800
M
C
C
LURE
& L
EE
: J
OURNAL OF
AOAC I
NTERNATIONAL
V
OL
. 89, N
O
. 3, 2006
Table 1. Comparison of simulated one-tailed 95 and 99% upper limits
MC
MC
95
99
,%
,%
and
and calculated
one-tailed 95 and 99% upper limits
95
99
,% ,%
and
for future sample percent relative reproducibility standard
deviations
Probability level, %
95
99
R
,%
a
(
b
No. labs
c
No. reps
d
MC
95
,%
e
95
,%
f
( )
*
p
g
MC
99
,%
e
99
,%
f
( )
*
p
g
2
1/2
8
2
2.76
2.78
0.955
3.11
3.10
0.990
5
2.69
2.71
0.955
3.05
3.00
0.988
20
2.67
2.67
0.950
3.04
2.95
0.985
20
2
2.47
2.47
0.950
2.68
2.67
0.991
5
2.43
2.43
0.950
2.63
2.61
0.990
20
2.41
2.41
0.950
2.60
2.58
0.988
2/3
8
2
2.68
2.71
0.951
3.01
3.00
0.990
5
2.59
2.59
0.950
2.92
2.83
0.984
20
2.52
2.51
0.949
2.80
2.73
0.986
20
2
2.44
2.43
0.949
2.62
2.61
0.989
5
2.36
2.36
0.950
2.54
2.50
0.986
20
2.31
2.31
0.950
2.47
2.44
0.987
16
1/2
8
2
22.32
22.51
0.955
25.44
25.31
0.989
5
21.83
21.95
0.952
24.99
24.51
0.987
20
21.44
21.65
0.955
24.36
24.09
0.988
20
2
19.82
19.92
0.954
21.83
21.59
0.987
5
19.60
19.59
0.950
21.25
21.11
0.988
20
19.39
19.41
0.951
21.08
20.85
0.988
2/3
8
2
21.81
21.94
0.953
24.77
24.49
0.988
5
21.01
20.93
0.948
23.25
23.05
0.988
20
20.47
20.35
0.946
22.79
22.22
0.987
20
2
19.59
19.59
0.950
21.35
21.11
0.987
5
18.97
18.89
0.950
20.42
20.25
0.988
20
18.66
18.63
0.949
19.90
19.75
0.987
64
1/2
8
2
108.31
109.45
0.954
142.35 142.35
0.990
5
103.31
105.86
0.957
131.18 135.24
0.991
20
100.96
104.03
0.955
126.23 131.70
0.993
20
2
88.26
88.64
0.951
102.69 102.31
0.989
5
86.08
86.86
0.956
99.45
99.39
0.990
20
85.10
85.93
0.954
96.75
97.89
0.991
2/3
8
2
102.82
105.28
0.955
135.37 133.87
0.989
5
97.41
98.97
0.956
119.42 121.87
0.992
20
93.48
95.63
0.958
116.67 115.81
0.989
20
2
86.27
86.63
0.952
99.26
98.96
0.990
5
83.73
83.42
0.948
94.12
93.76
0.989
20
81.41
81.68
0.952
90.96
90.99
0.990
a
R
,%= Population percent relative reproducibility standard deviation.
b
(
=
r
R
= Ratio of the population repeatability standard deviation to the population reproducibility standard deviation.
c
Number of laboratories.
d
Number of replicates/laboratory.
e
MC
95
,%
and
MC
99
,%
= Monte Carlo simulated one-tailed 95 and 99% upper limits for future sample percent relative reproducibility standard deviations.
f
95
99
,% ,% and
= Calculated one-tailed 95 and 99% upper limits for future sample percent relative reproducibility standard deviations.
g
(
p
*
) = Simulated percentile corresponding to a simulated
MC
value that equals
p
,%.
Recommended to OMB by Committee on Statistics: 07-17-2013
Reviewed and approved by OMB: 07-18-2013
31
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