press, 1987). I found the
books by Fisher et al. and Batschelet to be very helpful for developing
practical methods for data analysis, while those by Mardia were much more
theoretical.

I believe these methods are very useful for biomechanical analysis, though I
agree with Patrick, that they may be limited because they are not as
well-developed as linear statistics. With some work, it should be possible to
develop circular or spherical analogues of repeated measures or mixed factorial
design. I have developed Matlab functions for many of the basic directional
statistics and would happy to share them.

Patrick Sparto wrote:

> I would like to respond to Dr. Ghanna's previous question regarding the best
> way to analyze circadian rhythms. I believe the best method is using
> directional (aka circular)statistics, which is an area or statistics
> concerned with data that is arranged around a circle, such as a compass or
> clock. I have been reading two such texts:
>
> Circular Statistics in Biology - Batschelet, 1981, Academic Press
> Directional Statistics, Mardia and Jupp, 2000, Wiley
>
> The former is more didactic and the second more theoretical.
>
> I have three further questions associated with this topic.
>
> 1) Commonly in the biomechanics literature, statistical comparison of joint
> angles (i.e. circular data) is performed using conventional linear
> statistics such as ANOVA. Has anyone examined whether the assumption of
> linear normal distribution is appropriate in this case. I assume that a
> circular normal (i.e. Von Mises) distribution would be better, but how much
> of a difference is there? I know that ANOVA can be fairly robust with
> non-(linear)normally distributed data. One limiting factor that I can see
> with using the circular inferential stats is that the statistical models do
> not seem to be as well developed as the general linear models. Consequently,
> I have not seen in these textbooks ways to deal with repeated measures, or
> mixed factorial (crossed and nested) designs.
>
> 2) Has anyone developed their own Matlab toolbox of directional statistics
> functions that they would be willing to share. If not, I may have just
> volunteered myself.
>
> 3) Does anyone know of any Statistics list servers where I could cross list
> this posting, in order to get responses from the experts.
>
> Patrick Sparto, Ph.D., PT
> University of Pittsburgh
> Department of Physical Therapy
> and Otolaryngology
> psparto@pitt.edu
>
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