The use of Means
When faced with two or more groups of data relating to surrogates with values analogous to the measure of a dependent variable, the overall mean can be computed as the average of the groups’ means which then assumes the responsibility of representing the dependent variable as a single group which can now be regressed in an ordinary GLM against the underlying independent variables (Carey, n.d.; Conference & Pisa, 2007; Fritz & Berger, 2015; Fritz, Berger, Fritz, & Berger, 2015). The use of the mean as a unifying factor becomes inevitable in financial performance studies involving multiple surrogates of a dependent variable. However, the question remains - which type of mean do one employ: the arithmetic mean or the geometric mean? To answer this question, it is necessary to assess the effect of each type of mean. TheArithmetic Mean (AM) is a simple average derived by adding all-inclusive elements which have numerical values together and diving by the number of elements added. Despite its extensive use to report the central tendency of a data distribution, it suffers from statistical robustness because it is greatly influenced by outliers or extreme values included in the distribution. The Geometric Mean (GM) on the other hand also measures the central tendency but it does so by multiplying the numerical elements involved in the set and finding then th root of their product. A geometric mean is often used to find a single “figure of merit” for items with multiple properties when comparing different items. It is also used to analyse a set of numbers whose values are meant to be multiplied together or are exponential in nature such as investment interest rate or human population growth rate. It, however, applies only to positive numbers. Nevertheless, the geometric mean (GM) is more respectful of the intrinsic differences across all the dimensions of the data distribution than the arithmetic mean (Transaction Processing Performance Council, 2011; UNDP, 2011). For the reasons as earlier adduced, the use of geometric mean, is, therefore, favoured and will be used to unify the multiple surrogates of the dependent variables studied in this work.