This question stems from this post here: Levels of Measurement - Comparing Scores from Different Tests
Consider a student takes a test, and each question has a score divided by the maximum score of the question (e.g. $5/10$, $1/3$, etc.).
How can I compare the $5/10$ against the $1/3$? Can I compare the ratios of these normalizations? Or can I only compare the order (e.g. $5/10$ is greater than 1/3)?
What about comparing the differences (e.g. $5/10 - 1/3$)?
In my head, it seems that only comparing order is meaningful because they are not normalized against the same quantities. Is this thinking correct?