Fræðaþing landbúnaðarins - feb. 2010, Side 299

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Godfrey K. Kubiriza1,2, Albert Imsland3,4 and Helgi Thorarensen5
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The statistical analyses of growth studies in aquaculture are generally based on mixed
model ANOVA with hierarchal (nested) design (Scheffé, 1959; Imsland et al., 2008).
These studies compare the effects of different treatments, such as feed type or
environmental factors, on the growth of fish. It is necessary to test each treatment in
more than one fish tank. One reason why this replication is important is that
sometimes significant differences in growth are encountered among fish in replicate
tanks that are supposedly exposed to the same treatment. These are random
occurrences and may happen without any apparent difference in conditions or
treatment. Peer reviewed publications usually do not accept papers that are based on
studies without replication.
The null hypothesis tested in these growth studies is that all treatment groups come
from the same population and that there is no significant difference among the means
of different treatment groups. Two types of errors are associated with statistical
analysis. Type I error is observing a difference when in fact there is none (Whalberg,
1984; Hoenig & Heisey, 2001) or rejecting a true null hypothesis. The significance
level α (critical p value) describes the probability of committing Type I error and
usually the fiducial limits are set at less than 5% (p<0.05). A second type of error,
Type II error, is failing to reject a wrong null hypothesis, i.e. not finding a significant
difference when in fact it exists. The probability of Type II error is β and statistical
power is defined as 1 β. The design of experiments should aim for a minimum power
of 80% (Hoenig & Heisey, 2001; Araujo & Frøyland, 2007). Statistical analysis of
biological studies has traditionally mainly focused on significance levels and Type I
error, while less or no consideration is given to statistical power and Type II error
(Whalberg, 1984; Ling & Cotter, 2003; Festing, 2006; Ling, 2007).
The statistical power of these mixed hierarchical models depends primarily on five
factors: (1) The difference in means between treatment groups (effect size), (2) the
variance of the data, both within tanks and among tanks within the same treatment, (3)
the number of replicate tanks, (4) the number of fish within each tank and (5) the
number of treatments tested (Deng, 2005; António  2009). The statistical power
increases with increased effect size, number of replications, number of individuals,
number of treatments tested and reduced variance. As a result, it is of importance to
design the experiments with as many replications and individuals as possible.
However, the available facilities and funding are constraints when designing growth
studies. The number of available tanks is always limited and the cost of building and
running research facilities for aquaculture growth studies is high. Moreover, cost of
fish for experiments and the staff costs for husbandry and measurements are also high.
Therefore, experimental design must strike a balance between acceptable power and
available recourses.