I am looking to compare individual's scores on different factors which have been computed based on responses to a survey. Specifically, the survey data corresponds to 4 factors, [call them Factor A, Factor B, Factor C, and Factor D] and I would like to know whether any individual, or group of individuals, has a propensity for Factor A over Factor B (or other pairwise comparisons). Each computed factor is scored out of 5, with the higher scores representing a propensity for that factor. The factors are "distinct" and "independent"
If I am overlooking what should be a simple statistical test, please do let me know! Otherwise, I will go into slightly more detail below. I would not put it past myself to be thinking too much into this, or overlooking the obvious!
Survey data was collected which was based on previous research that derived a four-factor scale (think similar to MBTI or Big-5). A confirmatory factor analysis was run on the collected data to ensure that the factor structure made sense, and the results appear to be significant. With this data there are two types of comparisons that seem sensible to make:
Compare how different groups score relative to one another on the different factors. If I am not mistaken, this is relatively straightforward testing (i.e. using ANOVA + post-hoc analysis or t-testing or similar). The previous literature focused on these inter-group comparisons (men vs. women, etc.), and mostly studied two-distinct groups with simple T-testing.
Compare how the 4 factors vary within any given group, or by the individual. That is: if respondent A scores a 5 on Factor A and a 3 on Factor B, can we say anything statistically about this difference? Is there a test that can talk about relative affinities for the different factors given some group correspondence?
So an example research question would be: "Do women have a stronger affinity for Factor A as compared to Factor B?"
Part of me is skeptical that such a test could exist, and that it would take more of a theoretical development of the underlying factors to ensure that they can be compared apples-to-apples.
In theory, the question "Does individual A really score higher on A versus B?" is a valid question that a researcher may want to know, I do not know that the scale by which this is being measured makes sense to compare?
I apologize if I am missing something very obvious, and I thank you for any resources you can provide for me. Let me know if something needs to be clarified!