Wpn Damage and Attributes

When a weapon requires a certain attribute is that requirement just for the mods or also for the damage?

For example, if I have a rod of 11-22 light damage that requires 11 smiting prayers but I do not have smiting prayers will the rod do less than 11-22 damage?

Thanks

Yes it will. It goes the same for Focus items. If the item needs 12 air magic for example to add 12 energy. Having zero points in air magic, the effects are only half. I tried adding a few points, but still remains at half.

Well I will answer my own question:
I had a rod that did 10-20 (req 11 Divine Favor). Fighting a whiptail devourer in Old Ascalon I did the following damage averages:
Divine Favor @ 11: Average 42.25/Hit
Divine Favor @ 5: Average 25/Hit
Divine Favor @ 1: Average 21.25/Hit