The parallactic view, statistical testing, and circular reasoning

A "parallactic view" (i.e., subjectivity in interpreting data) is an important and perhaps essential tool for formulating hypotheses, but it also represents a hazardous contaminant to be avoided in testing hypotheses. Computer simulations demonstrate that statistical testing of data that are contaminated by even a modest level of such parallax can be very misleading; probability levels are greatly distorted. An even more insidious influence of the parallactic view arises when the fundamental assumptions for a statistical test are not adequately respected. Single-cosinor analysis, which has been used to "demonstrate" circaseptan rhythms (tau = about 7 days), lends itself to such abuse: The statistical test of the zero-amplitude hypothesis assumes that if any serial correlation is present in the data, it is due to a sinusoidal oscillation with period that is known a priori. One cannot, therefore, legitimately use this method to demonstrate the existence of such a rhythm.