The confidence limits are defined using the probability ( ‘p-value’ ). They are essentially the inverse of a t-test. You supply the p-value to get the corresponding confidence limits. As given by the CICalc function, there are separate confidence limits for the amplitude and acrophase.
The ‘confidence interval’ for any parameter are the probability that the true value of the parameter will be found within an interval defined by probability ‘alpha’. If, for a given parameter, these limits do not include zero (they are both of the same sign), the parameter is significantly different from zero at the defined probability ‘alpha’ and must be kept in the model. If the confidence interval includes zero, it is not needed in the model (it can actually be zero) and can be eliminated.
In the example of the cosinor, the confidence intervals tell the investigator if there is or is not a circadian rhythm present at the chosen probability ‘alpha’, with respect to the amplitude and acrophase. If there is, the investigator’s hypothesis that a ciradian rhythm exists is true, and if not, false.
I wasn’t aware that this function exists, so thank you for discussing it. I’ve been writing my own version. Note that circadian rhythm studies seem to have most recently incorporated different statistical criteria, so be aware of that and include the current statistical tests as well in your research. (I’ve not done circadian rhythm studies — in my research, hormone concentrations and related physiological parameters — in many years, so do a PubMed search to determine the current state-of-the-art.)
I have the Statistics Toolbox, but I also have my own one- and two-tailed t-probability and inverse t-probability anonymous functions that do not require the Statistics Toolbox. I wil give them to you if you need them.
