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J Circadian Rhythms. 2010 Nov 8;8:10. doi: 10.1186/1740-3391-8-10.

Statistical methods for detecting and comparing periodic data and their application to the nycthemeral rhythm of bodily harm: A population based study.

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Department of Psychiatry and Psychotherapy, University of Erlangen-Nuremberg, Schwabachanlage 6, 91054 Erlangen, Germany.



Animals, including humans, exhibit a variety of biological rhythms. This article describes a method for the detection and simultaneous comparison of multiple nycthemeral rhythms.


A statistical method for detecting periodic patterns in time-related data via harmonic regression is described. The method is particularly capable of detecting nycthemeral rhythms in medical data. Additionally a method for simultaneously comparing two or more periodic patterns is described, which derives from the analysis of variance (ANOVA). This method statistically confirms or rejects equality of periodic patterns. Mathematical descriptions of the detecting method and the comparing method are displayed.


Nycthemeral rhythms of incidents of bodily harm in Middle Franconia are analyzed in order to demonstrate both methods. Every day of the week showed a significant nycthemeral rhythm of bodily harm. These seven patterns of the week were compared to each other revealing only two different nycthemeral rhythms, one for Friday and Saturday and one for the other weekdays.

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