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jim mcnamara

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I can give you one possible sampling method - transects. But you have to define 'randomly spread' before we can do anything with any data. Do you mean kurtosis?

But this sampling method may not really be what you need. So: clear definition please. @Stephen Tashi probably knows more about what you need than I may be able to provide.

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jim mcnamara

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Hmm. This sounds like an XY problem - proposing solutions (maps with stats), and not stating the problem you want to solve. (google xy problem).

Can you state in one or two sentences what you are actually trying to do? The answer is not 'play with dots on maps.' Ex:(made up completely) I have map data about bubonic plague outbreaks in Kenya. Map A shows villages affected. Map B shows villages not affected. How do I show the vector rodent proximity?

You will find an enormous amount of help here with exact descriptions.

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Stephen Tashi

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I am familiar with the Chi-Square-Test for statistical distributions in 1d,

The "Pearson's" chi-square statistic is computed using "bins", which you can define in different ways. "Bins" can be 2D areas or a non-geometric concept like a a set of college courses. The standard tests with chi-square assume that if one thing lands in a bin, this does not prevent or encourage other things from landing in the same bin. If one group settling in a area discourages another group from settling in the same area, that would violate the assumption.

Even though the assumptions of the standard chi-square test are violated, you can still compute the chi-square statistic. What you cannot do is to assume the distribution of that statistic follows the standard chi-square distribution. If you can write computer programs, you can use Monte-Carlo simulations to determine what distribution the statistic does follow.

Applying statistics is a subjective process. For example, are you are addressing an audience that expects you back up assertions with statistical "hypothesis tests" and "levels of significance" ? Or are you addressing an audience that merely expects "descriptive statistics"? For example, if we say "The average hourly wage of a person in city A is $23.60/hr and the average hourly wage of a person in city B is $15.75/hr" then we have simply given "descriptive statistics" and left it to the reader to decide the implications of those numbers.

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You are completely right jim that the only way to rigorously approach a problem is to meaningfully state a question first, but note that my goal too is to learn about mathematics and have fun. So I may also be happy if I start, do something and come to the conclusion that it was of no use -- other than learning and having fun.

I really appreciate all the answers I got here at the moment, but I got the impression that the problem is far more complicated than I have assumed.

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jim mcnamara

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Only an incredibly small percentage of people who had ever lived prior to 1700, died more than 100km from their place of birth.

The reasons were simple - in paleolithic times, even, most good habitable places already had people living there. And they may not be friendly. Studies of New Guinea tribes showed that groups that were near each other were often more hostile to locals than to more remote groups. It's harder to fight a "war" if you have to walk 500 miles first.

This is sort of a sloppy precis of one of the theses in Jared Diamond 'The Third World Until Today'

And a corollary is probably the reason the world has become so very violent: locality expanded with travel and lately became virtual locality. Thanks to trains and planes, and later cell phones and the internet. Now we do not need to walk 500 miles. We fly drones instead.

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