Are confidence intervals useful?
2
$begingroup$
In frequentist statistics, a 95% confidence interval is an interval-producing procedure that, if repeated an infinite number of times, would contain the true parameter 95% of the time. Why is this useful? Confidence intervals are often misunderstood. They are not an interval that we can be 95% certain the parameter is in (unless you are using the similar Bayesian credibility interval). Confidence intervals feel like a bait-and-switch to me. The one use case I can think of is to provide the range of values for which we could not reject the null hypothesis that the parameter is that value. Wouldn't p-values provide this information, but better? Without being so misleading? In short: Why do we need confidence intervals? How are they, when correctly interpreted, useful?
...