Statistics Meeting Book (May 15, 2019)

Then:

POD(c) = (A+B)/N POD(r) = (A+C)/N dPOD = (B-C)/N

Report POD(c), POD(r) and dPOD for all levels tested.

Confidence Interval of the dPOD estimate:

For each level tested, calculate the standard error of the dPOD estimate:

ܵ (ܧ ܱ݀ܲ )ܦ = ඩ ቆ ܤ + ܥ + 2 ܰ + 2 െ ቀ ܤ െ ܥ ܰ + 2 ቁ ଶ ቇ ܰ

And the 95% confidence interval of the dPOD estimate is:

ܱ݀ܲ ܦ ± 1.96 × ܵ (ܧ ܱ݀ܲ )ܦ

Let

d i = x 1i – x 2i

denote the numerical difference of the two method results on test portion i. Note that d i must take on only the values –1, 0, or +1. The recommended method for estimating dPOD is the mean of differences d i : XXX

where N is the number of test portions. The recommended approximate 95% confidence interval is the usual Student- t based interval, with the standard error of dPOD computed in the usual manner from the replicate differences: XXX

XXX

and

LCL = d POD – t c ·SE d POD

UCL = d POD + t c ·SE d POD

where t c is the 97.5% quantile of the Student- t distribution for N-1 degrees of freedom, and the 95% confidence interval is (LCL, UCL). The degree of coverage accuracy for this approximate confidence interval will improve as N increases and the Central Limit Theorem forces the distribution of dPOD to become normal. Given the finite range of the d i ’s, this will happen quickly, even for small N.