8 Defining a Sampling Strategy for Okadaic Acid (OA) Toxins in Shellfish. . .
91
For Whitaker’s Method
Theoretical Distribution
Data Used
To examine okadaic acid in mussels, we used the data of Dr. Arne Duinker who
has supplied us (personal communication) with raw data on individual mussels
contaminated with okadaic acid toxin equivalents, obtained during field experiments
that led to a publication (Duinker et al. 2007). These data consist of OA levels in
mussels contaminated on collectors cultured at high density in a stratified fjord.
Four different lots were sampled, and all the samples from a given lot were taken at
the same sampling point, at the same time, knowing that each sampling point and
sampling time was specific to each lot. For each lot: 29 or 30 samples were taken,
each sample consisting of one mussel. Then each individual mussel was submitted
to chemical analysis. Given the Regulation 853/2004/EC, the data, expressed in
concentration in steamed mussels, must be converted to concentration in raw
mussels. This conversion is done according to McCarron (McCarron et al. 2008).
They published a theoretical conversion value: the concentration level in steamed
meat must be divided by 1.2667 to obtain the concentration level in raw meat.
Theoretical Distribution and Goodness of Fit Tests
Probability density functions of the observed data were drawn. They suggested
a possible skewness, orienting towards a theoretical distribution type. Once a
theoretical distribution is identified, its parameters can be calculated by the method
of moments. Then, the visual comparison between the observed and theoretical
cumulative frequency distributions is achieved. Finally, the goodness of fit of the
observed data to the theoretical distribution can be tested by the KolmogorovSmirnov statistical test, which is a goodness of fit test. This test measures the
differences between the theoretical and observed probabilities for each contaminant
concentration within one lot. It involves finding the maximum vertical distance
between the cumulative frequency distributions.
The hypothesis tested by Kolmogorov-Smirnov goodness of fit are:
H 0 : The observed distribution conforms to the theoretical distribution.
H 1 : The observed distribution does not conform to the theoretical distribution.
At the desired risk level, H 0 can not be rejected if the test statistic (D calc ) is
less than a critical value found in a table for the corresponding number of samples
in the lot. This means that the adjustment of the observed data to the theoretical
distribution test can not be rejected at the risk level chosen. The p-value is the
probability of obtaining a test statistic at least as extreme as the one that was actually
observed, assuming that the null hypothesis H 0 is true.
91
For Whitaker’s Method
Theoretical Distribution
Data Used
To examine okadaic acid in mussels, we used the data of Dr. Arne Duinker who
has supplied us (personal communication) with raw data on individual mussels
contaminated with okadaic acid toxin equivalents, obtained during field experiments
that led to a publication (Duinker et al. 2007). These data consist of OA levels in
mussels contaminated on collectors cultured at high density in a stratified fjord.
Four different lots were sampled, and all the samples from a given lot were taken at
the same sampling point, at the same time, knowing that each sampling point and
sampling time was specific to each lot. For each lot: 29 or 30 samples were taken,
each sample consisting of one mussel. Then each individual mussel was submitted
to chemical analysis. Given the Regulation 853/2004/EC, the data, expressed in
concentration in steamed mussels, must be converted to concentration in raw
mussels. This conversion is done according to McCarron (McCarron et al. 2008).
They published a theoretical conversion value: the concentration level in steamed
meat must be divided by 1.2667 to obtain the concentration level in raw meat.
Theoretical Distribution and Goodness of Fit Tests
Probability density functions of the observed data were drawn. They suggested
a possible skewness, orienting towards a theoretical distribution type. Once a
theoretical distribution is identified, its parameters can be calculated by the method
of moments. Then, the visual comparison between the observed and theoretical
cumulative frequency distributions is achieved. Finally, the goodness of fit of the
observed data to the theoretical distribution can be tested by the KolmogorovSmirnov statistical test, which is a goodness of fit test. This test measures the
differences between the theoretical and observed probabilities for each contaminant
concentration within one lot. It involves finding the maximum vertical distance
between the cumulative frequency distributions.
The hypothesis tested by Kolmogorov-Smirnov goodness of fit are:
H 0 : The observed distribution conforms to the theoretical distribution.
H 1 : The observed distribution does not conform to the theoretical distribution.
At the desired risk level, H 0 can not be rejected if the test statistic (D calc ) is
less than a critical value found in a table for the corresponding number of samples
in the lot. This means that the adjustment of the observed data to the theoretical
distribution test can not be rejected at the risk level chosen. The p-value is the
probability of obtaining a test statistic at least as extreme as the one that was actually
observed, assuming that the null hypothesis H 0 is true.