> If the chi-square is the same regardless, do my students need to say WHICH test they are doing? Is it enough just to say it's a chi-square test?
In the past, students have been expected to state the null and their conclusion differently depending on which design was involved. This has always troubled me because the null and the interpretation of the 'two" tests is the same -- it's the design that differs. I would not mind if they asked students about the design directly or asked which would be the better design for a particualr situation, but I can't see any point in burying the design difference in the test itself. You only have to read all the questions about this posted here to see that that did not work;-)
A similar situation is the use of a t test for a single mean or paired differences. It's the same test, but in that situation students are expected to understand the design difference, but not usually to change the wording of the null or conclusion to show that.