# Statistics Meeting Book (May 15, 2019)

All

76

44

120

Here, x = 76, N =120, and LPOD = 0.6333 (= 76/120). The repeatability standard deviation

XXX

XXX The current Appendix has 3 equations here which the first needs to be edited for typographic errors.

Current equations:

ݏ ଶ = σ (݊ െ 1) ݏ ଶ ୀଵ σ (݊ െ 1) ୀଵ = σ ݔ െ ൬ ݔ ଶ ݊ ൗ ൰൨ ܰ െ ܮ = ൣ൫7 െ 49 120 ൗ ൯ + ൫9 െ 81 120 ൗ ൯ + ڮ + ൫9 െ 81 120 ൗ ൯൧ 120 െ 10 ݏ ଶ = 0.2242 ݏ = ට ݏ ଶ = ξ0.2242 = 0.4735

Should be changed to:

ݏ ଶ = σ (݊ െ 1) ݏ ଶ ୀଵ σ (݊ െ 1) ୀଵ = σ ݔ െ ൬ ݔ ଶ ݊ ൗ ൰൨ ܰ െ ܮ = ൣ൫7 െ 49 12ൗ ൯ + ൫9 െ 81 12ൗ ൯ + ڮ + ൫9 െ 81 12ൗ ൯൧ 120 െ 10 ݏ ଶ = 0.2242 ݏ = ට ݏ ଶ = ξ0.2242 = 0.4735 where s 2 i is the variance of the results from laboratory i , x i is the number of positive detections from laboratory i , n i is the number of observations from laboratory i , N is the total

number of data, and L is the number of laboratories. And, suggesting s L will be small compared to s r . The among-laboratory standard deviation is

s 2 L = XXX

= XXX

= max {0, 0.02963 – 0.

= 0.01093

and s L = XXX, which is noticeably less than s r , as expected. The reproducibility standard deviation is

s 2 R = s 2 r + s 2 L

= 0.01093 + 0.2242 = 0.2351

so XXX The results are summarized in Table F2.

Table F2

Parameter

Value

LPOD

0.6333

s r

0.4735

s L

0.1046

s R

0.4850

p -Value for T -test

0.1703

The “homogeneity test” reported above is WKH 7 VWDWLVWLF EDVHG RQ WKH Ȥ 2 distribution, so the p -value of 0.1703 should be compared to 0.10. The test indicates the observed value of s L = 0.1046 is not statistically significant, so the study was not large enough to reliably detect an interlaboratory effect of this size.

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