1. Can I do one way ANOVA to know significant difference between my 3 groups on individual Likert items( each measured on 5 point scale). These Likert items are part of my unobserved latent variable. I have read that Likert items measured on atleast 5 point scale can be treated as interval / continuous data. Therefore I don't want to analyse it using non parametric Kruskal wallis test. 2. Am I correct in my approach?
Traditionally, a statistician would advise against it as it would violate the assumptions of ANOVA, but there is evidence to show that despite the violation of certain assumptions, ANOVA is capable of helping one reach the right conclusion.
Source- Article LIkert scales, levels of measurement adn the “laws” of statistics
At the end of the day, it is up to you. If you opt for the KW test, no one will question you. If you opt for ANOVA, someone might and you might need to cite this source to justify your decision.
Another option is to do both tests and see if they lead you to the same/similar conclusion. If it does, then you don't need to worry and can go ahead with ANOVA.
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