Re: [Rd] apparently incorrect p-values from 2-sided Kolmogorov-Smirnov test (PR#14145)

From: <tlumley_at_u.washington.edu>
Date: Fri, 18 Dec 2009 08:26:14 -0800 (PST)

I've fixed this by adding 0.5/mn to q. The problem (at least in principle) with multiplying them all up is integer overflow.

By the time 0.5/mn underflows to zero, missing one value in the distribution won't matter.

      -thomas

On Fri, 18 Dec 2009, David John Allwright wrote:

> Dear Thomas, Right, thank you. Yes, I haven't looked at the source code
> (because I don't know C) but something like what you mention could well cause
> the kind of problems I am seeing: a loop being exectued one too few or one
> too many times. And yes, I think those quantities should be multiplied up by
> m*n to all become integers so we escape rounding error problems. David.
> ------------------------------------------------------------------------------
> On Wed, 16 Dec 2009, tlumley_at_u.washington.edu wrote:
>
>> On Tue, 15 Dec 2009, allwrigh@maths.ox.ac.uk wrote; (in part)
>>
>>>
>>> x<-1:5
>>> y<-c(2.5,4.5)
>>> ks.test(x,y)
>>>
>>> The value of the D_2,5 statistic is calculated as 0.4 correctly, but the
>>> p-value is stated by R as 1, though in fact it should be 20/21=0.9524
>>
>>
>> What we seem to have here is a rounding error problem.
>>
>> In ks.c:psmirnov2x, there is a double loop including
>> if(fabs(i / md - j / nd) > q)
>> u[j] = 0;
>>
>> where md=2, nd=5, and q=3/10.
>>
>> Now, to full precision abs(1/2 - 4/5) > 3/10 is false, but at least on my
>> MacBook it is true in C double precision.
>>
>> I'm not sure why the loop is working with doubles, since multiplying by m*n
>> should make everything an integer.
>>
>> -thomas
>>
>> Thomas Lumley Assoc. Professor, Biostatistics
>> tlumley_at_u.washington.edu University of Washington, Seattle
>>
>>
>>
>

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley_at_u.washington.edu	University of Washington, Seattle

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