Conceptos Básicos De Estadística

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Resampling: The New Statistics

CHAPTER

2

Basic Concepts in Probability and Statistics, Part 1

“Uncertainty, in the presence of vivid hopes and fears, is painful, but must be endured if we wish to live without the support of comforting fairy tales.” Bertrand Russell, A History of Western Philosophy (New York: Simon and Schuster, 1945, p. xiv)

Introduction The Nature andMeaning of the Concept of Probability The Various Ways of Estimating Probabilities

Introduction
The central concept for dealing with uncertainty is probability. Hence we must inquire into the “meaning” of the term probability. (The term “meaning” is in quotes because it can be a confusing word.) You have been using the notion of probability all your life when drawing conclusions about what youexpect to happen, and in reaching decisions in your public and personal lives. You wonder: Will the footballer’s kick from the 45 yard line go through the uprights? How much oil can you expect from the next well you drill, and what value should you assign to that prospect? Will you be the first one to discover a completely effective system for converting speech into computer-typed output? Will the nextspace shuttle end in disaster? Your answers to these questions rest on the probabilities you estimate. And you act on the basis of probabilities: You place your blanket on the beach where there is a low probability of someone’s kicking sand on you. You bet heavily on a poker hand if there is a high probability that you have the best hand. A hospital decides not to buy another ambulance when theadministrator judges that there is a low probability that all the other ambulances will ever be in use at once. NASA decides whether or not to send off the space shuttle this morning as scheduled.

Chapter 2—Basic Concepts in Probability and Statistics, Part 1

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This chapter discusses what is meant by such key terms as “probability,” “conditional” and “unconditional” probability,“independence,” “sample,” and “universe.” It discusses the nature and the usefulness of the concept of probability as used in this book, and it touches on the source of basic estimates of probability that are the raw material of statistical inferences. The chapter also distinguishes between probability theory and inferential statistics. (Descriptive statistics, the other main branch of statistics, wasdiscussed briefly in the previous chapter.)

The nature and meaning of the concept of probability
The common meaning of the term “probability” is as follows: Any particular stated probability is an assertion that indicates how likely you believe it is that an event will occur. It is confusing and unnecessary to inquire what probability “really” is. (Indeed, the terms “really” and “is,” alone or incombination, are major sources of confusion in statistics and in other logical and scientific discussions, and it is often wise to avoid their use.) Various concepts of probability—which correspond to various common definitions of the term—are useful in particular contexts (see Ayer, 1965; Schlaifer, 1961, Chapter 1; for perhaps the best summary of the probability concept, see Barnett, 1973,Chapter 3). This book contains many examples of the use of probability. Work with them will gradually develop a sound understanding of the concept. There are two major concepts and points of view about probability—frequency and belief. Each is useful in some situations but not in others. Though they may seem incompatible in principle, there almost never is confusion about which is appropriate in a givensituation. 1. Frequency. The probability of an event can be said to be the proportion of times that the event has taken place in the past, usually based on a long series of trials. Insurance companies use this when they estimate the probability that a thirty-five-year-old postman will die during a period for which he wants to buy an insurance policy. (Notice this shortcoming: Sometimes you...