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

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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.