1) A sufficient statistic contains all the information needed to estimate an unknown parameter θ from a sample. 2) The factorization theorem provides a way to determine if a statistic is sufficient - if the likelihood function can be written as the product of two functions, one depending on the statistic and θ and the other not depending on θ, then the statistic is sufficient. 3) A minimal sufficient statistic is a sufficient statistic that is a function of all other sufficient statistics, representing the ultimate data reduction. The likelihood ratio test can be used to determine if a statistic is minimal sufficient.