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Analysis of circular data

Doherty Brian J brian at ada.brynmawr.edu
Mon Feb 5 18:18:34 EST 1996

Does anyone out there have any experience using
descriptive and inferential statistics with
data measured on a circular scale?

Such techniques have been described by Mardia (1972),
Zar (1984) and Batschelet (1978, 1981).

We are using these techniques to examine between group
and within subject differences in the phase of an
auditory evoked brain potential.  Using the formulae
from Zar, I have come up with some Excel spreadsheets
to analyze the data (being unable to find any package
to do it for me).

Most of these (and those that I can check against examples
in the book) seem to work fine, but some seem to result in
odd results.  For instance, an F with a negative value.  This
wouldn't happen with a traditonal ANOVA, of course, so I'm
curious if anyone knows that this can in fact happen when
working with such data.  Nothing in the formula seems to
preclude this possibility, but I'd like confirmation from
others who have conducted such analyses.

In particular, if anyone has conducted the parametric two-
sample second-order analysis of angles described by Zar
(p. 457) and can furnish sample data worked through to the
calculation of the F, I could apply my worksheet to it to try
to confirm my results.  Zar provides no example from the
point of calculating the second-order angles themselves.

And, if anyone does know of tools to automate the analysis
of such data, I'd love to hear about them.


Brian Doherty
brian at brynmawr.edu

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