# How do I get the critical value in statistical hypothesis testing?

What I am trying to do is to get the value of $\chi^2$ for given probability (let us say $\alpha$=0.01) and degrees of freedom (for example df=3).

How do I get that?

Inverse...Distribution functions return something quite different from expected.

So, Quantile[]? InverseCDF[]? InverseSurvivalFunction[]? You've seen them? Could you elaborate on "something quite different from expected." with a concrete example? –  Ｊ. Ｍ. Sep 7 '12 at 14:28
Tsk, tsk. If you read the docs for InverseChiSquareDistribution[], it's the distribution followed by the reciprocal of a $\chi^2$-distributed variate... –  Ｊ. Ｍ. Sep 7 '12 at 14:40
InverseSurvivalFunction[] is the nearest to what you want; for a given confidence level $\alpha$ and degree of freedom $\nu$, InverseSurvivalFunction[ChiSquareDistribution[ν], α] gives the result you want. Alternatives include InverseCDF[ChiSquareDistribution[ν], 1 - α] and Quantile[ChiSquareDistribution[ν], 1 - α].