Maybe the research should include an error or other discourse analysis of the writing produced.
So: "Student 29 scored x on the pen and paper test, and y on the computer test, and demonstrated the following linguistic forms and/errors on the one test, and these on the other..."
Or something. Qualitative, anyhow. The point is, are we engaging cognitively in a different way when we write at a keyboard compared to pen-and-paper?
If I do this, I need to reframe the central question beyond advantage and disadvantage.