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Ties
The K statistic is an "order statistic" - it is based on comparing
the order of the values in the two arrays - and it needs correction
if there are many identical values in either array. This is achieved
by counting the number of "tied pairs", which can be larger than the
number of array elements. For example the 10 element array: 1 2 2 3
7 7 7 7 7 9, contains a total of 11 ties (one tie in 2, and ten in 7).
KSTAT corrects for such ties automatically, and informs the user of
the number of ties in each input array. The correction factor applied
is
N_p/sqrt((N_p-N_t1)*(N_p-N_t2))
where N_p is the total number of pairs ( = 0.5*N*(N-1), where
N is the array length) and N_t1 and N_t2
are the number of tied pairs in each array. So long as the number of ties
is substantially smaller than the total number of pairs this correction
will be small (ie. near unity).
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