The Statistical Treatment of Hydrogen Ion Concentration and pH

A certain amount of confusion exists amongst respiratory physiologists about the statistical treatment of pH measurements taken from animals during replicated experiments. In some cases average pH (with standard deviations or standard errors as appropriate) is calculated directly whilst in others, pH determinations are converted to corresponding hydrogen ion concentrations before the statistical calculations are carried out. Values for pH may or may not then be recalculated but, if they are, the result of these manipulations is an asymmetry of standard deviations or errors about the mean which is neither useful nor acceptable to the statistician. Our interest in this subject was the result of a mild irritation on being told by a referee of one of our papers that we made the common error of taking simple pH averages. Further enquiry and thought led us to the present paper.