LETTER TO THE EDITOR

Significant figures or significant nonsense? To the Editor:

When a scientific study is reported to have been per- formed on 92 subjects, it is quite clear that there were more than 91 and fewer than 93 subjects in the study. But what should one make of recent reports that the mean AUC(0-24) of morphine in human subjects was 1006.83 ng-hr /ml and that the mean C,,,,x of atracurium was I7,894 p.g/L (both published in 1995 in different clinical pharmacology journals)? Was the AUC(0-24) really more than 1006.82 and less than 1006.84 ng• hr/ml? More im- portant, how can some of our colleagues measure plasma sample volumes and perform analytical manipulations with a precision of 99.999%? As a reviewer of scientific manuscripts for this and other journals, I have had the opportunity to ask many authors to disclose to the rest of us the secrets of their technique but all declined, prefer- ring instead to reduce their data to three significant fig- u r e s .

Further reading of the literature revealed what appears to be the solution to this mystery. The authors of a study on alfentahil published in 1994 reported individual clear- ance values for 14 subjects. The values ranged from 170 to 632 ml/min (not 170.00 or 632.01 ml/min) but the mean was reported as 359.36 ml/min! Apparently something happened between the input of the data into a calculator or computer and the output that miraculously enhanced the precision of the data more than one-hundredfold! Nor is this phenomenon limited to pharmacokinetics; similar "enhancements" are evident in reports of clinical mea- sures such as blood pressure and heart rate. Another frequent "enhancement" in clinical reports occurs when the number of subjects with certain characteristics in a larger group of examined subjects is converted to percent- ages. Thus (from a 1994 report in a leading journal) two of seven subjects becomes 28.6% and one of nine subjects becomes 11.1%. It is true that a frequency of one in nine is closer to 11.1% than to 11.0% or 11.2%, but a summary of the data expressed as a percentage would surely be misleading to readers.

Apparently many authors have forgotten the meaning of significant figures. The significant figures of a number include all certain digits plus the first uncertain digit. As such, they provide the reader with important information about the precision of the reported data. Increasing the number of significant figures in the course of averaging and reporting of that average without appropriate round- ing off is usually an unintended careless error, but its consequences may not be distinguishable from the inten- tional and therefore unethical alteration of data. A Cm,,x value of 17,894 Ixg/L is more appropriately rounded off to 17,900 ~g/L (assuming that the precision of the individual measurements in the assay procedure justifies expression of the results in three significant figures), but this leaves an uncertainty about the zero digits. Readers could ques- tion if the zeros are used merely to locate the decimal point or if one or both are significant figures. Several methods are available for clarification. The 17,900 ~g/L could be converted to 17.9 mg/L. They can be presented in decimal notation: 17.9 × 103 or 1.79 × 104 p.g/L, for example. Some textbooks suggest underlining the signifi- cant figures: 17,900 I~g/L. For clinical journals, it may be easiest to state in the Methods section that all data are rounded off to and reported in three significant figures unless stated otherwise. Textbooks such as Martin's Phys- ical Pharmacy ~ provide useful guidance for those con- cerned about proper presentation of data in significant figures.

Gerhard Levy, PharmD Department of Pharmaceutics

School of Pharmacy State University of New York at Buffalo

Amherst, N.Y.

Reference 1. Martin AN. Physical pharmacy. Philadelphia: Lea & Febigcr,

1960:2-19,

13/8/68999

CLINICAL PHARMACOLOGY & THEILa, PEUTICS MARCH 1996 363