# Correlations between test question scores with discrete and small number of values

I am a newbie at statistical analysis. I have been using the Pearson correlation coefficient for pairs of test question scores.

The test had questions some of which carried 1, some 2 and a few carried 3 marks. The questions were graded with a least count of 0.5 marks - so in a 3-marks question, a student can get either of the following scores: 0, 0.5, 1, 1.5, 2, 2.5,3.

I am not sure if using the Pearson correlation coefficient for such data that takes less number of possible values is still valid. I suspect that the values of $r$ that I get may not reflect the real correlations.

What is a better way to calculate correlations in this situation?

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