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.Q:

Kruskal-Wallis test on a categorical variable vs. a continous variable vs. any of both – pros/cons?

I’m having a hard time figuring out if it’s better to use one of the following options:

Categorical variable
Continuous variable

I was trying to put up an experiment to test the effect of the X-factor, X, to Y-factor, Y, but I’m not quite sure how to test it. I’ve seen a lot of comparisons on problems like this on the web (see e.g. here), however I’m having a tough time figuring out if the assumptions are met in my case or not.
For instance:
The effect of a Group 1, G1, to G2, G2, to G3, G3, for a continuous variable, X, should follow a linear model $G2, G3: m_{G2}=\beta_0 + \beta_1*G2$ and $G3: m_{G3}=\beta_0 + \beta_1*G3$, where $\beta_0$ represents the effect of G1 to G2 and $\beta_1$ represents the difference in the effect between G2 and G3. $\beta_0$ and $\beta_1$ are the main effects of the individual factor groups.

A:

I see it as very similar to comparing 2 separate treatments with one control condition.
Kruskal-Wallis isn’t what I’d choose. Its limitations are described in the wikipedia page, which are also discussed in the related questions that you’ve linked to.
I would probably use ANOVA, with repeated measures on the groups. Thus I would avoid the comparison of 3 groups.
In your case, you would compare Groups 1 and 2 to the pooled group with 3 levels. This difference shouldn’t be significant.
I think it would be an issue if you need to test the difference between G1 and G2 vs. G1 and G3, but you don’t need to run a test for G2 and G3. You could consider running a 2-way ANOVA on that. The results of that would not be a simple difference between Groups 1 and 2 vs. 3.

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