Density and bending strength in UK-grown Sitka spruce: correlated, not correlated, or a secret third thing?

Everybody who has never strength tested timber knows that the denser timber is, the stronger it is in bending. Only people who have timber testing laboratories have reason to doubt this. But exactly how much data do you need to be uncertain about the correlation, and is there a point when you can have enough data to begin to believe, once more, that there is a correlation? Pearson’s correlation coefficient (R) is not without problems that researchers commonly turn a blind eye to (e.g. Armstrong 2019), but if we calculate enough of them, can we confidently draw a conclusion out of our Rs? I should make it clear I am not talking about trends in average properties, across different species and different growth areas. It is definitely the case that, overall, denser types of timber are stronger. But what about when it comes to sorting individual boards from a particular resource; a certain species from a certain growth area. Is density of use for this? In this paper I present a very large (but still insufficient) amount of strength and density data from full-size four-point bending tests of spruce grown in UK. Two approaches are shown for considering the likely value of Pearson correlation coefficient, and whether the subsamples are consistent with the overall population. There does appear to be a very weak correlation (R ≈ 0.45, R2 ≈ 0.20) in this particular case.