Preaveraging or postaveraging of data measured in chronobiology: will the mean mouse please stand up?

Chronological measures are often made on several subjects, or for a period of days, or both, to define cycles of 24 hr in order to obtain a variety of information which can be submitted to statistical tests to characterize the subjects. In this paper, a simple theoretical model for two subjects is presented to examine the consequences of preaveraging. Preaveraging is defined as the summing of those temporal values which define the phenomenon in question. This type of operation is in fact the equivalent of filtering with moving averages. This model is then extended to N subjects exhibiting randomly assigned shifts. The disadvantages of preaveraging are illustrated from data drawn from experimental studies on mouse activity in three inbred strains: DBA/2, BALB/B6 and C57BL/6. Different effects of preaveraging, both voluntary and involuntary, are described. It is shown that preaveraging masks features that in fact discriminate across strains whereas postaveraging, because it does not suppress information, makes it possible to define the parameters of an "average" subject.