Confidence Interval (2 of 2)
What about situations in which there is no prior information? Even here
the interpretation is complex. The problem is that there can be more than
one procedure that produces intervals that contain the population parameter 95%
of the time. Which procedure produces the "true" 95% confidence
interval? although the various methods are equal from a purely mathematical
point of view, the standard method of computing confidence intervals has
two desirable properties: (1) each interval is symmetric about the point
estimate and (2) each interval is contiguous. Recall from the introductory section
in the chapter on probability that for some purposes,
probability
is best thought of as subjective. It is reasonable, although not required
by the laws of probability, that one adopt a subjective probability of
0.95 that a 95% confidence interval as typically computed contains the
parameter in question.
Confidence intervals can be constructed for any estimated
parameter, not just μ. For example, one might estimate the
proportion of people who could pass a training program or the
difference between the mean for subjects taking a drug and those
taking a placebo. Click below for details:
Mean, σ
known
Mean, σ
Difference between means, σ known
Difference between
means, σ estimated
Pearson's correlation
Difference between correlations
Proportion
Difference between proportions