Geoscience Reference
In-Depth Information
compares the dispersions of normally-distributed data, the Ansari-Bradley
test compares dispersions without requiring a normality assumption for the
underlying population, i.e., it is a non-parametric hypothesis test.
h e test requires that the samples have similar medians, which can be
achieved by subtracting the medians from the samples. h e test combines
both sets of measurements (samples 1 and 2) and arranges them together
in ascending order. h ere are dif erent ways to calculate the test statistic
A
n
.
Here we use the one given by Hedderich and Sachs (2012, page 463)
where the value of the indicator function
V
i
is 1 for values from sample 1
and 0 for values from sample 2. h e test statistic is therefore equal to the
sum of the absolute values of the deviations from the mean value (
n
+1)/2
(Hedderich and Sachs 2012). For this the data are concatenated and sorted, as
in the Mann-Whitney test (Section 3.11), and the smallest and largest values
are then assigned rank 1, the second smallest and second largest values are
assigned rank 2, and so forth. h e smaller
An
, the larger the dispersion of the
values between the two samples 1 and 2. Again, the ranking of the data may
also be corrected for tied values, as was previously carried out in the Mann-
Whitney test. For
n
≤20 we can i nd the critical values for the text statistic
A
n
in Table 1 in the open-access article by Ansari and Bradley (1960). For larger
values of
n
we use the standard normal distribution
with
