Bit of a stats newbie question here. I've got about 10,000 rows of data about pupil performance, annotated with school and teacher details, that look as follows:
Pupil School Grade(1-5) Teacher 123 Morley 4 Adams 124 Westlake 3 Morris 125 Morley 5 Adams 126 Westlake 2 Philips 127 St Xavier 4 Smith
I've calculated that the overall mean grade is 3.4 with standard deviation 1.0.
Now, say I want to work out whether one school (or one teacher) has overall a significantly lower or higher performance than average.
If I calculate that the overall mean grade at Morley is 3.9, with s.d. 0.8, the overall mean grade at Westlake is 3.2, with s.d. 0.7, and the overall mean at St Xavier is 3.8, with s.d. 0.5, what test can I use to say whether any of these schools have a significantly different performance from the average?
From my knowledge so far, I'm guessing I want to use some form of t-test, probably Student's t-test - although I'm not sure how to adapt it for multiple groups.
(Of course, there are lots of factors influencing why grades might be lower at one school than another and yet that school might still be performing well - I'm not getting that deep here. I just want to know how to compare means across sub-groups.)
Many thanks for your help.