R devel - Oct 2001 - ks.test (PR#1004)

The note to 1004 says "fixed for 1.3.1"

Uh.  No.  It ain't.

The problem was more serious than guessed as even the simplest testing
would show.

For example, Example 5.4 in Hollander and Wolfe (Nonparametric Statistical,
Methods, 2nd ed., Wiley, 1999, pp. 180-181)

R Version 1.3.1 (SuSE Linux 7.1)
> X <-
read.table(url("http://www.stat.umn.edu/geyer/5601/hwdata/t5-7.txt"),
+     header = TRUE)
> names(X)
[1] "x" "y"
> attach(X)
> ks.test(x, y)
 
        Two-sample Kolmogorov-Smirnov test
 
data:  x and y
D = 0.6, p-value = 0.01234
alternative hypothesis: two.sided

Not hardly.  Hollander and Wolfe say the exact P-value is 0.0524.  Note
> ks.test(x, y, exact = FALSE)
 
        Two-sample Kolmogorov-Smirnov test
 
data:  x and y
D = 0.6, p-value = 0.05465
alternative hypothesis: two.sided

Agrees.  Thus the algorithm for the exact null distribution of the two-sample
K-S test statistic is erroneous.  I. e., there is something wrong with the
function "psmirnov2x" in ks.c.  I don't yet know what the problem
is.

-- 
Charles Geyer
Professor, School of Statistics
University of Minnesota
charlie@stat.umn.edu

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charlie@muskrat.stat.umn.edu writes:
> For example, Example 5.4 in Hollander and Wolfe (Nonparametric Statistical,
> Methods, 2nd ed., Wiley, 1999, pp. 180-181)
> 
> R Version 1.3.1 (SuSE Linux 7.1)
> 
> > X <-
read.table(url("http://www.stat.umn.edu/geyer/5601/hwdata/t5-7.txt"),
> +     header = TRUE)
> > names(X)
> [1] "x" "y"
> > attach(X)
> > ks.test(x, y)
>  
>         Two-sample Kolmogorov-Smirnov test
>  
> data:  x and y
> D = 0.6, p-value = 0.01234
> alternative hypothesis: two.sided
> 
> Not hardly.  Hollander and Wolfe say the exact P-value is 0.0524.  Note
Here's part of the problem:

Browse[1]> .C("psmirnov2x", p = as.double(STATISTIC),
as.integer(n.x),
as.integer(n.y), PACKAGE = "ctest")$p
[1] 0.9876594
Browse[1]> .C("psmirnov2x", p = as.double(0.6), as.integer(n.x),
as.integer(n.y), PACKAGE = "ctest")$p
[1] 0.9475524
Browse[1]> STATISTIC
[1] 0.6

Perplexed? The reason is of course that

Browse[1]> STATISTIC-0.6
[1] 1.110223e-16

and the KS distribution is discontinuous, so the point probability at
0.6 didn't get counted. Looks like we need a fudge factor.

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)             FAX: (+45) 35327907
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