Please refer to the table attached. For dependent variable
(Y) where the difference in slope is not significant, i have labelled them in yellow.
1. If i am not mistaken, the convention is to just report that the interaction factor is not significant. However, i performed the Kruskal-Wallis test and presented those results instead because I feel that for insignificant slope models, the KW test is more representative and can better display the difference compared to just the intercepts (lowest values) in the regressions. Is what i did okay?
2. For reporting the linear model and the coefficients as shown in the table, how should i do it? "a" and "b" are coefficients of intercept and slope respectively. Since the slope is not significantly different, can i present only "a" and blank-out "b" for aesthetic purposes? Would that be okay/correct for reporting a model?
3. Alternatively, can i report some figures/values from the KW test as model coefficient instead of "a"?
Thank you...
It's really not clear from your question what you are trying to do. It would help to be more explicit as to what model you are starting with and what the a's and b's in your image represent. The best approach is to make up some toy data, and present your analysis and results, so readers know exactly what you are doing.
1)
If you are starting with a general linear model, it would be weird to switch to a nonparametric test like Kruskal-Wallis as a post-hoc test. If the interaction term is not significant, why not use something like lsmeans or emmeans (in SAS or R) to present the marginal means and their statistical separations for the effect in question? (Maybe after dropping the interaction term). Would this not do what you want? Or, why not use something akin to a Tukey HSD rather than the Kruskal-Wallis?
It's difficult to know what advice I might give because I don't know what model you are starting with, or what you are trying to show with the K-W test.
2)
It think that would be okay.
3) Again, it might just be weird for readers if you combine reporting OLS models and a nonparametric test. Might be okay. Although would be difficult to label in one table.
Thank you Salvatore.
I apologise for the not-very-clear question and the confusing a's and b's.
1. The reason i thought of switching to another more representative and comprehensive test (not necessarily KW) is because with insignificant interaction terms, what is left is only the intercept comparison (the minimum value, hence does not represent the data very well). The reason i choose KW is because of the unbalanced design and highly non-normal distribution of the data in all ways (Heteroscedasticity, skewness, kurtotic, etc.).
Thank you for the suggestion of using lsmeans and emmeans. This is new to me and i have never used it before. I did click into cran and read the description. Looks like it can fulfill what i am trying to do pretty well. But considering that it is a test of means, it is okay for me to use it (considering the nature of my data)?
2. Understood!
3. Yes it would be weird. I thought the same as well. Still considering this option.
Thank you for your words!
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