In humans, the sinus size is directly correlated with the size of the frontal lobe:
Ancient Beat 35 – Hominin Sinuses Dual Stelae and New Dating Methods

The frontal lobe is mainly responsible for speech, regulation of emotions and strategic planning. Researchers have found that they can study the neural abilities of ancient hominis through the size of their sinuses (i.e. by directly measuring the skull, no brain scans needed!).