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I have a rather difficult dataset. One measurement is non-normal and zero-inflated and could not be transformed to normality. Thus, a glm was used. Another set of measurements requires a multivariate approach. I tried a MANOVA but the data is non-multivariate normal (confirmed with mshapiro.test() from the mvnormtest package) and I cannot achieve normality with any transformation. I also cannot find a solid answer on how to perform a multivariate glm in R. Thus, I believe I am left with the non-parametric adonis function from the vegan package (for permutational manovas). So my question is, is it a faux pas to include a parametric test (glm) and a non-parametric test (permanova) in the same publication for a single dataset?

Not sure if this will help but here are the outputs of adonis and Anova(manova) of the same dataset. Significance follows same the trend.

> adonis
Permutation test for adonis under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999

adonis2(formula = data[, 4:ncol(data)] ~ Sample * Treatment, data = data, permutations = 999)
                 Df SumOfSqs      F Pr(>F)    
Sample            4  0.21326 4.1826  0.001 ***
Treatment         4  0.13082 2.5658  0.003 ** 
Sample:Treatment 16  0.34364 1.6850  0.005 ** 
Residual         50  0.63733                  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


> Anova(manova)

Type II MANOVA Tests: Pillai test statistic
                 Df test stat approx F num Df den Df    Pr(>F)    
Sample            4    2.8008   3.6704     84    132 1.209e-11 ***
Treatment         4    2.7037   3.2775     84    132 5.071e-10 ***
Sample:Treatment 16    7.2608   1.7804    336    720 9.870e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
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  • $\begingroup$ Welcome to CV, J.Con. This is an interesting question. Why not simply go completely nonparametric? (Are you hurting for power in your data set?) Leaving editorial policy aside, I think the issue is how compelling a narrative are you creating with mix-n-match methods vs a unified approach? $\endgroup$
    – Alexis
    Commented Apr 18, 2018 at 6:00
  • $\begingroup$ @Alexis thank you for the reply. These may not be the best reasons, but reasons they are. 1. I spent a lot of time and effort figuring out the glm for the first part of the data. I was helped by a professor and am positive it is correct. 2. Two papers with VERY similar designs that are directly relatable to this study used glms and it is necessary that I emulate them for that part of the dataset. Cheers $\endgroup$
    – J.Con
    Commented Apr 18, 2018 at 6:04
  • $\begingroup$ I frequently see varied analyses presented. Often it is useful to see results from multiple analyses - helps to confirm findings or show that findings vary under certain conditions. Regarding MANOVA, it is very likely your analysis will be fine without normality assumption being confirmed - MANOVA is robust to violations of normality with larger samples except in cases with extreme outliers. If the sample is large enough, and did not have have extreme outliers, I would use MANOVA. $\endgroup$
    – Bryan
    Commented Apr 18, 2018 at 6:38
  • $\begingroup$ @Bryan thanks for the comment. There are 15 samples per treatment, no extreme outliers. $\endgroup$
    – J.Con
    Commented Apr 18, 2018 at 6:40
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    $\begingroup$ There is no reason to not match parametric and non parametric methods in a paper, if there is a reason for analyzing things in the respective ways. If you seem to randomly vary methods with no rationale given, then there might be a concern that you picked methods based on what results they give. $\endgroup$
    – Björn
    Commented Apr 18, 2018 at 7:02

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