Some core connections between the basic rules of probability, frequency-type probability, and statistical stability. These facts provide the foundations for frequency reasoning. The chapter ends by stating Bernoulli's Theorem, one of the most fundamental facts about probability.
Now we move from three chapters using the belief perspective to four chapters using the frequency perspective. Chapters 13 and 14 gave one reason why belief-type probabilities should satisfy the basic rules of probability. Chapter 15 showed how to apply that result to “learning from experience.” Chapters 16–19 do something similar from the frequency perspective.
THE PROGRAM
▪ This chapter describes some deductive connections between probability rules and our intuitions about stable frequencies.
▪ Chapter 17 extends these connections.
▪ Chapter 18 presents one core idea of frequency-type inductive inference–the significance idea.
▪ Chapter 19 presents a second core idea of frequency-type inductive inference–the confidence idea. This idea explains the way opinion polls are now reported. It also explains how we can think of the use of statistics as inductive behavior.
All the results described in this chapter are deductions from the basic rules of probability. The results are only stated, and not proved, because the proofs are more difficult than other material in this book.
BELIEF AND FREQUENCY COMPARED
The basic rules are for any type of probability. Belief-type and frequency-type probabilities emphasize two fundamentally different types of consequences of the basic rules.
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