When explaining the meaning of a confidence interval don’t say “the probability that the parameter is in the interval is 0.95” because probability is a precious concept and this statement does not match the meaning of this term. Instead, say “We are 95% confident that the parameter is in the interval”. Â Admittedly, I don’t know what people will make of the word “confident”. But I also don’t know what they will make of the word “probability”

### Recent Posts

### Recent Comments

- Anonymous on Miserly Millennium Prizes
- afinetheorem on Miserly Millennium Prizes
- rvohra on Miserly Millennium Prizes
- Sid Banerjee on Miserly Millennium Prizes
- Anonymous on Medawar’s Test

Academic Politics
advertising
alfred tarski
apple
Ariel Rubinstein
auctions
aumann
axiom of choice
bayesian
bayesianism
behavioral economics
Blackwell
bloggingheads
chairing
common knowledge
computability
Dawkins
dynamic programming
economics
Elsevier
ergodic
erice
experiments
expert testing
falsifiability
fixed point
game theory
global warming
healthcare
infinite games
intermediate microeconomics
ipad
israel
krugman
large games
latex
learning
macfreedom
matching
measurability
merging
michael rabin
mixed strategies
modeling
morgenstern
multiple selves
Nash equilibrium
normal form
notworking
open problems
pararallel sessions
pdf
peer review
pricing
prisoner's dilemma
projective determinacy
purification
puzzles
quantum games;
Samuelson; martingales; probability
shapley-folkman
Simpsons did it
springer
Springer-Verlag
stability
statistics
strategy
teaching
the greatest show on earth
Trump
uncertainty
von Neumann
zeno
zermelo
zero-sum games

### Blogroll

### Archives

- December 2017
- September 2017
- August 2017
- July 2017
- June 2017
- September 2016
- August 2016
- June 2016
- April 2016
- March 2016
- February 2016
- January 2016
- December 2015
- November 2015
- October 2015
- September 2015
- August 2015
- July 2015
- June 2015
- May 2015
- April 2015
- March 2015
- February 2015
- January 2015
- December 2014
- November 2014
- October 2014
- September 2014
- August 2014
- July 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- August 2013
- July 2013
- June 2013
- March 2013
- February 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009

## 3 comments

April 7, 2016 at 12:28 pm

AaronBut “the probability that the parameter is in the interval is 0.95” is exactly correct. Its just that the randomness over which the probability is taken is not the randomness of the parameter, but the randomness of the interval.

April 7, 2016 at 12:37 pm

EranGood catch Aaron !

The situation I had in mind is after we already came up with the interval, say [3.7, 5.4]. So we should not say there is 95% chance that the parameter is between [3.7, 5.4].

April 7, 2016 at 2:08 pm

JI’m not entirely certain I agree with you. Your entire argument rests on the premise that probability is not valid way to represent uncertainty.

That is to say, your argument is dependent on saying that the true parameter is either in or not in the interval. Thus, there cannot be a chance that it is in the interval (other than 1 and 0) because either p=1 or p=0 is the true probability.

However, if we allow the probability to represent our uncertainty, a probabilistic statement is totally valid. I don’t know if the parameter is in the interval. Based on the math I’ve done, 95% of the time it will be. Thus, I can say there is a 95% chance, because I’m uncertain.

Now, the question is “should we let probability represent uncertainty?” To which I would answer yes unequivocally. You may disagree, but then you need a different system of representing uncertainty. Probability, being the system used in forecasting as well as gambling is natural in this context. If you disagree, I would ask what it means when Nate Silver says the chance of someone winning an election is 60%. There is a response regarding repeating the election over and over, but it isn’t as sensible as saying that the probability is representing his uncertainty.