Besides its workplace uses, like Charisma in Living Quarters, Strength in Power Generators, Agility in Diners.
Do we know if Endurance increases HP in the Dwellers, or that strength helps in melee damage / survivability in the wastelands? And Perception?
Best Answer
Do note that nothing has been made official, and this is a compilation of observations/hypotheses.
Strength
Perception
Endurance
Charisma
Intelligence
UPDATE:
Agility
Luck
Further reading and sources:
Tip:
UPDATE: If you want to nerd out on more specifics, I recommend Section 7 of this Fallout Shelter Efficiency Data.
Also, here someone suggests that skills above 10 continue to benefit the dweller/explorer: