# Minimal sufficient statistics

Suppose we have data $$X = X_1,\ldots,X_n$$, $$Y = Y_1,\ldots,Y_n$$ that is i.i.d. generated by a distribution $$\mathbb{P}_\theta$$. Let $$T$$ be a test statistic such that that $$T(X) = T(Y)$$ if and only if $$\mathbb{P}_\theta [X] = \mathbb{P}_\theta [Y]$$ for all possible values of $$\theta$$.

Question: is $$T$$ a minimal sufficient statistic? It is clear that it is a sufficient statistic. But it is not clear to me that it's minimal sufficient.