Significance of association between categorical variables

Question

I am analyzing survey data collected among plant breeders. I want to know if there is any association between some of the variables we collected, namely their perception of climate change and the region where they work. I have 200 answers from breeders who belong to one out of 6 regions. They were asked about 10 climate change parameters (drought, rainfall, temperature, etc.). For each of these, their answers could be "increased", "no change", "decreased".

I want to know if breeders' perception of each climate variable is significantly related to their region of work. I'd like to know this to be able to say, for example, that breeders working in East Asia are observing a greater increase in rainfall than those in Central America.

I am working in R. I have tried creating contingency tables between breeders' regions and each climate variable using CrossTab from the gmodels package, but I am not sure how to interpret the output (in a table with so many relationships, what does the significance level apply to?). Also, most of my cells (well over 60%) have expected frequencies < 5 which I understand makes the test less reliable.

I have tried fisher test but I get error messages about a too small workspace, which I am not sure how to solve, and in any case I don't know if this is a good test either.

I would appreciate your help in choosing the best statistical method for my objective.

Answer 1

Because your dependent variable is ordinal in nature, you probably want to use an analysis that accounts for this fact. A chi-square test of association knows that "increase" is different than "decrease" but doesn't know that "increase" > "no change" > "decrease".

If you want to analyze each question separately, an appropriate test would be a Cochran-Armitage test expanded to more than two categories, which is available in R with the coin package. Note that appropriate measures of effect size include Freeman's theta and epsilon-squared.

If you want to include all the questions in a single analysis, you probably want to use ordinal regression, which is available in R with the ordinal package. You could include an independent variable for Question-number and one for Region. However, there may be a problem with interpretation here, since an "increase" in "rainfall" is not likely to be commensurate with an "increase" in "drought". You may want to reverse the scales on some questions so that all the "bad" outcomes are on the same end of the scale. The ordinal regression will allow you to look at differences among Regions, among Questions, or among the Region x Question interaction.