Instead of 1.5, you get twice your strength modifier.
Example: Harry the Half-orc has a 18 strength and swings a great axe, dealing 1d12+6.
Tommy Two-Hands is a fighter with the two handed archetype. He has an 18 strength and swings his great axe for 1d12+8 points of damage.
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A related question:
Overhand Chop (Ex)
At 3rd level, when a two-handed fighter makes a single attack (with the attack action or a charge) with a two-handed weapon, he adds double his Strength bonus on damage rolls.
This ability replaces Armor Training 1.
This ability allows the fighter to add double his strength bonus to damage as long as he is only making a single attack.
Backswing (Ex)
At 7th level, when a two-handed fighter makes a full-attack with a two-handed weapon, he adds double his Strength bonus on damage rolls for all attacks after the first.
This ability replaces Armor Training 2.
This ability allows the fighter to add double his strength bonus to damage with every attack after the first.
It seems to me that the two abilities are mutually exclusive and as such the fighter doesn't get double his strength bonus to all his attacks no matter what. Am I reading that right? Because if so, then my question becomes why? Why gimp the first attack on the full-round? I wouldn't mind the restriction untill lvl 7 but why after?
Probably the same reason that Furious Focus only works on the first attack each round.