Confidence Interval Meaning (semantics confusing me)

evolving_doors

Well I though I knew what the confidence interval meant and largely was agreeing with this guy here

http://www.statisticssolutions.com/misconceptions-about-confidence-intervals/

but then ....

Some of the most common misconceptions about confidence intervals are:

“There is a 95% chance that the true population mean falls within the confidence interval.” (FALSE)
“The mean will fall within the confidence interval 95% of the time.” (FALSE)
So what exactly is a confidence interval? A confidence interval is an estimate of the possible values of a population mean; the key word here being estimate. Just as with any statistic estimated from a sample, the upper and lower bounds of the confidence interval will vary from sample to sample. For a given population, the 95% confidence interval from one random sample might be between 2 and 5, but for another random sample it might be between 1 and 4. Some of the intervals calculated from these random samples will contain the true population mean, and some will not. A 95% level of confidence means that 95% of the confidence intervals calculated from these random samples will contain the true population mean. In other words, if you conducted your study 100 times you would produce 100 different confidence intervals. We would expect that 95 out of those 100 confidence intervals will contain the true population mean.

Does the second 'True' underlined part not mean the same as the first underlined part which he claims to be 'false'.

Is the phrasing of this textbook answer below in line with what a confidence interval is?

confidence_Interval.JPG

Explain to me like im 5

MathsManiac

Did you read the original article referenced:
www.ejwagenmakers.com/inpress/HoekstraEtAlPBR.pdf

It's pretty subtle stuff. I wouldn't be too worried about it. They basically assert that as soon as you make any tentative conceptual leap towards a Bayesian interpretation of what is a frequentist concept, you are wrong. In my view, if you followed their logic to conclusion, you'd pretty much be saying that you can't make any useful inferential jump at all from a confidence interval. (Which is probably what they want, given the note that the article got funding from "Bayes or Bust")

Since they have said that there are loads of statistics lecturers floating around that would endorse these supposedly false statements, you're not in bad company.

It seems to me that they would happily allow you to say "95% of the time, the confidence interval will contain the population mean", but they won't allow you to say "95% of the time, the population mean will fall within the confidence interval". Their argument is that the first statement is a statement about how the confidence interval is likely to behave, which is ok because the CI is a thing whose behaviour is variable, while the second is a statement about how the population mean is likely to behave, which is not ok because the pop mean is a fixed immutable thing that cannot change, so cannot have a probability assigned to its likely behavior.

Philosophically lovely and all, but in practice, just bonkers. In my view, the two statements at the start of my last paragraph are synonymous, and do not carry any implication as to which of the two things I am talking about is fixed and which is changeable.

In my view, there really are important misunderstandings out there about confidence intervals, and SOME of those are captured by some of these six "false" statements, but putting them all into this same category of sinfulness does a disservice to the discipline.

[P.S. Explaining it to you like you're 5: don't mind these silly people, you are very good at statistics for someone your age.]