Is grade of course discrete or continuous variable?**

[Deepty Sarder]

Is grade of course (e.g. value starts from 2.00, 2.25, 2.50,............3.50,3.75, 4.00) discrete or continuous variable? if grade of course is dependent variable of a study, what should be appropriate regression model for that study?

[Maarten Buis]

At the very least grades are ordinal. Whether or not is interval, i.e. the "distance" between 2.00 and 2.25 is the same as the distance between 3.75 and 4.00, is questionable. If the grade is based on lots of multiple choice questions, and the grade is basically a transformation of the number of correct answers, then you could make that case. If the grade is based on essay questions than probably no. However, you also have to be practical: a model is not supposed to be true, but a simplification of reality. Treating grades as interval scaled certainly simplifies things. The question is does it simplify too much, and that is up to you to answer and than justify (typically that happens in a footnote saying something like "I also tried a ordered logit model and it did not change the conclusions").

[Nick Cox]

For more discussion, see (e.g.) https://stats.stackexchange.com/questions/67551/calculate-mean-of-ordinal-variable

My answer got most votes (I like that bit, but feel compelled to underline that democracy doesn't always work to select the smartest and most truthful alternative on offer) while there were some disagreements too (par for the course here, and you may like that bit).

[Marcos Almeida]

Thanks for sharing the link. Great discussion, great lessons. ‘Polemos pater panton’.