The foto gallery sub-folder (in this folder) contains two graphs of physics STAR scores of an HS physics class.  The first shows the data supplied by the teacher.  He selected the most recent five years to show the monotonic improvement.  Curious, I graphed it and concluded that perhaps the improvement was not solely from “better” teaching, but also due to self selection.  (A greater proportion of the more “capable” students were electing to “take” physics.)  After receiving some umbrage from the teacher, I extracted from the STAR web site all the data for that physics class (i.e. all presented in the same format) and found a much reduced correlation.  So I think the problem is too small a sample.  So my question is:  Is there a test for the confidence in concluding there is a valid correlation derived from the sample number and the correlation coefficient?

Incidentally, for the last ten years of physics in all the tested California classes the scores have increased much, and the proportion of all subjects tested students, tested in physics has increased also.  No sampling error there!