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.