Good evening Fady,

If I understand your question correctly you are trying to test whether a continuous dependent variable (parameter A) has meaningful differences across an ordinal independent variable (degree of deformity).

The Kruskal Wallis H test is the appropriate test in this circumstance. References on how to implemement the text can be found on wikipedia and on many other sites on the internet.

Let me know if I understood your question correctly and if the Kruskal Wallis H test is sufficient to test your hypothesis.

Best,

Aran

Close! I want to test whether the CHANGE in a continuous dependent variable (parameter A) has meaningful differences across an ordinal independent variable (degree of deformity) before and after a surgical intervention. I think the Kruskal Wallis H test would work for comparing parameter A pre- and post-intervention, but would not help me compare the change.

Your second question (compare changes between different degrees of deformity) is similar to the first (comparing changes between different treatment groups). Io answer your second question you won't need to consider the data of the control group (no surgery) at all.

This was the simple solution. Another, possibly theoretically better solution is to think about an appropriate model that explaines the expected outcome depending on the rest of the available information (surgery, deformation, whatever else...), and possibly adress interesting interactions between these predictors.

I like your idea for building a model of all available information. I am comfortable performing a multiple regression, but I am curious what the best method for testing the interaction between SEVERITY and TREATMENT would be. Should I include an additional independent variable "SEVERITY*TREATMENT"? If I do include this variable should I also include SEVERITY and TREATMENT alone, or should I only use the combined variable?

Thank you both for your help!

Yes, the interaction between SEVERITY and TREATMENT is modelled by their product, when both variables are also in the model. So you need all (both alone and their product). The interpretation of the coefficients for the simple effects (not the product) depends on the kind of predictors (categorical or numeric) and how they are coded. I would consider centering numerical predictors.

@Fady

You said,

"Using simple t-tests we can say that Parameter A improved more in the group that did undergo the surgery vs. the group that did not [undergo surgery]."

Does this imply that the non-surgery group also improves? Your t-test shows that surgery results in better improvement?

You are also,

"... trying to see if there is any difference in that change for patients with mild, moderate or severe deformity."

This implies that patients are ranked by severity in, at least, three levels.

Is it possible to rank the patients in more levels? Say, if you have twenty patients, can the patients be rank 1 to 20 based on severity?

Ranked individuals allow plotting by quantiles. Plotting in quantiles will allow observation of the change in shape of the quantile plots and easy comparison of before and after, treated and untreated. You can, also, observe if individuals maintained their ranking or if a few individuals influenced the average change in any subgroup.

that’s a great suggestion! Unfortunately the mild, moderate, severe rating is an accepted system for descring this deformity. I appreciate your suggestion.

I think I successfully measured the interaction of SEVERITY and TREATMENT using multiple regression. Thanks everyone for the help!