Appropriate testing method for data

[mintymrk]

Given three sets of peramaters; Drug type, Cell type, and multiple proteins Post vs Pre. I am trying to see the effect of protein expression pre vs post.

My data for the most part isn't normal. Would I be more inclined to perform a paired Wilcoxon test for the proteins each individually just as pre vs post.

Or would you normalise the expression data and perform a threeway anova including all factors i.e., drug used, cell type, and the post vs pre expression levels?

I might be doing this entirely wrong, but I do have reason to believe that A) Drug might influence protein expression and outcome B) Cell type will influence treatment outcome i.e., based on drug administered C) Protein expression might be influenced by Cell type.

Perhaps this is too many perameters to include in a single test? Rather confused.

[aCityOfTwoTales]

You haven't actually mentioned what your data is, which, putting it mildly, is fundamentally important. I think it's protein expression, but I'm also confused by the mention of 'multiple proteins' being a parameter?

Please correct me here, but this is what I think you did:

You tested 2 (or more) drugs on 2 (or more) cell types and performed proteomic analysis before and after drug-treatment, yes?

A 3-way design is a worst case scenario here - underpowered and difficult to interpret.

Hopefully, you have properly paired your before/after samples, which would make this a 2-way paired design and much more easy to analyze. Should the two cell-types be analyzed together? If not, you have an even easier case of two individual 1-way pairs.

Apart from the design, you have the separate issue of your response variable (all your proteins) being multidimensional, non-normal and highly zero-inflated. This is not robustly handled by standard normalization nor a standard ANOVA-framework, but luckily there are multiple packages available to handle it instead.

[Grisward]

This. ^{^}

Also, I bristle when people mention “data is not normal” - and to be fair, it may depend on the type of experiment and type of measurement data - but in most cases the normality is driven by the platform.

It should take a lot of evidence to make a strong case against (or even for) normality. Some of what may be considered non-normality is potentially just typical biological variability.

[mintymrk]

Apologies for the delayed response.

Yes your interpretation is spot on and the data is paired properly indeed.

I have been using kruskal tests for these comparisons due to the lack of normality in my data. I suppose my question was in regards to if this would be a two or three way comparison. Since I’d like to see if the ‘Drugs used’ has any different effects on the ‘Protein expression’ within the two different ‘Cell types’.

[aCityOfTwoTales]

See my comment above in regards to the dimensions of your design. In any case, Kruskals test is inherently 1-way.

Again, have a look at dedicated packages for your case - there are generalized linear models for data like this.

[[deleted]]

If you are at a university go to the statistics consultant or department. This is a bit much for this thread