B Statistical comparasion of maps

[servres]

I have two different maps of dots representing locations of settlements of two different populations in the same geographical area. I want to compare both maps to know in which of both maps the dots are more "randomly spread". How can I proceed?

 

[jim mcnamara]

Something like this is common in Biology.

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.

 

[FactChecker]

You might divide the map into squares of equal area and compare each set of dots with an expected uniform distribution. The Chi squared goodness of fit statistic can tell you which one matches uniform better. This has some obvious weaknesses. For instance, dots that are regularly arranged in a grid would score as very uniformly random. I am not aware of a test that would detect that type of non-randomness.

 

[servres]

Thank you for your answers. jim, I am actually not sure what 'randomly spread' means exactly, but I assume it would be a statistic deviation from an uniform distribution in 2d. FactChecker, I am familiar with the Chi-Square-Test for statistical distributions in 1d, but I will have to take my time to understand your proposal; I still cannot figure out how calculate it in this problem.

 

[jim mcnamara]

When you do not know exactly what you are testing for, you cannot propose a question and get a meaningful answer.

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.

 

[Stephen Tashi]

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.

 

[servres]

Actually I am not doing any kind of rigorous research on a subject (thats why I used the label „basic“). After reading an article in a popular newspaper about settlements and migration of humans in europe in the upper paleolithic, I just got curious about idea that statistics may tell us something about correlations between different settlement maps in different cultures or periods depending on the willingness of those humans to migrate and settle down in a more or less nearby location.

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.

 

[jim mcnamara]

With regard to human migration, there is old bit of knowledge that very definitely applied up until the 1700's.
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.