Statistical measures of the central tendency for H+ activity and pH

Abstract

AbstractDespite the numerous papers on the statistical analyses ofpH, there is no explicit opinion on the use of arithmetic mean as a measure of the central tendency forpHandH+activity. The problem arises because the transformation of the arithmetic mean for one does not give the arithmetic mean for the other. The paper presents 1) the theoretical considerations on the distribution of pH andH+activity and relation between them, properties of these distributions, the choice of distributions which should be consistent with the distribution ofpHand the distribution ofH+activity and measures of central tendency for features of such distributions and 2) examples of calculations of measures of central tendency forpHandH+activity based on the literature data on soil and lake waterpH. These data analyses included distributions ofpHandH+activities, properties of distribution, descriptive statistics forpHand for theH+activity and comparison of arithmetic mean with the geometric mean. From the results, it could be concluded that a uniform approach to the choice of measure for the central tendency ofpHandH+activity requires the determination of the type of measure (mean) for one of them and then consistent transformation of this measure. The choice of measure of the central tendency for the variable should be preceded by determination of its distribution. Normal probability distribution ofpHand thus lognormal distribution ofH+activity indicate that the arithmetic mean, and its corresponding geometric mean should be used as proper measures of the central tendency for pH and for H+activity. Besides, the position statistic that is a median can be used for each of those variables, irrespective of their probability distributions.