文档介绍：316 Resampling: The New Statistics
CHAPTER
Confidence Intervals,
Part 2: The Two
21 Approaches to Estimating
Confidence Intervals
Approach 1: The Distance Between Sample and Population Mean
Approach 2: Probability of Various Universes Producing This Sample
There are two broad conceptual approaches to the question at
hand: 1) Study the probability of various distances between
the sample mean and the likeliest population mean; and 2)
study the behavior of particular border universes.
Computationally, both approaches often yield the same result,
but their interpretations differ. Approach 1 follows the con-
ventional logic although carrying out the calculations with
resampling simulation.
Approach 1: The distance between sample and population mean
If the study of probability can tell us the probability that a given
population will produce a sample with a mean at a given dis-
tance x from the population mean, and if a sample is an unbi-
ased estimator of the population, then it seems natural to turn
the matter around and interpret the same sort of data as tell-
ing us the probability that the estimate of the population mean
is that far from the “actual” population mean. A fly in the oint-
ment is our lack of knowledge of the dispersion, but we can
safely put that aside for now. (See below, however.)
This first approach begins by assuming that the universe that
actually produced the sample has the same amount of disper-
sion (but not necessarily the same mean) that one would esti-
mate from the sample. One then produces (either with
resampling or with Normal distribution theory) the distribu-
tion of sample means that would occur with repeated sam-
pling from that designated universe with samples the size of
the observed sample. One can pute the distance be-
tween the (assumed) population mean and (say) the inner 45
Chapter 21—Confidence Intervals, Part 2: Two Approaches to Estimating Confidence Interval