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The item depends on the number of super-effective (S) and not-very-effective (N) hits you land during the entire battle. It appears the difference S-N becomes your number which determines the item. Within a specific number (and possibly range of numbers, see below), what item you receive seems to be random. Moves with normal damage have no effect. I'm not sure if you need to hit an exact number or just a range if you want a specific item as I've yet to receive an item twice. Below is a list of all the Items I received, sorted by the number of S hits I landed. I have not factored in N hits because I only had those on rare occasions and previously thought they had no impact, so some of the numbers might be slightly off. The most recent tests all took the new formula (S-N) into account and are marked with a . Long-term, I plan to confirm all results with the new formula and subsequently remove the old results and the s.

0: Oran Berry
1-3: Sitrus Berry
4-6: Type-resisting Berry
7-9: Evolutionary Stone (includes Everstone)
10+: Rare Candy

And here's my list of Items received on each number, starting with the Berries (which are noted by the type they make the carrier resist), followed by the Stones. As promised, I will update this list as more results come in (* denotes results confirmed since I found out the formula is S-N):

4: Dark, Flying, Psychic, Rock, Normal*
5: Poison, Grass, Fighting
6: Fairy, Dragon, Steel*

7: Sun*
8: Moon, Fire*
9: Dawn, Shiny, Everstone

Source: http://gaming.stackexchange.com/questions/150736/what-determines-psychic-invers-reward

Hope I helped!

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