I didn't, all I did was test the max hit. If a weapon's max hit is higher than another, then its dps is, naturally, higher, if everything else (Rotation, accuracy, no auto attacks, etc) would also be higher.
How do I test Max hit? By hitting a critical strike with an ability. Hitting a critical strike with an Ability will always inflict the maximum possible damage from that weapon, the image proofs lie in the hide tags.
Note: all following critical strike were performed without any prayer or potions, and with 99 strength
Result: Ability crits are always the same, given the exact same weapons, stats, prayers
After some testing, I have decided to test weapon damage from Crits achieved by using Punish (as conveniently it hits for exactly 100% weapon damage at crit)
The following weapons were used:
Rune Claw, Rune Long Sword, Rune Battleaxe, Rune 2h Sword
Dragon Scimitar, Dragon Long Sword, Dragon Battleaxe, Dragon 2h
Perculiarly enough, the results doesn't show what we always assumed... the weapons do not all do the same damage on the same tier...
For one handed weapons, slower weapons are actually better, though the margin is quite small (of the order of around 1% between best and worst)
I will post my findings with regards, to DW, and 2h tomorrow, but it follows largely the same pattern.
Also, Dual wield weapons do NOT depend on Tier, it depends on Normalised weapon damage, which, under nearly every circumstance, would have been the same as tier, but EE is the only, and one major exception. In short, EE's damage is 'real' (as in equipping it does improve your damage by what it says on the description).
Lastly, Mixing different weapon speeds of the same tier has a very small effect on damage.