Bland C Is
See List Of Modifications To Neymans Theory. (I’m going to make this wiki do apostrophes in links, but it’s not quite working yet.)
From Interpretation Of Confidence Intervals :
“There is one sense in which the CI is less extreme’it covers a broader range of values then the point estimate; both lower and higher. But it is only less extreme (in a sense important to decision makers) if you take into account that the `true’ value is more likely to be lower than the point estimate; i.e. in the lower region of the CI. This, however, is not permitted. The CI is an interval. And whatever it says of the relation between the data and theta, it says it for the entire interval.”
I (as of 5 minutes ago) call this the Bland CIs rule. Within a confidence interval, everything is bland. In particular, it’s not a humped probability distribution. It’s just featureless.
This is right according to some versions of confidence interval theory but not others. One very influential recent version of confidence interval theory which denies it is Gardner and Altman’s. Right in the first two pages (of the book version, at least), they say:
—>“the middle half of the confidence interval (13% to 27%) is more likely to contain the population value than the extreme two quarters (6% to 13% and 27% to 34%)—in fact the middle half forms a 67% confidence interval.” (pp.3—4)
@article{M.J.Gardner:1986, Author = M.J.Gardner and D.G.Altman, Date-Added = 2007-07-09 13:13:02 +1000, Date-Modified = 2007-09-18 11:18:40 +1000, Journal = British Medical Journal, Pages = 746—750, Title = Statistics in medicine: confidence intervals rather than P values: estimation rather than hypothesis testing, Volume = 292, Year = 1986}
@book{J.Gardner:1989, Address = London, Author = Martin J.~Gardner and Douglas G.~Altman, Publisher = British Medical Journal, Title = Statistics With Confidence — Confidence intervals and statistical guidelines, Year = 1989}
Is Neyman’s original theory a Bland C Is theory? I’m not sure. To discuss.