Imprecise definition in S&W
Hi again. Hope you are all preparing well for the exam. I want to highlight an imprecise definition in S&W that I was made aware of today (Thanks to Trond V):
Key concept 5.3 claims that "A 95% two-sided confidence interval for B1 is an interval that contains the true value of B1 with 95% probability (...)"
This is at best an imprecise interpretation of a confidence interval. Note that the interpretation of CIs should be done asymptotically and NOT on basis of a single CI. I made this clear on my seminars, but since the book is being quite imprecise, I want to highlight it here. Bottom line (how one should interpret CIs):
For the single confidence interval, the probability of the true value being within this interval is either 0 or 1. It will be 1 if the true parameter is actually covered in the interval, 0 otherwise. We trust the theory, NOT the single confidence interval. When creating many such intervals, using the same method, we will suspect that 95% of those intervals will contain the true value. But this is not equivalent to a single CI having a 95% probability of containing the true value.
Best of luck on your exam.
Herman.