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I looked at R for Spatial Statistics (spatstat) and I actually found out that it doesn't always have to be that below -1.96 is necessarily clustered and that above 1.96 must be uniformed.

There is also a one side test. I encountered that in monte carlo testing where it is possible to pass a parameter for the alternative hypothesis.

My question is can anyone explain how there can be one side test for Point Pattern Analysis? And how they work?

Thanks

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Tests for Complete Spatial Randomness (CSR) are usually Monte Carlo tests, so 1.96 and -1.96 (which relate to a normal null distribution for the test statistic) are not of any relevance.

As to how there can be a one-sided test: To make things specific, assume that you are testing on the basis of the K function and that you have (before peeking at a plot of the K function) specified a value of r_0 to use in your test procedure. If your alternative hypothesis is that the process is "clustered" (at distance r_0), then values of K-hat(r_0) that are above the upper envelope at r_0 indicate that H_0 (i.e. CSR) should be rejected in favour of the alternative. If your alternative hypothesis is that the process is "regular" (at distance r_0) then values of K-hat(r_0) that are below the lower envelope at r_0 indicate that H_0 (i.e. CSR) should be rejected in favour of the alternative.

If your alternative hypothesis is simply that the null is false ("not CSR", at distance r_0) then values of K-hat(r_0) that are either above the upper envelope or below the lower envelope indicate that H_0 should be rejected.

Similar considerations apply if you use the Diggle-Cressie-Loosmore-Ford test (dclf.test()) which saves you from having to chose a value of r_0 a priori (this being, usually, an effectively impossible task).

As is always the case, the advantage of using a one-sided test is that you get a wee bit more power at the same significance level.

For more detail read Chapter 10 of "Spatial Point Patterns: Methodology and Applications with R" by Baddeley, Rubak and Turner. (See http://spatstat.github.io/.)

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