[R] ks.test "greater" and "less"

[Prof Brian Ripley]

On Sat, 16 Dec 2006, R. Villegas wrote:

> 2006/12/15, Carmen Meier <carmei3 at web.de>:
>> Hello r-group
>> I have a question to the ks.test.
>> I would expect different values for less and greater between data1 and
>> data2.
>> Does anybody could explain  my point of misunderstanding the function?

The help page says:

      This is a comparison of cumulative distribution
      functions, and the test statistic is the maximum difference in
      value, with the statistic in the '"greater"' alternative being D^+
      = max_u [ F_x(u) - F_y(u) ].

data1 and data2 have the same empirical CDF, so should and do give the 
same value of the test statistic.

We cannot know what you misunderstanding is, since you have not explained 
your expectations.


>> data1<-c(8,12,43,70)
>> data2<- c(70,43,12,8)
>>
>> ks.test(data1,"pnorm")
>> ks.test(data1,"pnorm",alternative ="less")    #expected < 0.001
>> ks.test(data1,"pnorm",alternative ="greater") #expected =1
>>
>>
>> ks.test(data2,"pnorm")
>> ks.test(data2,"pnorm",alternative ="less")  #expected =1
>> ks.test(data2,"pnorm",alternative ="greater") #expected < 0.001
>>
>>
>> With regards Carmen

> Possible  you are unable to use the KolmogorovÿÿSmirnov test given that
> the sample size is small.

You can: the distribution theory is exact.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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