What test should be used to test if DV1 is significantly higher than DV2, where both DVs are continuous over the same range?

Question

I am looking at relationships between student scores in different subjects.

I have the following 4 variables:

• V1: score subject 1: continuous from 0-30, converted to categorical: low (<10), medium (<20), high (>=20)
• V2: score subject 2: continuous from 0-40, converted to categorical: low (<20), high (>=20)
• V3: score subject 3: continuous from 0 to 10
• V4: score subject 4: continuous from 0 to 10

I want to test a hypothesis of the following form:

Students that have a high score in subjects 1 and 2 score better in subject 3 than in subject 4.

So I am considering V1 and V2 as independent variables (IV) and V3 and V4 as dependent variables (DV).

What statistical tests can I use and which one would be most appropriate?

Because V3 and V4 are of a similar nature and have the same range, it seems like it should be possible to compare their means in some sort of ANOVA. Is that correct?

My current thoughts are:

• They cannot be compared because they are two separate dependent variables? Is there any test to compare the means of two separate variables?

• I need to create a special continuous variable to evaluate which score is better and then compare the mean of that between groups. Ex: V5 = V3 - V4

• I need to create a special binary variable to evaluate if V3>V4 and then do a logistic regression of that versus V1 and V2 as continuous variables instead of categories.

• Flip it around so that V1 and V2 are DVs and V3 and V4 are IVs.

Answer 1

I would first of suggest the following, if you still have V1 and V2 as continuous (as you stated), use this instead of converting it to categorical variables. There is more data ('power') in this than in the categories alone.

If I read it correctly:
V1 is predictor var (continuous)
V2 is predictor var (continuous)
And your dependent var (outcome var) is then V3 -V4? (also continuous)

If done like this you can use multiple regression. Yes technically this requires your data to meet the assumptions for parametric testing. But in practice it is not very common that this would give you a significant results when there isn't one or vice versa.

If you were to use the categorical version of your predictor variables (V1 & V2), you would aside from multiple regression have factorial ANOVA as option (but this would also not alleviate that your data would technically need to meet the parametric assumptions).

I hope this helps!

//I expect there exist special non-parametric test/algorithms for designs with multiple predictor variables (as you have), as there are a lot of common ones for single predictor variable designs (e.g. Spearman Correlation, Kendall's tau, Kruskall Wallistest, Mann Whitney etc).. Perhaps you can try specifically googling for this, if the multiple regression approach does not cut it for you