sufficiency and the likelihood

Let $\{P_{\theta }\}$ be a statistical model and $T$ a sufficient statistic for $\theta$. By the Neyman-Fisher characterization (see sufficient statistic: Neyman-Fisher characterization), we can write the likelihood as

$$\mathcal{L}(\theta )=p(x^n;\theta )=h(x^n)g(T(x^n);\theta ).$$

We’re interested in the likelihood as a function of $\theta$ (eg in MLE) so $\mathcal{L}(\theta )=\propto g(T(x^n);\theta )$. Therefore, to do any analysis on the likelihood, it suffices to know a sufficient statistic of the data, as opposed to the data itself.