This chapter reviews two topics from mathematical statistics, where the second topic is slightly technical and may be skipped. In Sect. 3.1, A. P. Dawid’s notation for conditional independence is reviewed. This material is used in later chapters, is brief, and is not difficult. The notation is introduced in the context of two toy models, one for randomized experiments and the other for observational studies. In contrast, Sect. 3.2 connects randomization inference in experiments and permutation inference in population models. Under many conditions, randomization inferences based on randomized treatment assignment in Chap. 2 are identical to permutation tests in population models, and seeing this connection is helpful in understanding both perspectives. That said, the material in Sect. 3.2 is mentioned only briefly in later parts of the book; so, it is not essential reading.

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Some Background Topics in Statistics

  • Paul R. Rosenbaum

摘要

This chapter reviews two topics from mathematical statistics, where the second topic is slightly technical and may be skipped. In Sect. 3.1, A. P. Dawid’s notation for conditional independence is reviewed. This material is used in later chapters, is brief, and is not difficult. The notation is introduced in the context of two toy models, one for randomized experiments and the other for observational studies. In contrast, Sect. 3.2 connects randomization inference in experiments and permutation inference in population models. Under many conditions, randomization inferences based on randomized treatment assignment in Chap. 2 are identical to permutation tests in population models, and seeing this connection is helpful in understanding both perspectives. That said, the material in Sect. 3.2 is mentioned only briefly in later parts of the book; so, it is not essential reading.