Hello Dendy,

Yes.

1. Use either exact/permutation or bootstrap/resampling versions of the parametric program. Either approach allows you to ignore normality requirements. More statistical packages include bootstrap/resampling options.

2. Try the aligned ranks procedure: https://rcompanion.org/handbook/F_16.html

Good luck with your work.

I agree that bootstrap methods are a possible solution, but you should have a resonable amount of information about the distribution in your data - what means that your sample size should be rather large - what means that the normality assumption of the ANOVA is possibly not really relevant.

I don't see how interactions can be analyzed in any meaningful way with ranks. Using rank-based methods (Kruskal-Wallis, Friedman, Wilcoxon etc) are already a nightmare if the tested (and possibly rejected) hypothesis should be interpreted in a way that would make sense for the research question.* This may be highlighted with the question at what scale the interaction is to be analyzed. Interactions can exists on an additive (linear) scale but not at a multiplicative (log-linear) scale. rank transformations are invariant under monoton transformation (like the logarithm), so how should the interaction in a rank-based model be interpreted?

My advice would be to get a better understanding of the variable you are analysing to identify a sensible distribution model and then check options how to proceed. This could be recognizing that the non-normality is irrelevant, using a transformation, using a test designed to work with that distribution, etc.

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* The hypothesis can always be framed as stochastic equivalence, but this may not at all be the hypothesis that is intended to be tested. It's easy to construct examples of the two-sample problem where mean(A)>mean(B) and at the same time median(A)

Friedman’s two-way ANOVA by ranks is considered the nonparametric equivalent of the two-way ANOVA. The following publications could be relevantly helpful.

MacFarland, T. W., & Yates, J. M. (2016). Friedman two-way analysis of variance (ANOVA) by ranks. In T. W. MacFarland & J. M. Yates (Eds.), Introduction to nonparametric statistics for the biological sciences using r (pp. 213–247). Springer International Publishing. https://doi.org/10.1007/978-3-319-30634-6_7

Pereira, D. G., Afonso, A., & Medeiros, F. M. (2015). Overview of Friedman’s test and post-hoc analysis. Communications in Statistics - Simulation and Computation, 44(10), 2636–2653. https://doi.org/10.1080/03610918.2014.931971

Good luck,

Hi, Mohialdeen Alotumi . As the original poster notes, Friedman's test cannot be used with a design where there is more than one observation per cell. That is, with "replicated data". Instead, Friedman's test works only with unreplicated complete block design. Literally, there is no way to put replicated factorial data into the Friedman test. I know it's common on the internet, but I wish authors wouldn't characterize Friedman's test as analogous to a two-way anova. I was particularly dismayed to read the synopsis of the MacFarland and Yates chapter, which seems to just make a muddy mess of the differences.

If there is any traditional nonparametric analysis that is analogous to a two-way (replicated, factorial) analysis of variance, it's the Scheirer–Ray–Hare test. But this test isn't always well-regarded.

It's probably better to use aligned ranks transformation anova, or, as appropriate, ordinal regression, quantile regression, a generalized linear model, permutation anova, and so on.

What assumptions failed that decided you go with non-parametric methods? Just curious to know because parametric ANOVA is pretty robust to failing assumptions.

Factor analysis can be done

Ravishankar Suryanarayana please explain, how factor analysis would answer the research question Dendy Gusmawan has? Please elaborate on it, I am curious!

If you have one treatment and one blocking factor, then you can try Friedman test

Read more here https://www.reneshbedre.com/blog/friedman-test.html

Renesh Bedre , The original post mentions Friedman's test and explains why it's not a possible solution.