Question about plural "basis of observation"

[DanLand]

We use the phrase "basis of observation"
is the plural "basis of observations" or "bases of observations"

[Anglika]

That surely will depend on whether the observations are plural or the bases.

[Chris86]

"That surely will depend on whether the observations are plural or the bases." I don't quite understand. Can you help me with a specific question please?

I am writing a resume and discussing a previous tutoring position and one of the bullet points reads:

"Selected on the basis of teaching skill and academic achievement in the disciplines tutored"

However, in this context, since I am referring to two things, should it be:

"Selected on the bases of teaching skill and academic achievement in the disciplines tutored" ?

I am obviously referring to the disciplines of math and physics . Thanks for your help.

[Raymott]

"That surely will depend on whether the observations are plural or the bases." I don't quite understand. Can you help me with a specific question please?

I am writing a resume and discussing a previous tutoring position and one of the bullet points reads:

"Selected on the basis of teaching skill and academic achievement in the disciplines tutored"

However, in this context, since I am referring to two things, should it be:

"Selected on the bases of teaching skill and academic achievement in the disciplines tutored" ?

You could use 'bases', but it's not necessary, in my opinion.
Your skill base could consist of more than one component.

Another example: My foundation is in math and physics (not 'foundations are'). You have one foundation with two components - especially given that they are complementary.
If you had two separate unrelated skills, such as a PhD in physics and an MA in philosophy, you might say "My foundations are in physics and philosophy", or "Selected on the bases of teaching skill in physics and published articles on the philosophy of science."

I would use "basis" for your sentence.

I am obviously referring to the disciplines of math and physics . Thanks for your help.

PS: It is anything but obvious that you are referring to math and physics. I could find no evidence at all for this inference.