Random Effects in Magnetobiology and a Way to Summarize Them

In magnetobiology, it is difficult to reproduce the nonspecific (not associated with specialized receptors) biological effects of weak magnetic fields. This means that some important characteristic of the data may be missed in standard statistical processing, where the set of measurements to be averaged belongs to the same population so that the contribution of fluctuations decreases according to the Central Limit Theorem. It has been shown that a series of measurements of a nonspecific magnetic effect contains not only the usual scatter of data around the mean but also a significant random component in the mean itself. This random component indicates that measurements belong to different statistical populations, which requires special processing. This component, otherwise called heterogeneity, is an additional characteristic that is typically overlooked, and which reduces reproducibility. The current method for studying and summarizing highly heterogeneous data is the random-effect meta-analysis of absolute values, i.e., of magnitudes, rather than the values themselves. However, this estimator-the average of absolute values-has a significant positive bias when it comes to the small effects that are characteristic of magnetobiology. To solve this problem, an improved estimator based on the folded normal distribution that gives several times less bias is proposed. We used this improved estimator to analyze the nonspecific effect of the hypomagnetic field in the Stroop test in 40 subjects and found a statistically significant meta-effect with a standardized average of magnitudes of about 0.1. It has been shown that the proposed approach can also be applied to a single study. © 2021 Bioelectromagnetics Society.