Robustness of the t Test Applied to Data Distorted from Normality by Floor Effects

Abstract

In calculus, plaque, and gingivitis trials, measures are taken on subjects both prior to the use of an active treatment and after its use. When the trial is short-term, or when a cleaning of the mouth takes place after the baseline measurement, distributions of such measures (e.g., the Volpe-Manhold score or the Loe and Silness scale) are approximately normally distributed above zero but also can have a proportion of subjects who attain scores of zero. When the effects of an active treatment are compared with those of a control, the two-independent-sample t test can be applied to outcome scores or to differences between the baseline and outcome scores. Robustness of these t tests, in the presence of distributions "distorted" from normality as described, was investigated by computer simulation. In general, both t tests produced actual significance levels which were close to nominal significance levels, even in the presence of small samples and distributions in which as many as 50% of the subjects attained scores of zero.