
corrections
Section 2 of the paper posits that it is desirable for dissimilarity
measures in detrital geochronology to exhibit the following four
properties:
1. δ_{i,j} is independent of sample size N 

2. δ_{i,j} = 0 if i = j and
δ_{i,j} > 0 otherwise 
(nonnegativity) 
3. δ_{i,j} = δ_{j,i}

(symmetry)

4. δ_{i,k} ≤ δ_{i,j} + δ_{j,k}

(triangle inequality)

Although this may appear reasonable at first glance, it turns out that
the first two requirements are mutually incompatible. The paperâ€™s
assertion that the effect sizes of statistical tests such as
Chisquare and KolmogorovSmirnov (KS) fulfill all four requirements
is incorrect on three levels. First, the effect size of the Chisquare
test fulfils requirement 1 but not 2. Second, the KS test does not
have a calculable effect size. And third, the KS statistic fulfils
requirement 2 but not 1. The reason for the incompatibility of
requirements 1 and 2 is simple. To guarantee nonnegativity, the
definition of dissimilarity measures commonly includes quadratic terms
or absolute values, which inevitably introduce positive bias. Note
that this is not only the case for the KS statistic, but also for
Euclidean distances such as the Aitchison dissimilarity.
Interestingly, the removal of requirement 1 is good news for the
applicability of multidimensional scaling to provenance research,
because doing so greatly increases the number of suitable
dissimilarity measures. With requirement 4 also being optional (in
nonmetric scaling), MDS turns out to be even more flexible and widely
applicable than proposed in the original paper.
The observant reader may also note a slight mismatch between Equation
13 and the plot coordinates of Figure 3a. This is because Equation 13
was calculated by classical MDS whereas Figure 3a was calculated by
metric MDS. Equation 13 further implies that twodimensional MDS
configurations are given by the first two dimensions of any higher
dimensional case. Although this is true for classical MDS, it is
important to note that it is not necessarily the case for (non)metric
MDS. Fortunately, neither the examples nor the computer code provided
with the paper are affected by this inaccuracy.
