Hi all,
I hope you are all doing well. I have a mixed design (2x2) with a Likert (1=I strongly not agree, 5=I strongly agree) scale dv and med based on 3 items. I created one unweighted scale for both variables.
Now I wanted to do a two way mixed anova but when checking for the assumptions (normality etc) it was absolutely not normal distributed when looking at Shapiro Wilk test (sig 0.000) I found out you sometimes can use a summated Likert scale as "interval" but not always, and in my case I think not as I believe my scale is ordinal? Then I was thinking about an ordinal logistic regression but I am not sure if this works for a mixed design. (p.s. both Moderator and IV are manipulated).
Does anyone would like to share their thoughts or have experienced the same issue, let me know!
Kind regards,
Maayke
Hello Maayke,
If, by mixed design, you mean that one factor (IV) is a between-subjects factor (having two levels), and the other IV is a repeated-measures factor, then your choices would be:
1. treat the measures as interval strength (more on this below), and use ordinary, one-between, one-within anova;
2. treat the measures as ordinal strength, and use aligned ranks procedure (https://rcompanion.org/handbook/F_16.html)
3. use ordinal regression.
The interval strength option can be embraced more confidently if you first were to compute measure scores via item response theory (possibly using the graded response model) or factor the scores (and use factor score estimates as the measures).
Good luck with your work.
You can use Kruskal Wallis or Chi Squared tests. Don't transform the data because it's better to be transparent and analyse actual data. But a one way anova can tolerate non-normal data except if the sample size is low :)
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