I am trying to relate a professional group's level of understanding of a concept to the safety practices the group subscribes to, and to the safety practices the group engages in. My survey utilised a 5 scale Likert, with one question determining the level of understanding of the concept, seven questions regarding safety practices subscribed to, and another seven questions determining level of engagement in those safety practices. I have done the chi-square test with the 'understanding' question against each of the fourteen questions mentioned above, to determine a significance/relationship. Now I am wondering if I would be better served by something other.
Chi-square have certain limitations to explain the hierarchy of relationship. ANOVA can show you the linear relationship. The entire analytical pathway depends upon your experiment design, and your setting of the hypothesis. For identifying relationship after removing effects of other variables, regression analysis is helpful. Sometimes I do the dependent variable dichotomous and do regressions.
I do not see how ANOVA can be used here. Firstly, the data is nominal (at best ordinal) and not metric, and secondly I wonder what kind of "hierarchy" should be there to analyze.
I think that Chi² will give you a hint which frequency distributions are different. This is ok, but it ignores a correlation. This means: it might be interesting to know if (the rank of) safety practice of a subject correlates with (the rank of) understanding. This, I think, can be analyzed better using rank correlation (Spearman's rho or Kendall's tau).
I agree with Jochen (although I'd also add somer's D to the mix). Additionally, given that you have several questions, perhaps you're better off using factor analysis (or perhaps IRT) to generate a proper tool with a composite score?
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