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https://issues.apache.org/jira/browse/MATH-1246?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14744096#comment-14744096
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Otmar Ertl commented on MATH-1246:
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I still have doubts:
# There is a difference, if there are ties within one sample, or if the same
value exists at least once in both samples. In the first case the D-statistic
is well defined. In the latter case the D-statistic is undefined. For example,
if x = (1, 3, 3, 5) and y = (2, 4, 4, 6) D = 0.5. On the other hand, if x =
(1, 3, 3, 5) and y = (2, 3, 3, 6) the D-statistic could be any value between
0.25 and 0.75. The current implementation returns the minimum (0.25 in this
case), but this seems to be a quite arbitrary choice. Furthermore, the
implementation does not distinguish between these two cases (see hasTies()
method).
# If the current implementation of exactP() follows the definition you
described, I do not really understand why the following two statements return
different values:
{code}
new KolmogorovSmirnovTest().exactP(new double[]{0.9, 1.0, 1.1}, new
double[]{0.0, 0.0}, false)
new KolmogorovSmirnovTest().exactP(new double[]{1.0, 1.0, 1.0}, new
double[]{0.0, 0.0}, false)
{code}
The D-statistic is well-defined and equal to 1 in both cases.
# \[1\] describes estimating the p-Value using bootstrapping. I am not sure, if
an exact definition can be derived from there, since bootstrapping in general
is not a consistent estimation method.
> Kolmogorov-Smirnov 2-sample test does not correctly handle ties
> ---------------------------------------------------------------
>
> Key: MATH-1246
> URL: https://issues.apache.org/jira/browse/MATH-1246
> Project: Commons Math
> Issue Type: Bug
> Reporter: Phil Steitz
>
> For small samples, KolmogorovSmirnovTest(double[], double[]) computes the
> distribution of a D-statistic for m-n sets with no ties. No warning or
> special handling is delivered in the presence of ties.
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