Statistical ritual in clinical journals: is there a cure?--II.

The shambles mentioned at the beginning of Part I referred to the confusion in the use of standard deviations and standard errors of means,1 with the latter apparently more popular, perhaps because they are so much smaller than their parent standard deviations and thus suggest higher precision. The author denned the standard deviation as representing the variation among the individual measurements,2 but this does not help us unless we know what multiple of standard deviation would enclose a certain percentage of the observations. The formula commonly used is mean ?1-96 SD (or 2 SD), on the assumption that we have individual measurements that, if increased in number, would form approximately a Gaussian distribution?an assumption for which most medical data provide scanty evidence. Bell shaped is not synonymous with Gaussian; and a trick such as the logarithmic transformation cannot be guaranteed to make the approximation safe. We should remember that the Gaussian curve started as the "normal curve of error," a mathematical invention that was believed to represent the scatter of the variable (chance) errors in physical measurements, but thorough investigation3 failed to substantiate the belief. Perhaps, however, some authors producing a standard deviation do not visualise any distribution. If they did, I would expect to see comments when mean minus 2 SD (or even minus 1 SD) leads to a ridiculous negative value in data such as: sodium concentration in saliva before and after a certain drug treatment; days off work after minor surgery for haemorrhoids ; activity of an enzyme in ascitic fluid in hepatic cirrhosis; serum concentration of amyloid in rheumatoid arthritis; duration of labour; number of vaginal examinations during labour. The widespread use of the Gaussian distribution to express inter subject variation has been apparently due, firstly, to the illegitimate application of the mathematical term normal (Gaussian) as if synonymous with healthy,4 5 and, secondly, to the use of standard deviation to produce standard error of the mean in the Gaussian based t test.