92
N. Wesolek et al.
Variance
Data Used
Variance and mean concentration data were gathered from the literature. Variance
data were compiled from 11 publications (Carmody et al. 1996; Duinker et al. 2007;
Edebo et al. 1988; Godhe et al. 2002; Kacem et al. 2009; Kl¨ opper et al. 2003;
Lindegarth et al. 2009; Mak et al. 2005; Reizopoulou et al. 2008; Sidari et al. 1998;
Svensson and F¨ orlin 2004) from various countries (Sweden, Italy, Germany, Ireland,
Hong Kong, Tunisia) and one thesis (Wrange 2008) from Sweden. The literature
review revealed a much higher number of publications about okadaic acid levels
in mussels, but all were not relevant for variance data gathering. Moreover, it was
decided to take into account variance data for as many countries as possible, to
ensure that the sampling plan validation would not be country specific, but would
represent a global validation.
Equation of Variance as a Function of the Concentration
The variability, more precisely the total variance, between sample concentrations is
due to sampling, sub-sampling and analytical errors. We know that total variance
is the sum of variance components, due to the fact that variance components are
additive because they are due to independent sources of random error. So, we
assume, according to Whitaker et al., that total variance (S
2
t ) is the sum of sampling
variance (S
2
s ), sub-sampling variance (S
2
ss ) and analytical variance (S
2
a ) in Eq. 8.1:
S
2 t D S
2 s C S
2 ss C S
2 a
(8.1)
In Whitaker’s method, S
2
t , S
2
ss , and S
2
a are accurately quantified. But, given the
fact that, when working on experimental data, Whitaker et al. always found that
S
2
ss , and S
2
a were negligible in comparison with S
2
t we decided not to calculate the
negligible variances. This is a slight modification of Whitaker’s method that makes
the method easier to undertake, with little loss of accuracy. When assuming that S
2
ss
and S
2
a are negligible, the following approximation can be made:
S
2 t D S
2 s
(8.2)
This approximation is now used to define sampling variance instead of total
variance.
In order to determine which type of experimental data to use, further definition of
the sampling variance is required. In two samples with different means, but which
are drawn from the same population, then the difference between the means is
simply due to sampling error. Two factors determine the magnitude of the sampling
error: population variance, and the number of individuals in the sample:
N. Wesolek et al.
Variance
Data Used
Variance and mean concentration data were gathered from the literature. Variance
data were compiled from 11 publications (Carmody et al. 1996; Duinker et al. 2007;
Edebo et al. 1988; Godhe et al. 2002; Kacem et al. 2009; Kl¨ opper et al. 2003;
Lindegarth et al. 2009; Mak et al. 2005; Reizopoulou et al. 2008; Sidari et al. 1998;
Svensson and F¨ orlin 2004) from various countries (Sweden, Italy, Germany, Ireland,
Hong Kong, Tunisia) and one thesis (Wrange 2008) from Sweden. The literature
review revealed a much higher number of publications about okadaic acid levels
in mussels, but all were not relevant for variance data gathering. Moreover, it was
decided to take into account variance data for as many countries as possible, to
ensure that the sampling plan validation would not be country specific, but would
represent a global validation.
Equation of Variance as a Function of the Concentration
The variability, more precisely the total variance, between sample concentrations is
due to sampling, sub-sampling and analytical errors. We know that total variance
is the sum of variance components, due to the fact that variance components are
additive because they are due to independent sources of random error. So, we
assume, according to Whitaker et al., that total variance (S
2
t ) is the sum of sampling
variance (S
2
s ), sub-sampling variance (S
2
ss ) and analytical variance (S
2
a ) in Eq. 8.1:
S
2 t D S
2 s C S
2 ss C S
2 a
(8.1)
In Whitaker’s method, S
2
t , S
2
ss , and S
2
a are accurately quantified. But, given the
fact that, when working on experimental data, Whitaker et al. always found that
S
2
ss , and S
2
a were negligible in comparison with S
2
t we decided not to calculate the
negligible variances. This is a slight modification of Whitaker’s method that makes
the method easier to undertake, with little loss of accuracy. When assuming that S
2
ss
and S
2
a are negligible, the following approximation can be made:
S
2 t D S
2 s
(8.2)
This approximation is now used to define sampling variance instead of total
variance.
In order to determine which type of experimental data to use, further definition of
the sampling variance is required. In two samples with different means, but which
are drawn from the same population, then the difference between the means is
simply due to sampling error. Two factors determine the magnitude of the sampling
error: population variance, and the number of individuals in the sample: