Max integrity of crafted objects and quality of crafted items.
Higher durability items don't have to be repaired as often, higher quality items have higher value.
Charisma
Chances of successfully recruiting strangers, chances of creating positive relationships, chances of getting cheaper trade deals.
Party leader charisma affects chance of successfully trading during an encounter.
Perception
How many items are located when searching, time given to disarm traps.
Scavenging is one of the most important game mechanics, so this skill is likely important.
Fortitude
Max health, radiation resistance, how long an illness lasts.
Possibly also resistance to contracting an illness to begin with.
A character's starting stat also determine their maximum potential stat.
Stat Maximums
Start
Max
Start
Max
Start
Max
1
10-12
2
12-14
3
14-16
4
16-18
5
18-20
6+
18-20
This means if you start with a 1 in Strength, your maximum possible strength will be randomly between 10 and 12. You can "experiment" on a character to raise a stat, but this can only happen once per stat per character (and each attempt has a 10% chance to succeed and causes a -30 mood modifier with each attempt).
Each stat also has their own skill tree. Leveling up a stat gains 1 point to spend in the tree. All of a character's starting skill tree points are randomly spent.