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I have to analyse 8 independent variables (IV) toward 8 dependent variables (DV) in my research. The IV is nominal while DV are ordinal (Likert-scale). I run the normality test and the result is zero (p<.05) which lead me to perform non-parametric statistical test to the data. I chose the Kruskal Wallis test at first, because I wanted to test the differences among the groups (involved lots of groups) in influencing the DV. Since my hypothesis is just wanting to know if either of the IVs are significantly associated or not with the DV, I neglected the role of post hoc analysis (for instance Mann-Whitney U test), because my aim is not to know which group causes the differences.

My question:

  1. Is it a must to do post hoc analysis for Kruskal-Wallis test? i'm afraid my analysis go wrong if I just report the significant value of Kruskal Wallis result. I found some article that just report the result of mean rank, rather using Mann Whitney U test. Is it acceptable if I just report the significant value and mean rank of the result? If I proceed with Mann-Whitney U test, I am gonna end up producing lots of result (possibly more than 1000 tables for that purpose).

  2. I consult with several people and they suggest that I use MANOVA because my study involved lots of variables. Therefore, they suggest MANOVA which assist in producing result based on the whole data, not segregated like Kruskal Wallis analysis. However, I found that the data shall be in normally distributed in order to proceed with it. My data are totally non-normally distributed. How can I proceed with it? Is it wrong if I used MANOVA for non-normally distributed data?

I confuse in choosing the appropriate analysis. Which one should I use for my research? Thank you so much for your help! Please let me know if there is any other information I should provide.

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    $\begingroup$ Welcome to CV, farah! The Mann Whitney $U$ test is inappropriate as a post hoc test following rejection of a Kruskal-Wallis null hypothesis, because (1) the Mann Whitney $U$ test does use the same rankings as K-W (it uses pairwise rankings), and (2) the Mann Whitney $U$ does not incorporate the pooled variance estimate implied by the K-W test. Dunn's test, and the (less well know, but strictly more powerful) Conover-Iman test are appropriate post hoc tests folling the rejection of K-W. $\endgroup$
    – Alexis
    Commented Apr 17, 2020 at 4:19
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    $\begingroup$ The general sentiment on Cross Validated is that a formal test of normality is unhelpful. You got a small p-value...okay, but p-values do not just measure how large the deviation from the assumed null hypothesis is. Sample size plays a huge role, and fairly large sample sizes can result in normality testing rejecting even though the difference is not enough for us to care to change our methodology. Graphical examination of your data, such as a normal quantile-quantile plot, is likely to be more helpful. $\endgroup$
    – Dave
    Commented Apr 17, 2020 at 7:09
  • $\begingroup$ Even with @Dave's good comment, a semiparametric model is likely to work better. The proportional odds model is a generalization of Kruskal-Wallis-Wilcoxon. It won't handle multivariate Y but will handle the univariate part of the problem very well. For multivariate you might use the Peter O'Brien approach of averaging ranks across DVs. $\endgroup$
    – Frank Harrell
    Commented May 29, 2021 at 12:11
  • $\begingroup$ I’m looking at this a year later and think I might have jumped on the normality test issue without reading the context. What did you test for normality, the independent or dependent variables? $\endgroup$
    – Dave
    Commented May 29, 2021 at 12:45

2 Answers 2

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For 8 input variables and 8 outcome variables, you need multivariate multiple regression or MANCOVA.

MANOVA is used in case of one input and multiple outcomes.

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    $\begingroup$ It might be worth making a comment about the normality requirements, since that is a large part of the OP's concern. $\endgroup$
    – Silverfish
    Commented Mar 16, 2016 at 11:29
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Can I ask what your sample size is? Are you planning on running all those tests?

Is there no other way of reorganizing your data?

If not, why not use the following multinomial model:

DV = IV1 + IV2 + IV3 + IV4 + IV5 + IV6 + IV7

where each of your nominal categories are dummy variables (1,0) and your IV 8 is your baseline?

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