Out of the following, which tests are best to use on uniformed data to make sure it is indeed dispersed
- $\chi^2$
- Simple NNA
- High/Low clustering (Getis - ord)
- KNN (Ripley)
- Moran
- Monte Carlo
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4 Answers
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$\chi^2$ is the standard test for discrete data.
You might be interested in reading this question: Verifying that a random generator outputs a uniform distribution
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1$\begingroup$ Thanks Uri, the post is very interesting. I now understand how $\chi^2$ is good for discrete data, but not sure how is it better than the other tests for uniformed point pattern? $\endgroup$ Commented Apr 13, 2016 at 12:22
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The answer to "what the 'best' test of a hypothesis" depends on what the alternative hypothesis is. It also depends on what you really mean by 'best'; usually people mean 'most powerful'.
I would conjecture that even if the alternative hypothesis were clearly specified, determining which of the several tests for CSR is most powerful would be challenging. Simulation techniques might possibly help.
A general comment: This question and the many others that you have asked in this forum indicate that you are WAY out of your depth, or trying to run before you can walk, or some other metaphor. Your questions are mostly mis-directed and indicate conceptual confusion and mis-understanding. Instead of continuing to bark up the wrong tree I would suggest that you undertake a serious learning exercise about spatial point processes.
There are a number of books that you might find useful, but the one that I would (of course! :-) ) recommend is "Spatial Point Patterns: Methodology and Applications in R" by Adrian Baddeley, Ege Rubak & Rolf Turner. It is published by Chapman & Hall/CRC. See http://spatstat.github.io/ for useful pointers.
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$\begingroup$ Thanks for the criticism, the metaphors, and the recommendations. I will certainly try to ask questions that are not way out of my depth in the future. To the specific issue in question, it is not much about what H1 is, but about which test would provide the overall result to identify uniform data.One way to look at it is which test(s) you would choose for a classic uniform sample/population such as cells (Ripley 1977) and why these and not others, Another way is to go through the tests listed and describe the cons in each when analyzing the cells data and think which tests are less effective $\endgroup$ Commented Apr 13, 2016 at 23:44
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$\begingroup$ I just realized you are the author if the R book, that's great to have you in this forum! Would you mind having a look at this other question of mine - stats.stackexchange.com/questions/206977/… - in your book page 165 I think there are quadrats that are not equal in size $\endgroup$ Commented Apr 13, 2016 at 23:56
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Except in very simple situations, there is no 'best' test of a hypothesis.
The $\chi^2$ test may be 'standard' because it is relatively simple to use, but it is sub-optimal in many contexts - including the context of testing for uniformity based on quadrat counts. It is outperformed by the Likelihood Ratio Test, for example.
See Chapter 10 of the spatstat book
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Your assertion "it is not much about what H1 is, but about which test would provide the overall result to identify uniform data" makes no sense at all to me. I think it indicates that you really don't understand hypothesis testing. Anyway "provide the overall result to identify uniform data" is a meaningless expression.
BTW your question seems (it's hard to tell) to imply that you think that the cells data are uniformly distributed!!! Far from it. They are way too evenly spaced to be uniform in distribution. Just about any test would reject the null hypothesis of uniformity at any of the usual significance levels. The intra-occular test in particular is completely convincing.