When stating that “95 out of 100 times…,” wouldn’t the only way we could be completely accurate is to include all possible combinations of sample size X?
Although I use a shortened version for regular use—similar to “with 95% confidence, we believe the parameter is between LL and UL”—when I explain the theory
to students initially (and repeatedly), I explain it the following way:
-
If we collected
every possible combination of sample size X and created a confidence for each sample, 95% of the time, the population parameter would be between the lower and upper limits. The other 5% of the time, the confidence interval would not capture the
population parameter.
Obviously, if we had every possible combination of sample size X, we would have the population data and wouldn’t need to do any inferential statistics. But,
for teaching purposes, I think the way I state it is accurate.
What do you think?
Fred
From: A UK-based worldwide e-mail broadcast system mailing list [mailto:[log in to unmask]]
On Behalf Of Nicola Novielli
Sent: Friday, October 30, 2015 12:39 PM
To: [log in to unmask]
Subject: Re: [allstat] 95% confidence interval: best description.
I mainly agree with Martin. However, i think both definitions are incomplete and miss some points.
I ask whether the definition should describe or interpret a confidence interval: the first case looks like an extremely simplified attempt to describe a CI (regardless whether using frequentist, classic or whatsoever theoretical
franework); the second looks like an attempt to give an interpretation to a CI.
In both cases some points are missing:
- the parameter is a sample mean ( not a population mean) ?
- don't forget the role of the power (calculation of CI if functional to hypothesis thesting, that is a diagnosis with 2 types of errors) ?
- what about the distribution of the population ? And the sample size?
This is to say that attempts to simplify complex things may produce misleading (or incomplete) definitions. On the other side even complex stuff must be shared with professionals from other disciplines (who may be more interested in interpretation
than definition).
I guess whether it is more interesting to know that "Pinocchio is a wood-carved puppet", or listen to some of his adventures.
Hope I didn't go off topic!
Sent from my iPhone
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.
On 30 October 2015 at 12:29, John Sorkin <[log in to unmask]> wrote:
I would appreciate thoughts about the following two descriptions of a 95% CI:
You'll need Skype CreditFree via Skype
For a given parameter X, a 95% CI round X is:
1) A range of values which we can say with 95% confidence contains the true value of the parameter.
2) A range of values constructed such that if an experiment is conducted 100 times, 95% of the time X will lie with the range.
I would welcome comments of the above descriptions, and any better descriptions that you might have.
John David Sorkin M.D., Ph.D.
Professor of Medicine
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
Confidentiality Statement:
This email message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized use, disclosure
or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message.
You may leave the list at any time by sending the command
SIGNOFF allstat
to [log in to unmask], leaving the subject line blank.
--
***************************************************
J. Martin Bland
Prof. of Health Statistics Emeritus
Dept. of Health Sciences
Seebohm Rowntree Building
University of York
Heslington
York YO10 5DD
Email: [log in to unmask]
Phone: 01904 321334 Fax: 01904 321382
Web site: http://martinbland.co.uk/
Statement by the University of York:
This email and its attachments may be confidential and are intended solely for the use of the intended recipient. If you are not the intended recipient of this email and its attachments, you must take no action based upon them, nor must you copy or show them
to anyone. Please contact the sender if you believe you have received this email in error. Any views or opinions expressed are solely those of the author and do not necessarily represent those of The University of York.
***************************************************
You may leave the list at any time by sending the command
SIGNOFF allstat
to [log in to unmask], leaving the subject line blank.
Nota di riservatezza : Il presente messaggio, corredato di eventuale/i allegato/i, contiene informazioni da considerarsi strettamente riservate ed è indirizzato esclusivamente al/i destinatario/i sopra indicato/i unico/i autorizzato/i
ad usarlo, copiarlo e, sotto la propria responsabilità, eventualmente diffonderlo. Chiunque ricevesse questo messaggio per errore o comunque lo leggesse senza esserne legittimato è avvertito che trattenerlo,copiarlo, divulgarlo, distribuirlo a persone diverse
dal destinatario è
severamente proibito ed è pregato di rinviarlo immediatamente al mittente distruggendo l'originale.
Federazione delle Banche di Credito Cooperativo di Puglia e Basilicata Centralino 080 2205211 Fax 080 2205214 You may leave the list at any time by sending the command
SIGNOFF allstat
to [log in to unmask], leaving the subject line blank.
You may leave the list at any time by sending the command
SIGNOFF allstat
to [log in to unmask], leaving the subject line blank.