Crew Upgrades in Detail

Combat Training
+15 Str
+15 Dex
+5 Sta
+5 Fin
+5 Sen
Increases allowed weapon Quality by 4 (Default = Level of crewmember, regardless of training)

Defense Training
+10 Str
+5 Dex
+10 Sta
+10 Fin
+10 Sen
Increases allowed armor Quality by 4 (Default = Level of crewmember, regardless of training)

Medical
+45 Int
+100 to corruption capacity (Corruption gained = levelxCP removed from victim)

Engineering
+5 to everything
+540 To Repair (secondary stat used to refill ship health)

Chef
+5 to everything
+540 to Meals (secondary stat used to heal FP and MP)

Navigation
+10 Str, Dex, Spd
+5 Sta, Fin, Sen
Increase piloting skill. In air combat, it's compared against the enemy's level.

Advanced
+45 Speed
+1 Skill