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Appendices
Appendix3
Calculatingbinomialconfidencelimitsnotcontainedin
Appendix1
The following methods enable exact binomial confidence limits to be interpolated or
extrapolatedfromthetablesinAppendix1:
1. IfrisgreaterthanthetabulatedvaluesinaparticularcolumnofN
Look up the corresponding values of the confidence intervals for N-r. The required
confidenceintervalsarecalculatedasfollows:
LCI=100-UCI
Equation1
(N-r)
UCI=100-LCI
Equation2
(N-r)
where: LCI=lowerconfidenceleveland
UCI=upperconfidenceinterval
For example, to interpolate the 95% confidence intervals where N = 21 and r = 15, look
up the corresponding values of the confidence intervals for N-r = 21-15 = 6. LCI = 100-
52.18=47.82,UCI=100-11.28=88.72.
2. IfrisliesbetweentwovaluesinaparticularcolumnofN(r
)
1
2
r
Calculate
,thenlookupthecorrespondingpvaluesforr
andr
.Therequired
p
100
1
2
r
N
confidenceintervalscanthenbecalculatedbyapplyingthefollowingformula:
p
p
r
r
1
Equation3
CI
CI
CI
r
1
r
2
r
1
p
p
r
2
r
1
For example, to interpolate the 95% confidence intervals where N = 200 and r = 85,
r
85
calculate
, look up the corresponding p values and confidence
p
100
42.5
r
200
N
intervalsfor80and90andinsertthemintotheformula:
42.50
40.00
LCI
33.15
37.98
33.15
35.56
45.00
40.00
42.50
40.00
UCI
47.15
52.18
47.15
49.67
45.00
40.00
3. IfNliesbetweentwocolumnsofN(N
)
1
2
r
Calculate
100
, then look up the corresponding confidence limits for p
and p
p
1
2
r
N
wherep
forN
andN
respectively.Next,determinetheinterpolatedconfidence
1
r
2
1
2
limitsforp
forbothN
andN
asinEquation3.Finally,therequiredconfidenceintervals
r
1
2
canbecalculatedbyapplyingthefollowingformula:
N
N
1
Equation4
CI
CI
CI
pr
lower
1
pr
upper
pr
lower
N
N
2
1
Forexample,tointerpolatethe95%confidenceintervalsforN=270andr=22whereN
r
lies between N
= 200 and N
= 300, firstly calculate
then look up the
p
100
8.15
1
2
r
N
correspondingpvaluesforp
andp
wherep
forN
andN
respectivelyandapply
1
2
1
r
2
1
2
Equation3:
HandbookonImportRiskAnalysisforAnimalsandAnimalProducts,Volume2,2004
121
-481-

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