# One-way ANOVA method validation

Here is my case:

Let's say we have 50 polygons(looks like this: and a point set distributed within these 50 polygons. So that for each polygon, there is an associated point density. What I want to test if whether the distribution pattern of this data set (for example, the fluctuations in density across 50 polygons) is kind of realization of spatial randomness.

The method I use is: in the uniform random case, the number of points of each ring follows a binomial distribution, i.e. X~B(n, p), where n is the total number of points and p is the probability of each point to be inside a particular polygon (p = Area_polygon/Area_semicircle). So that for each polygon, I can calculate the expected number of points and upon which we can calculate the density. And then I can apply the one-way ANOVA to compare two groups: the actual density group and the theoretical density group.

However, I found a problem: when calculating the density, I actually divide the expected number over the area. But, considering the expected number

E = N(total number)*Area_polygon/total area,

thus the density:

D = N(total number)/total area which means for each polygon, the expected density is the same number.

So in that case, is it still suitable to use one-way ANOVA to compare my actual density group to a group within which all numbers are the same?

What if use numbers rather than density? Or is there any other more suitable tests?

• Are you familiar with Poisson Generalized Linear Models? – whuber Dec 5 '19 at 22:09
• Hi Whuber, thank you for your reply! I am not so familiar with this, can you briefly explain it for me? – HAOYANG MI Dec 5 '19 at 22:14
• Our site has extensive materials about GLMs: see this search for instance. – whuber Dec 5 '19 at 22:24
• @whuber Thank you, I will look into it. But before that I want to ask a silly question: why Poisson distribution is suitable in my case? – HAOYANG MI Dec 5 '19 at 22:27