Let's say I have two dimensions:
Dimension 1: 2 categories
Dimension 2: 4 categories
If I were to code information based on these dimensions and I wanted to compare the agreement (e.g., dimension 1 = 90% vs. dimension 2 = 70%), considering the difference of categories in each one, is there a statistic that weights by the number of categories?
Would it be more appropriate to dichotomise the categories of dimension 2 to calculate agreement? I mean calculating the agreement for each category of dimension 2 separately, so that it is "category 1 = yes or category 1 = no", "category 2 = yes or category 2 = no", etc., instead of calculating it for all 4 categories together. This way you would calculate the agreement for each category in dimension 2 separately, but the results could be compared with the results for dimension 1.
I would also appreciate bibliography on the topic.
Thank you!
I would suggest that you use the 2 category variable as the DV in a binary logistic regression. Use the remaining variables as predictor variables in your regression. This approach should yield the maximum amount of information in your data. I am attaching some course notes that cover the topic. There many more with examples that you can find with a Google search. Best wishes David Booth
As I understand, you would like to know if, when you analyse your data, the number of categories you use matters. To my knowledge, there is no statstic which weighs this. What you could do is, each time, for each number of categories, you calculate the chi-square on the number of yes/no answers.
Maybe if you only use 2 categories, the chi-square is not significant, while when you use 4 categories, the chi-square is significant.
In attachment a -- maybe extreme/ unrealistic -- example of a case in which this is be true, primarily due to the differences between the number of dimensions for "categorie1".
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