Blackwell and Howard University discuss a method for comparing two sampling procedures or experiments. They define that one experiment α is more informative than another β (α ⊃ β) if, for every possible risk function, any risk attainable with β is also attainable with α. They show that if α is a sufficient statistic for β, then α ⊃ β. In the case of dichotomies, the converse is proven. The equivalence of ⊃ and �ucc is not known in general. Properties of ⊃ and �ucc are derived, such as the combination of two experiments (α, γ) being more informative than (β, γ) if α ⊃ β and γ is independent of both. An application to a 2×2 table problem is discussed. The paper defines an experiment as a set of probability measures on a Borel field. A decision problem is a pair (a, A), where A is a bounded subset of N-space. A decision procedure is a function specifying the action to take based on the sample point. The range of a loss vector is a subset of N-space, and the convex closure of this range is called the set of attainable loss vectors. The paper shows that if the range of α is a superset of the range of β for every closed convex A, then α ⊃ β. The paper presents several theorems that provide equivalent conditions for α ⊃ β. These include conditions involving the minimum of linear combinations of loss vectors and the minimum of maximum components of loss vectors. The paper also discusses the reduction of experiments to standard experiments, where the outcome is a point in a probability space. It shows that any experiment is equivalent to a standard experiment whose outcome is a point in this space. The paper proves that if a standard experiment M is sufficient for another standard experiment m, then M ⊃ m. It also shows that if M ⊃ m, then M is more informative than m. For N = 2, the paper provides a geometric interpretation of the conditions for sufficiency and informativeness. It also discusses the combination of experiments and shows that if α ⊃ β and γ ⊃ δ, then (α, γ) ⊃ (β, δ). The paper concludes with an application to binomial experiments, where it compares different experiments based on their informativeness. It shows that certain experiments are more informative than others, and provides conditions under which this is true. The paper also discusses the comparison of binomial experiments in the context of a 2×2 table problem, where the goal is to determine whether the proportion of HS in the general population is hs or a different value. The paper concludes that the experiment which always selects the characteristic which is rarest in the general population is more informative than any other procedure of the class considered.Blackwell and Howard University discuss a method for comparing two sampling procedures or experiments. They define that one experiment α is more informative than another β (α ⊃ β) if, for every possible risk function, any risk attainable with β is also attainable with α. They show that if α is a sufficient statistic for β, then α ⊃ β. In the case of dichotomies, the converse is proven. The equivalence of ⊃ and �ucc is not known in general. Properties of ⊃ and �ucc are derived, such as the combination of two experiments (α, γ) being more informative than (β, γ) if α ⊃ β and γ is independent of both. An application to a 2×2 table problem is discussed. The paper defines an experiment as a set of probability measures on a Borel field. A decision problem is a pair (a, A), where A is a bounded subset of N-space. A decision procedure is a function specifying the action to take based on the sample point. The range of a loss vector is a subset of N-space, and the convex closure of this range is called the set of attainable loss vectors. The paper shows that if the range of α is a superset of the range of β for every closed convex A, then α ⊃ β. The paper presents several theorems that provide equivalent conditions for α ⊃ β. These include conditions involving the minimum of linear combinations of loss vectors and the minimum of maximum components of loss vectors. The paper also discusses the reduction of experiments to standard experiments, where the outcome is a point in a probability space. It shows that any experiment is equivalent to a standard experiment whose outcome is a point in this space. The paper proves that if a standard experiment M is sufficient for another standard experiment m, then M ⊃ m. It also shows that if M ⊃ m, then M is more informative than m. For N = 2, the paper provides a geometric interpretation of the conditions for sufficiency and informativeness. It also discusses the combination of experiments and shows that if α ⊃ β and γ ⊃ δ, then (α, γ) ⊃ (β, δ). The paper concludes with an application to binomial experiments, where it compares different experiments based on their informativeness. It shows that certain experiments are more informative than others, and provides conditions under which this is true. The paper also discusses the comparison of binomial experiments in the context of a 2×2 table problem, where the goal is to determine whether the proportion of HS in the general population is hs or a different value. The paper concludes that the experiment which always selects the characteristic which is rarest in the general population is more informative than any other procedure of the class considered.