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05-01-2017 12:42 PM

Is there a way to conduct a bivariate Kolmogorov-Smirnov test in SAS? That is, I want to know if two or more samples differ in their bivariate probability distributions. For example, do genotypes differ in the *combinations* of temperature and moisture that they germinate in? NPAR1way allows comparisons of temperature distributions or moisture distributions separately, but I'd like to compare the bivariate distributions.

Thanks!

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Posted in reply to kdonohue

05-01-2017 02:29 PM

I don't think bivariate K-S tests are available, but there are other options, mostly from the field of spatial data analysis. If you can upload your data, we might have more to suggest.

I assume you have a set of (x,y) pairs for each sample. There are many ways to analyze spatial point patterns in SAS. The SPP procedure in SAS/STAT enables you to graph the empirical distribution of nearest-neighbor distances between points in a point pattern. There are many distance functions that you can choose to compute. PROC SPP also enables you to model the intensity (=density) of the points. However, the GOF tests in PROC SPP tend to be for comparing data to theoretical models, rather than the nonparametric comparison of two patterns.

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Posted in reply to Rick_SAS

05-02-2017 09:21 AM

Thanks a lot. I'll look into these methods of spatial statistics. Need a non-parametric test, though....

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Posted in reply to kdonohue

05-02-2017 08:51 AM

It seems that you want perform MANOVA .

Check the example of GLM in documentation.

proc glm;

class group;

model temperature moisture =group/ nouni;

quit;

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Posted in reply to Ksharp

05-02-2017 09:19 AM

Thanks! The data are highly non-normal, though (and can't be transformed to normality), so I need a non-parametric test. Otherwise, GLM would be OK for some analyses. Also, I'm interested in the higher moments of the distribution as much as the first.

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Posted in reply to kdonohue

05-02-2017 10:49 AM

The best way to get answers that are appropriate is to upload data that demonstrates the problem you are trying to solve.

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Posted in reply to kdonohue

05-02-2017 03:37 PM

Have you looked at Proc NPAR1Way and the Exact test statement with the EDF option?

EDF produces Kolmogorov-Smirnov D statistic for two-sample data.

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Posted in reply to kdonohue

05-02-2017 03:49 PM

I have never heard about a two-dimensional K-S test. I dont think there is any theory on the distribution of the test statistic.But don't give up!

Lets say you want to make a K-S test of whether a set of coordinates comes from a bivariate N(**0****,I)** distribution. You can then simulate the distribution of the test statistic. You simply simulate n bivarite N(**0,I**) distribution, find the max value of the difference from the empirical distribution function distribution function of a twodimensional bivarite N(**0,I**) . Do that many times (1000 at least) and you then have the distribution of the test-statistic. Then compare your value with the simulated distribution to get a p-value.

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Posted in reply to kdonohue

05-03-2017 08:38 AM

Emm. Maybe you need some data simulation skill. Check this and you can expand it into multiple variables scenario easily . http://blogs.sas.com/content/iml/2014/11/21/resampling-in-sas.html