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The investigator gets an ability called studied strike.

At 4th level, an investigator can choose to make a studied strike against the target of his studied combat as a free action, upon successfully hitting his studied target with a melee attack, to deal additional damage. The damage is 1d6 at 4th level, and increases by 1d6 for every 2 levels thereafter (to a maximum of 9d6 at 20th level). The damage of studied strike is precision damage and is not multiplied on a critical hit; creatures that are immune to sneak attacks are also immune to studied strike.

If the investigator's attack used a weapon that deals nonlethal damage (like a sap, whip, or an unarmed strike), he may choose to have the additional damage from studied strike be nonlethal damage instead of lethal damage. If the investigator chose to make an attack with a lethal weapon instead deal nonlethal damage (with the usual –4 penalty), the studied strike damage may also deal nonlethal damage.

The investigator must be able to see the target well enough to pick out a vital spot and must be able to reach such a spot. An investigator cannot use studied strike against a creature with concealment.

Uncanny Dodge

Starting at 4th level, a rogue can react to danger before her senses would normally allow her to do so. She cannot be caught flat-footed, nor does she lose her Dex bonus to AC if the attacker is invisible. She still loses her Dexterity bonus to AC if immobilized. A rogue with this ability can still lose her Dexterity bonus to AC if an opponent successfully uses the feint action (see Combat) against her.

Improved Uncanny Dodge

A rogue of 8th level or higher can no longer be flanked. This defense denies another rogue the ability to sneak attack the character by flanking her, unless the attacker has at least four more rogue levels than the target does.

Under common terms I found mention of precision damage, and it talks about it being a category of damage.

Precision damage is a special type of damage, which might more appropriately be called a "category" of damage because any of the other damage types listed here might also be considered "precision" damage under the right circumstances. Precision damage is usually dealt by classes like the rogue when he is able to catch an opponent unable to fully protect itself. Precision damage assumes that the target has a somewhat normal anatomy or at least has a physical form which might have weak spots which could be detected or taken advantage of. Previous editions of this game limited what sorts of creatures are vulnerable to precision damage more than this one does. This was a deliberate change to make a key class feature of classes like the rogue more frequently usable. Attacks which affect areas (such as splash weapons) usually do not deal precision damage.

In the Rogues sneak attack damage section it mentions "See Precision Damage & Critical Hits FAQ for more information" but theres no link and when I googled it I got nothing.

I bolded the section of interest from the investigator class. It specifically mentions that creatures immune to sneak attack damage (which is precision damage like studied strike, and the investigators parent class is rogue), which improved uncanny dodge protects against. It doesn't say its immunity, but since the parent class is rogue, the damage is precision, and it mentions sneak attack, it should also affect studied strike, right?

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No, it does not.

All that Improved Uncanny Dodge does is this:

A rogue of 8th level or higher can no longer be flanked.

In particular, it does not make you immune to sneak attacks (if you lose your Dex to AC from some other way you can still be sneak attacked, for example).

The fact that they are both precision damage, or that the parent class is rogue doesn't do anything here since Improved Uncanny Dodge does not care about that.

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