The arithmetic mean of ratio-normalized experiments overestimates the true E/C ratio

Biological assays often suffer from large systematic variation between sets of experiments. This variation is sometimes countered by normalizing the results of an "exposed" (E) experiment to that of a simultaneously performed "control" (C). We demonstrate that the arithmetic mean of such ratios overestimates the "true" E/C ratio. Fortunately, the overestimation may be calculated from experimentally accessible information, and it is generally possible to correct for this factor using formulas presented in this paper. We have studied the impact of this effect on a set of studies in the bioelectromagnetics literature and find that, although most results are weakened by the correction, few are significantly altered. Some of the papers used for our literature study are controversial; we believe that the present study may strengthen the quoted results by removing doubts about the statistical treatment of E/C ratios. Both false positives and negatives are possible if the proper correction is not made to the arithmetic mean of a set of E/C data. Realistic examples of erroneous statistical conclusions demonstrate that this is a real concern for E/C data which are marginal in both magnitude (mean < 2) and variance (standard deviation > 0.5).