Calculating p-value for two-sample Kolmogorov-Smirnov test

[ewolin]

Is there a function I can call directly that will calculate the p-value given the K-S d-statistic and the number of entries in the two distributions?  I need the function that NPAR1WAY uses behind the scenes.  The problem is that I can't give NPAR1WAY what it needs (unweighted data, mine is weighted) so I use NPAR1WAY to get the d-statistic and I need to calculate the p-value myself.  I could scale up the reported p-value except for my weighted data NPAR1WAY always says p<0.0001, i.e. it doesn't return a value I can scale!

I need something like:   myPvalue = KS_pValue(dStatistic,n1,n2);

Ranges for n1,n2 in my case are:  1000 < n1 < 100,000, 50 < n2 < 2000.

[data_null__]

You can get the actual p-value in the output data set.  The value you are seeing is the formatted value using PVALUE format.

data Arthritis;
   input Treatment $ Response Freq @@;
   datalines;
Active 5 5 Active 4 11 Active 3 5 Active 2 1 Active 1 5
Placebo 5 2 Placebo 4 4 Placebo 3 7 Placebo 2 7 Placebo 1 12
;

proc npar1way data=Arthritis KS;
   class Treatment;
   var Response;
   freq Freq;
   output out=ks;
   run;
proc print;
   run;

[ewolin]

I looked in the output data, all the p-values are 0.  The problem is my weights are huge, as high as 200,000.  But the true p-value calculated properly should not be 0.

Might EXACT help?  I fiddled with EXACT, MC, MAXTIME, etc. but it just sat there for long periods of time and I had to kill it.  Have to try N= as well.

Anyway, if I could just access the function NPAR1WAY uses I'd be fine...

[lvm]

The help function in SAS can take you to the details of the KS test. Or just check out the web page

SAS/STAT(R) 9.2 User's Guide, Second Edition

New versions have the same information.

With the samples sizes you have, even the smallest difference will be significant.

[ewolin]

Yes, I saw the equations, I was hoping a function exists to do the work.  I understand in practice no one sums from zero to infinity, only a few terms are kept and special corrections are applied, so I'd much rather find a working function written by experts than have to research this on my own.

[lvm]

Part of your message looks like you are concerned about getting p<0.0001, instead of the actual (small value), say p = 1.67*10^(-8). You can get a more exact printout by storing the relevant statistics with an ODS output statement, and then printing the stored file. Here is a simple example (without frequencies) where the printout gives < .0001. The last column of the KS2 file has two rows. First row is D and second row is p (in scientific notation). Variable is called nValue2 (for some strange reason).

data a;

do group = 1 to 2;

do rep = 1 to 10000;

y = group*.1 + rannor(1);

output;end;

end;

run;

proc npar1way data=a edf ks;

class group;

var y;

ods output KolSmir2Stats=ks2  ;

run;

proc print data=ks2;run;

[ewolin]

I tried that previously, it just printed exactly 0 for all the p-values (see column of zeros below).  Perhaps my weights are so large that it's hopeless to get a non-zero p-value that I can correct for the weights.  Seems like I'll just have to calculate the p-value myself.

I sure would like to find a function in SAS that does the calculation...

1	Male	(<20)	ApoB	.002233328	6.2103	0.22041	0	.000002242	17.335	0.22293	6.2813	0
2	Male	(20-29)	ApoB	.002473620	7.3677	0.12183	0	.000003057	27.119	0.12511	7.5660	0
3	Male	(30-39)	ApoB	.005193976	15.9733	0.16763	0	.000011119	105.162	0.16785	15.9943	0
4	Male	(40-49)	ApoB	.003007115	9.7514	0.07357	0	.000002399	25.230	0.09987	13.2380	0
5	Male	(50-59)	ApoB	.004811441	14.8999	0.09631	0	.000006126	58.747	0.12704	19.6538	0
6	Male	(60-69)	ApoB	.007293936	19.9366	0.13297	0	.000009974	74.515	0.19752	29.6162	0
7	Male	(70-79)	ApoB	.005602209	11.4631	0.09621	0	.000004495	18.821	0.15906	18.9521	0
8	Male	(>=80)	ApoB	.005729162	7.4794	0.09921	0	.000011073	18.872	0.13626	10.2727	0
9	Female	(<20)	ApoB	.002512096	6.9934	0.22836	0	.000002821	21.866	0.22836	6.9934	0
10	Female	(20-29)	ApoB	.002397185	7.4033	0.09843	0	.000002358	22.488	0.09896	7.4432	0
11	Female	(30-39)	ApoB	.005747304	17.9301	0.16782	0	.000014166	137.876	0.18721	20.0008	0
12	Female	(40-49)	ApoB	.004009143	12.3046	0.08878	0	.000007887	74.293	0.10704	14.8363	0
13	Female	(50-59)	ApoB	.005250789	17.1014	0.10402	0	.000006173	65.481	0.15556	25.5739	0
14	Female	(60-69)	ApoB	.005870556	16.3198	0.10203	0	.000011481	88.728	0.15890	25.4182	0
15	Female	(70-79)	ApoB	.004183428	9.3058	0.07472	0	.000003132	15.496	0.14135	17.6047	0
16	Female	(>=80)	ApoB	.008706090	14.2755	0.16290	0	.000015396	41.394	0.19818	17.3680	0

[lvm]

Not my area. But any formula other than the exact one will be an approximation.I doubt if the p value will scale linearly with n, so there would be no simple upscaling.