Say I administer a test to 30 students. I randomly divide the test questions into two parts and score each half for each student. I then calculate the correlation coefficient between scores on each half, across students.
How can I, nonparametrically, evaluate the uncertainty associated with this correlation coefficient?
One idea that occurred to me would be to repeat this procedure many times, each time dividing the questions in half using a new random partition. Would the resulting distribution of correlation coefficients be equivalent to a bootstrap?