I've been doing data analysis for a while, but recently I questioned my understanding of the oft-misunderstood confidence interval. So, I read multiple sources.
Many of them say explicitly that the confidence interval is
NOT the probability that a specific confidence interval contains the population parameter. Rather, it is the
percentage of times a confidence interval will contain the population parameter after many samples.
I honestly can't tell the difference between these: Isn't the latter the same as the probability? If not, how is it different? I suppose the definition of
probability might be throwing me off here.
Here's one of the sources I used: http://blog.minitab.com/blog/adventures-in-statistics/understanding-hypothesis-tests%3A-confidence-intervals-and-confidence-levels