# Confusion around Probabilistic Interpretation of Confidence Intervals

My professor told me that a confidence interval provides a measure for the resampling uncertainity. That is, if I were to re-sample this dataset a large number of times, 95% of those would contain the true parameter in this range.

To make this more probabilistically concrete, is it valid to say that a confidence interval is: the probability that the next time I re-sample, that the true parameter would fall in this interval?

• – user83346 Mar 28 '16 at 6:59
• There are several ambiguities here. If you are resampling the dataset, then the confidence intervals as computed in the resamples are giving information about the original sample but not (directly) about the population. What, then, does "true parameter" refer to: the value of the original sample or the population? Second, what does "this interval" mean at the end? The CI computed from a resample of the data or the original sample? – whuber Mar 28 '16 at 14:55
• @whuber I was taking 'resample' in the question to mean 'draw another sample from the population' rather than resampling in the sense of drawing with replacement from the sample itself. I still think that was the intent; I have edited my answer below to clarify that I take that interpretation. – Glen_b Mar 28 '16 at 15:12