A Rebuttal to The “Reply”

At the outset a brief background from a pharmaceutics perspective is presented here. Pharmaceutical industry is one of the most tightly regulated industries. Statistics naturally plays an important role in the implementation of the compendial, regulatory and in-house requirements. The minimal requirement consists of a set of basic statistics, such as mean and standard deviation (SD), associated with each group of sample experimental data intended for submission. However, not only each statistic is individually subjected to a set of compendial, regulatory and in-house specifications, but also the individual observation is required to be within specific range for compliance (e.g. content uniformity). Hence these basic statistics are often referred to as the stand-alone sample (SAS) statistics, meaning that each statistic has to meet its own requirements. In this context, the geometric mean is indeed a SAS statistic. It is meaningful and interpretable directly from its face value. The geometric standard deviation (GSD) as derived in ref(B) is also a (SAS) statistic. It is meaningful and easily interpretable directly from its face value. It has the same sample information and the same interpretation as that of the regular SD. Sometimes, it shares essentially the same magnitude as the regular SD. Besides, it also has essentially the same magnitude as that of the jackknife GSD statistic, GSD(JK). For decades, these geometric statistics have been in practice, particulary, since the author of ref(B) was a member of the USP In-Vitro Bioavailability Testing Subcommittee (1970-1975). It has also been accepted fully and freely by the above-mentioned over-sight agencies.