Type I Error Inflation in the Presence of a Ceiling Effect
Many variables in biomedical research (e.g., indices of health status) are measured with ceiling effects, in which a substantial number of subjects attain the highest possible scale value because the scale only discriminates among individuals in the low to moderate range. Furthermore, in social surveys, variables such as income and alcohol consumption may be subject to ceiling effects to protect the privacy and identity of those at the upper end of the distribution for a given variable. This article shows that if one attempts to control for such a variable using ordinary linear regression, and then test another independent variable that is actually unrelated to the outcome, the result can be an increase in the rate of Type I Error (false significance). We present simulations in which standard tests conducted at the 5% significance level actually have the Type I error rates approaching 100% for large samples. Statistical solutions are explored, but the best recommendation is to construct scales that are not subject to ceiling effects.
Peter C. Austin. "Type I Error Inflation in the Presence of a Ceiling Effect" The American Statistician 57 (2003): 97-104.