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In Gardner & Altman, BMJ 1986, we wrote:
“More exactly, in a statistical sense, the confidence interval means that if a series of identical
studies were carried out repeatedly on different samples from the same
populations, and a 95% confidence interval for the difference between the
Systolic blood sample means calculated in each study, then, in the long run, 95% of these
confidence intervals would include the population difference between means.”
This definition could be shortened a bit but it’s scarcely surprising that people shorten it, and in particular that they say (and
indeed I myself sometimes say but I try not to) that we can be 95% sure that the true value of the quantity we are estimating lies within the 95% CI. Although it’s a neater definition, it is wrong.
As Greenland (among many I’m sure) has observed, the latter simpler definition is false, because the true value either is or is not
with the 95% confidence interval – the probability is thus either 0 or 1, but we know not which.
Also, the CI reflects only uncertainty from sampling error and cannot reflect any other sort of uncertainty including selection bias
and model misspecification.
It is preferable to consider the CI as a (minimum) range of imprecision or uncertainty around the estimate rather than trying to turn
the CI back into a test.
Doug
PS A long paper by Greenland and Poole may of interest -
http://heinonline.org/HOL/Page?handle=hein.journals/juraba51&div=10&g_sent=1&collection=journals
[Greenland S, Poole C. Problems in common interpretations of statistics in scientific articles, expert reports, and testimony. Jurimetrics.
2011;51:113–129]
It’s aimed at lawyers and addresses lots of statistical issues.
From: A UK-based worldwide e-mail broadcast system mailing list [mailto:[log in to unmask]]
On Behalf Of Martin Bland
Sent: 30 October 2015 15:39
To: [log in to unmask]
Subject: Re: 95% confidence interval: best description.
I don't like 1) because it simply repeats the word confidence without explaining it. I don't like 2) because if the experiment were carried out 100 times we might get 95 intervals which include the population value, we might get 94, 96,
etc.
I would say that a 95% confidence interval is a range of possible values which we estimate to contain the required quantity, calculated so that if were to repeat the sampling many times, 95% of intervals thus calculated would include the
required quantity. That is strictly a frequentist view, but non-frequentists calculate credible intervals instead and we should keep the two things clear.
Martin
On 30 October 2015 at 12:29, John Sorkin <[log in to unmask]> wrote: