Statistics Meeting Book (June 20, 2018)

POSSIBLE LARGE-SAMPLE CONFIDENCE INTERVALS Among the choices for confidence intervals here, the best performing can only be reliably determined by only by simulation. Factors for selection include: 1. Use of eq.(2b) to estimate dPOD, or the continuity-corrected versions (b – c) / (n + 2 ε) of eqs.(3) or (4). 2. Use of continuity correction for SE(dPOD) of ε = 0 (none), ε = ½, or ε = 1. 3. Use of degrees of freedom bias adjustment in the SE(dPOD) with use of Student-t quantile, or no adjustment with a z quantile. This gives rise to 18 different sets of formulas, all of which have the same asymptotic limits as n becomes large. Preliminary validation simulations have indicated that ε = 1 with dPOD = (b – c) / (n + 2) and SE(dPOD) without degrees of freedom adjustment appears to give generally good coverage. Down-selection to a final method should await more definitive sets of simulations. For the moment we recommend the estimates dPOD(A,B) = (b – c) / n (13) and SE(dPOD) = √{ [ (b+c+2)/(n+2) – ( (b – c)/(n+2) ) 2 ] / (n -1) } (14) with confidence interval for the true dPOD(A,B) of dPOD + t SE(dPOD) (15) These are the most conservative estimates of those described.

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