The graph below shows the cross-subjects correlation between scores on two different tests, taken by each subject. The scores are z-transformed at group level, separately for each test.
My question is: shouldn't the z-scores for each test by definition add up to zero for each of the two tests? In other words, shouldn't the scatterplot (cloud) be symmetrical around the zero point of both axes?
Could there be a mistake in how this graph was made, or simply in reporting how the z-scores have been computed?