The regression effect as a cause of the nonlinear relationship between short- and long-term radon concentration...

The relationship between four-day charcoal canister radon measurements and year-long alpha-track detector measurements in 983 New Jersey homes has been recently examined by others. The ratio of canister measurement to long-term measurement for the homes in the survey, a common parameter of interest, was found to increase as the canister measurement increased. The examination presented considerable discussion of the variation of the ratios as functions of various parameters. Although we did not examine the raw data used in the study, it appears that many of the results (and perhaps those in other papers) are consistent with a simple model in which both the long-term and rescaled short-term measurements provide measurements with error of the annual-average radon concentration in the home with no nonlinearity or other unusual functional dependence on radon concentration. We provide an example and discussion of this result, which is due to the widely known but frequently misunderstood phenomenon called "regression toward the mean," or simply the "regression effect." This does not invalidate the work of others; we merely wish to bring attention to the fact that the results in these papers may have a very simple explanation.