Comparing categorical data for a relationship - alternatives to a chi-square test?

Hi Everyone,

This is my first post here, and I am very new to statistical testing, so I'm going to try to make this question as clear as possible (but please feel free to correct terminology, or ask for more clarification if I am missing information in my question).

I am working with categorical data, and am trying to find out where there are significant relationships between different variables. I have a 4x5 table, with a list of four species as rows, and a list of five main types of research as columns. What I'm trying to find out is which species show more association. When I graph them proportionally, it appears as if species a & b are closely matched, and so are species c & d. However, when I run a chi-square test for independence on species a & b, and another on c & d, the results are not significant. This is (I assume) because the observed values do not match up close enough with the expected values. However, the proportions of the types of research, when I look at them on a graph, are clearly (to me) closer for a & b, and c & d.

I'm wondering if there are any other tests to run for this. For example, is there a test that will compare the proportions of each of the five types of research, rather than looking at the expected values?

Secondly, perhaps there is a post-hoc test I can run that will show me where the areas of relationship and difference are in the test, rather than just whether or not there is a relationship.

Third, is there a test that I can run on all four independent variables that will show me which ones are more closely associated, or am I stuck running 6 individual chi-square tests to compare each species with all the others?

Thanks very much in advance for the help. I've found plenty of literature on post-hoc tests to show the strength of association when results are significant; and plenty on tests such as ANOVA, but nothing for tests that use categorical data.