Comparison of Cosinor Parameters of Two Populations
Description
Runs the tests that compare MESORs, amplitudes and acrophases of two different populations.
Usage
cosinor.poptests(pop1, pop2)
Arguments
pop1
An object of the population.cosinor.lm class calculated on the first population.
pop2
An object of the population.cosinor.lm class calculated on the second population.
Details
Bingham et al. (1982) describe tests for comparing population MESORs, amplitudes and acrophases. These tests are esentially F-ratios with df1=m−1 and df2=K−m, where m is the number of populations and K is the total number of subjects. The tests for MESOR, amplitude and acrophase differences respectively are calculated as follows:
where 2ϕ~ lies between −2π and 2π if the denomanator is positive or between 2π and 23π if the denominator is negative, kj is the number of subjects in the jth population, Mj, Aj and ϕj are the cosinor parameters of the jth population and σβ,σγ and σβγ are the estimates of pooled standard deviations (and covariance) calculated as following:
σβ=K−m∑j=1m(kj−1)σβj
σγ=K−m∑j=1m(kj−1)σγj
σβγ=K−m∑j=1m(kj−1)σβjγj
where σβj, σγj and σβjγj are the standard devations and covariance of β and γ parameters in the jth population.
Note
These tests should only be performed on independent samples. If the acrophases of two populations are significantly different, the results of the amplitude difference test are not reliable and should not be interpreted. While it's possible to perform tests which compare more than two populations, this function can only compare two populations.
References
Bingham, C., Arbogast, B., Guillaume Cornélissen, G., Lee, J.K. & Halberg, F. (1982). Inferential Statistical Methods for Estimating and Comparing Cosinor Parameters. Chronobiologia, 9(4), 397-439.
Examples
fit.extraverts<-population.cosinor.lm(data = PA_extraverts, time = PA_time,
period = 24)
fit.introverts<-population.cosinor.lm(data = PA_introverts, time = PA_time,
period = 24)
cosinor.poptests(pop1 = fit.extraverts, pop2 = fit.introverts)