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Endurance matters regardless of activity, if your dwellers are not level 50 already. Once at level 50, endurance is not as critical. Endurance does not seem to help much with combat radiation damage inflicted by radscorpions and ghouls.
Perception, Agility, and Luck are the other known useful stats for questing. Perception slows down the arrows for the critical mini-game so you can get better criticals. Luck increases the frequency of the critical mini-games. Agility increases attack speed, but boosts past A10 are lot smaller (A10 attacks speed is not much slower than A17).
Of the remaining stats (Strength, Charisma, and Intelligence), there is unconfirmed theory that Strength boosts damage with the new melee weapons. Unknown if Intelligence provides any bonus on using Stimpacks and Radaway. Completely unknown if Charisma has any effect at all.
P slows down the speed of the "crit"-thingy.
E increases health on level up and reduces radiation gain.
C propably usefull to get more friendly encounters during exploration
I no idea.
A increases attack speed.
L increases chance to get a crit.
So for questing PEAL would be the best possible.
For exploring... dunno I recently send out a guy with mixed stats and he did fine for like 9h and only used 3stims and 1 radaway. Called him back at that point.
https://github.com/therabidsquirel/The-Fallout-Shelter-FAQ/wiki/Section-2:-SPECIAL
Every room benefits from L, even if indirectly.
Every stat matters for textual part of exploration(not quests).
Luck also gives more caps for successful rush.
With save editor you can see HP numbers.
Redditors tested stats for exploration, and have break-down for each of them
https://github.com/therabidsquirel/The-Fallout-Shelter-FAQ/wiki/Section-10:-The-Wasteland#101
Currently there's no evidence that strength, charisma, and intelligence do anything in quests.
https://en.reddit.com/r/foshelter/comments/4tbfme/there_was_a_hint_in_the_loading_screens_that_said/d5g7b95/