**The stats themselves don't change**

...but the *effective* stats will.

Though in the game-world, the animal **becomes** its larger self, with all that implies, the mechanical truth is you don't **replace** the stats with those of the new form, only **add modifiers** appropriate to it.

The flavor text along each step of the way describes in-fiction reality, but we'll have to go through a bit of a process to find the mechanical "how-to", rather than just flavor text.

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The mechanical description of *polymorph any object* states that:

> This spell functions like *greater polymorph*, except that it changes one object or creature into another.

So, the spell exclusively changes objects and creatures into those of different types, and offers absolutely no mechanical description of what that looks like, until we get to what's almost a footnote in  PFSRD:

> This spell can also be used to duplicate the effects of *baleful polymorph*, *greater polymorph*, ...

To be clear this spell provides no unique mechanics for changing and animal into another form, aside from its duration table - the details of transformation are left to those other spells listed.  The mechanical effects of this particular transformation would be handled under the rules of *greater polymorph*, as the only one that could actually do what you describe.

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[Greater Polymorph][1] further redirects you:

> If you use this spell to cause the target to take on the form of an animal or magical beast, it functions as *beast shape IV*.

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So among other steps in [*beast shape IV*][2]'s transformation process, we finally get to the stat effects:

> *Huge Animal* - If the form you take is that of a Huge animal, you gain a +6 size bonus to your Strength, a -4 penalty to your Dexterity, and a +6 natural armor bonus.

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One last thing to take into account, and it's up for interpretation - the wording of the *beast form* spell seems to assume the target is a Medium, humanoid race (like any PC), and thus offers non-size-related bonuses for turning from that into a Medium animal:

> *Medium animal*: If the form you take is that of a Medium animal, you gain a +2 size bonus to your Strength and a +2 natural armor bonus.

Were I GMing your game, I would subtract these bonuses from the above *Huge Animal* bonuses, leaving you with +4, +4, and -4.  Otherwise, there'd be no reason not to just change your Medium Allosaurus into a Medium Allosaurus, and get a free (and redundant) bonus for being an animal rather than humanoid race.

  [1]: http://www.d20pfsrd.com/magic/all-spells/p/polymorph/
  [2]: http://www.d20pfsrd.com/magic/all-spells/b/beast-shape/