The gap between Shanghai and the second place finisher for the math scores is somewhat more spread out than the corresponding segments in reading and math. The rest of the distributions appear fairly constant. So the most likely explanation for this would be that the Shanghai schools were specifically trained for the “PISA” exam and this training was most effective for the math subject test. Once again the jumbling and narrow range of scores in the top third in all test categories (except Shanghai which appears to be an outlier) is also supportive of the idea that Shanghai is “gaming” the exam.

What we are ultimately left with from a strict statistical numerical point of view are pretty modest distinctions. Based on correlations between rankings in the three subject area tests supports the idea that there might be statistically significant outcome differences as measured by this test between countries in the top and bottom thirds of the rankings. In my view even this relatively modest inference would be weakened and might not stand up to real critical examination of the sampling (how the representative groups were chosen for comparison)