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Summary
Effective skills are applied through different sources, such as Aspect Armor or Mastery Chain Links.
They don't show up in the skill gump as they are only applied in certain calculations (listed below).
They are intended to give further bonuses to templates utilizing the skills in question, not as a secondary source of skill points to free up points to use elsewhere.
Things that are affected
Formulas for spell or melee damage
Inscription scroll refund chance and buff duration increase
Harvesting chances
Things that are NOT affected
Crafting chances (for example effective inscription doesn't increase crafting or exceptional chances of spell books)
Hard caps for abilities or spells to cast/activate (with the exception of casting from a magery spell scroll)