Analysing Cycles in Biology and Medicine: A Practical Introduction to Circular Variables and Periodic Regression

This book makes periodic regression readily accessible.  It provides worked-out examples, and text that describes why each step is taken (and what steps to not take).  Periodic regression is suited to situations where a Y variable is measured over (around) a cycle, e.g. "air temperature over the course of a day, or year";  this is sometimes called the "cylindrical" situation---think of a 24h clock, lying flat, and temperatures marked on bars at times around its circumference.    The uses or periodic regression are not restricted to only those situations where one had a direct interest in the cycles.  Even if the interest is the effect of A and B on Y,  if a third variable C also affects Y then any analysis obtains improved accuracy for A and B when C is included.  Likewise, cycles can affect many measures, so their inclusion improves the analysis for the effects of the variables of main interest.  This would apply to many examples of ecological, biological, and medical research.   Written in a welcoming style, written to be accessible --- for instance Sec. 11.1.2 "The very basics (stats in the wild west)" --- the book anticipates readers ranging from apprehensive to advanced. Most tricky concepts are explained more than one way.  It is copiously illustrated with conceptual diagrams and worked-out examples.     If you are an advanced reader you may wish to go straight to Ch. 6, the chapter on periodic regression itself, referring to the cross-referenced sections as needed.    Resource chapters provide the basic geometry, key tools for circular stats, the handling of dates and natural cycles, and a simple notation system to make formulas and calculations more readable.  There is an index, a glossary, and a Day-of-Year table.     Some special tools and topics are addressed.  Sec. 6.4.5 shows how to calculate the joint significance of one or more variables in a regression; this is needed because each cycle will always be expressed by two variables.  Sec. 6.4.6 addresses some cautions and uses simulation to illuminate the issue of non-orthogonality in data with uneven spacing or missing or replicated values, as is liable to happen in field work or any system where logistics interfere with the plan; the simulations show that the effect on inference is, at least, surprisingly small.  Sec. 10.2.1. provides the text for some core macros that can simplify and add reliability to data conversion and calculation (e.g.) of the phase angle implied by any pair of sine and cosine.  And if you think sines and cosines are material for headaches, Figure 3-1 is better than an aspirin.     Even where the topics are somewhat advanced, the book attempts to maintain accessibility.  It is written to help people enjoy statistics, and use and judge them well.