Spearman Ranks
Spearman’s Rank correlation coefficient yields a perfect positive correlation for data that follows the x2 function. Pearson’s Product Moment correlation coefficient will yield a lower value, as the coefficient measures the extent to which the data follows a straight line.
In was walking through this kind of thinking with a group and explaining tied ranks, when someone asked ‘why bother with the ranking’? I pulled up a photo of the kind of calculator that Pearson and Spearman were using at the turn of the 19th century, and they got the point straight away… The history of calculation is part of the reason Maths is like it is. Perhaps in 20 years we will be using exact distribution methods for statistical tests.