title: How to determine if a pattern of distribution is different from a random/uniform distribution
body: <p>Here is my case:</p>
  
  <p>Let's say we have 50 polygons(looks like this:
  <a href="https://i.stack.imgur.com/t6Fft.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/t6Fft.png" alt="1"></a></p>
  
  <p>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.</p>
  
  <p>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.</p>
  
  <p>However, I found a problem: when calculating the density, I actually divide the expected number over the area. But, considering the expected number</p>
  
  <blockquote>
    <p>E = N(total number)*Area_polygon/total area,</p>
  </blockquote>
  
  <p>thus the density:</p>
  
  <blockquote>
    <p>D = N(total number)/total area </p>
  </blockquote>
  
  <p>which means for each polygon, the expected density is the same number.</p>
  
  <p>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?</p>
  
  <p>What if use numbers rather than density? Or is there any other more suitable tests?</p>