# [R] ks.test() with 2 samples vs. 1 sample an distr. function

peter dalgaard pdalgd at gmail.com
Thu Nov 16 17:00:48 CET 2017

```I suspect that that reply just replicates the question.

There are two issues: The distribution of the test statistic is different, which may be unsurprising. However, the test statistic itself is also different which may be a bit more subtle. It may help to plot(ecdf(xi)) and similarly x. The 2-sample KS statistic will is the maximum vertical distance between two step functions, so with 2x8 points, it will be a multiple of .125. The 1-sample version is the max distance between a step function and a smooth curve.

-pd

> On 15 Nov 2017, at 16:56 , David L Carlson <dcarlson at tamu.edu> wrote:
>
> In the first example you are performing a one-sample test against a continuous cumulative distribution (in this case a normal distribution). In the second case you are performing a two-sample test. You drew your values for x non-randomly by specifying fixed intervals along a normal distribution, but ks.test() just sees that you have provided two samples, not one sample and values along a cumulative distribution.
>
> ----------------------------------------
> David L Carlson
> Department of Anthropology
> Texas A&M University
> College Station, TX 77843-4352
>
>
> -----Original Message-----
> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of tonja.krueger at web.de
> Sent: Wednesday, November 15, 2017 3:47 AM
> To: r-help at r-project.org
> Subject: [R] ks.test() with 2 samples vs. 1 sample an distr. function
>
> Dear all,
> I have a question concerning the ks.test() function. I tryed to calculate the example given on the German wikipedia page.
> xi <- c(9.41,9.92,11.55,11.6,11.73,12,12.06,13.3)
> I get the right results when I calculate: ks.test(xi,pnorm,11,1) Now the question: shouldn't I obtain the same or a very similar result if I commpare the sample and a calculated sample from the distribution?
> p<- c(0.125, 0.250, 0.375, 0.500, 0.625, 0.750, 0.875, 0.9999) x <- qnorm(p,11,1)
> ks.test(xi,x)
> Why don't I?
> Thanks for helping me!
> Tonja
>
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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