Hello everyone! I was attempting to run a Two-Way MANOVA for my analysis but my data has failed both normality and linearity assumptions. In regards to this, the sample size is small and unequally distributed so it is expected. However after looking online some people question for example, the normality of MANOVA, saying that if it is not met one could report Pillai's Trace as opposed to Wilk's Lambda. Is this valid? Furthermore, is this still valid if linearity is not achieved as well? Many thanks.
Regards,
Flávio Gomes
Hello Flavio. You say ANOVA in the headline, but MANOVA in the question itself. You also omit information about what you believe the assumptions to be and how you went about assessing whether they were violated too grossly. I think it would help if you started over and provided a lot more detail. Here are some questions to get things started:
Thank you for clarifying. There may be other questions depending on your answers to those questions.
Bruce Weaver
1. There are two DV. Distress and Worry scores. Yes they can.
2. I have one multivariate question.
3.I am not sure I understand what this asks for, I am sorry.
4.I am not sure I understand what this asks for, I am sorry.
5. Sample size is short (45 participants) but I was advised from my supervisor to run the analysis as it is anyways and comment on that issue.
6. I run Shapiro Wilk's and both values were P>.05
7. Linearity was checked for using Box Plots; no eliptical was formed from bottom left to upper right corner.
8. It is for a dissertation :) My supervisor is not answering me during the weekend which is absolutely normal but I would like to have this finished by today.
Hello Flávio,
As you probably understand, manovas based on N = 45 are not likely to have a lot of statistical power unless the effects are large.
Bruce Weaver's question #3 has to do with identifying your independent variables/factors (and their levels).
Bruce's question #6 asks you to describe how you evaluated the multivariate normality assumption (Shapiro-Wilk, as implemented in most statistical packages, is a univariate check). As well, you should either: (a) estimate case residuals for each of your 45 data cases, then check these for normality after fitting the manova; or (b) run the normality checks separately by cell of your design.
For Q #7, it's not clear how box plots are going to help you with linearity checks.
Finally, you may wish to consider the use of bootstrap/resampling significance tests or confidence interval estimates for the parameters of interest, as this family of methods allows you to ignore distributional assumptions.
Good luck with your work.
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