Independence and strength of association between categorical variables

Question

I am pursuing my master's thesis in Global Health at Uppsala University. One step in my statistical analysis involves "consumption of ultra-processed food (UPF)" as the independent variable (having 3 mutually exclusive categories: number of subjects who consumed 1-2 UPFs, 3-4 UPFs, and 5 UPFs in the last 24 hours) and "dietary diversity" as the dependent variable (having 2 mutually exclusive categories: adequate dietary diversity and inadequate dietary diversity). The dependent variable was actually a (discrete, numerical) score, the dietary diversity score, ranging from 0 to 10; that was dichotomized by a cut-off score of 5- those scoring 5 and above categorized as having adequate dietary diversity and those scoring below 5 as having inadequate dietary diversity (cut-off based on WHO recommendation).

My questions are:

1. What test should I choose to test for statistical significance? My guess is Pearson's Chi-squared test; as I have the assumptions fulfilled by the data.

2. What co-efficient should I choose to reflect the strength of association? I read about the following two options: Goodman-Kruskal's Lambda and bias-corrected Cramer's V. I am not sure which one to use, or there is another more appropriate option, as I don't have the in-depth knowledge of statistics to assess the strength and weakness of these to co-efficients. I am really confused here.

Sincere thanks in advance.

Answer 1

What is your hypothesis? - i.e. can you put what you want to test into individual questions? The ideal tests then become more obvious.

e.g. Your hypothesis might be that higher consumption of ultra-processed food is negatively correlated with dietary diversity. This is a statement/hypothesis that you can then test to see whether your data provide (statistically significant) support for the hypothesis or not.

To me, it appears that you have ordinal data: the original dietary diversity score from 0 to 10. The consumption of ultra-processed food is counts data/ordinal data/categorical data depending on how you look at it. Perhaps consider exploring ordinal regression first?

1. A chi-squared test seems reasonable if you decide to keep your data grouped as you have it at the moment.

2. You might consider Goodman-Kruskal's gamma given that you have ordinal data. But in general to choose between the tests, look at the assumptions of each test and try to work out which one of them your data conforms to better.