That may sound a bit complicated, but it's not too bad and it's a critically important distinction to make. Basically, the idea is that numbers which are greatly outside the norm, tend to skew results.
Taking that idea into consideration, we go from correlation of 0.30 (that's on a scale of -1 to 1) to a correlation of 0.72 with Pearson Correlation and even to an astonishing 0.95 using a Spearman Correlation.
A 0.95 correlation is nearly a statistical causation, meaning at a 1.0 correlation there's a certainty that more links mean better rankings.
This is a study which I think will have significant impact on the world of SEO, and in fact it's already getting some well deserved attention here: http://searchengineland.com/new-google-ranking-study-shows-links-incredibly-important-ranking-algorithm-254188 for example.