This definition of accuracy could possibly be distinctive for the just one the OP is referring to but it ought to be crystal clear now what Efron's definition is and why it is important to become correct. Now In case you have two procedures which have been correct, we are able to favor a single in excess of the opposite if for virtually any self-confidence level it has the smaller sized anticipated width.

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$begingroup$ @user31466 your First statement was appropriate sometimes (almost certainly most). Nonetheless it's probably not a priority because self confidence intervals usually are not about person observations.

But formal speculation exams of normality don't remedy the correct dilemma, and lead to your other methods that happen to be carried out conditional on regardless of whether you reject normality to no longer have their nominal Homes. $endgroup$

The primary monotonicity house implies that whenever you reduce the confidence level (by expanding $alpha$) you can get a far more exact (narrower) assurance interval and vice versa

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It isn't going to generalize to higher Proportions, nonetheless it's fairly very simple to indicate in the various linear regression formula for $hat beta $, wherever the reciprocal element emanates from. $endgroup$

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