文档介绍：140 Resampling: The New Statistics
CHAPTER
On Variability in
9 Sampling
Variability and Small Samples
Regression to the Mean
Summary and Conclusion
[Debra said]: “I’ve had such good luck with Japanese cars and
poor luck with American...”
The ’65 Ford Mustang: “It was fun, but I had to put two new
transmissions in it.”
The Ford Torino: “That got two transmissions too. That
finished me with Ford.”
The Plymouth Horizon: “The disaster of all disasters. That
should’ve been painted bright yellow. What a lemon.”
(Washington Post Magazine, May 17, 1992, p. 19)
Does the headnote above convince you that Japanese cars are
better than American? Has Debra got enough evidence to reach
the conclusion she now holds? That sort of question, and the
reasoning we use to address it , is the subject of this chapter.
More generally, how should one go about using the available
data to test the hypothesis that Japanese cars are better? That
is an example of the questions that are the subject of statistics.
Variability and small samples
Perhaps the most important idea for sound statistical infer-
ence—the section of the book we are now beginning, in con-
trast to problems in probability, which we have studied in the
previous chapters—is recognition of the presence of variability
in the results of small samples. The fatal error of relying on
too-small samples is all mon among economic fore-
casters, journalists, and others who deal with trends and pub-
lic opinion. Athletes, sports coaches, sportswriters, and fans
too frequently disregard this principle both in their decisions
and in their discussion.
Chapter 9—On Variability in Sampling 141
Our intuitions often carry us far astray when the results vary
from situation to situation—that is, when there is variability
in es—and when we have only a small sample of out-
comes to look at.
To motivate the discussion, I’ll tell you something that almost
no American sports fan wi