The increase in strength between a 1.5" and 2.0" plank depends on how it is loaded. If the load is parallel to the 2.0" dimension (used as a beam) it will be 1.95 times stronger (1.25 cubed) and if the load is perpendicular to the 2.0"(used like a plank) it will be 1.25 times as strong.

In practice, rough saw lumber needs to be degraded for defects, so the above is true only if both pieces have the same defect density.

Rafter and joist tables take the actual vs. nominal dimensions into account.