Fræðaþing landbúnaðarins - feb. 2010, Side 300

| FRæðAÞING LANdBúNAðARINS 7, 2010300
The main objective of this study is to provide the necessary background information
to estimate the expected power in aquaculture growth studies. The variance
(expressed here as coefficients of variance) in data for growth studies of different
species of fish were calculated and used to model the expected effects of number of
replications and individuals within replication on the statistical power of aquaculture
growth studies.


Data derived from 24 independent aquaculture growth trials of Arctic charr
( ), Atlantic halibut ( ), Atlantic cod
(), turbot () and tilapia ()
were used to estimate the coefficients of variation amongst fish within a tank (CV
error) and between tanks within a treatment (CVwithin). The data were analysed with
a mixed model ANOVA in SPSS to obtain the mean sums of squares which were then
used to derive CVerror and CVwithin as described by Ling & Cotter (2003). These
values were then used to model the predicted statistical power of growth studies given
different number of fish within tanks and replications. The power was calculated
using G*Power 3.0 (www.softpedia.com).


The variance in the data from most species stabilised as the experiments progressed.
The mean CVerror was 30.4 ± 1.0% for all species. The CVerror ranged from 15%
to 37% at the end of the studies. Slight differences existed amongst fish species with
cod and tilapia having the highest CVerrors of 35% and 37% respectively at
termination of experiments. Arctic charr (average CVerror  21. ± 7.3%) and turbot
(CVerror 28%) showed the least variance. The CVwithin treatment ranged between
0 and 11% with a mean value of 4.8 ± 0.04%. There was no apparent difference in
CVwithin among species
The expected power in growth studies was modelled for a hypothetical growth study
with five treatments and a CVerror of 25% which is similar to the mean values for
Arctic charr and turbot. The CVwithin was set at 5% which is close to the mean
value for all species. The statistical power was modelled as a function of replications
and number of fish within each tank assuming 15% difference between the mean
levels of the largest and smallest treatment group (Fig. 1). The results show, as
expected, that power increases with the number of replications. It doubles when the
replication level is increased from a duplicate to triplicate. To reach a statistical power
over 80% with effect size of 15% it is necessary to have at least quadruplicates. The
power increases with increased number of fish within each tank. However, increasing
the number of fish above 100 does not improve power significantly.
The minimum effect size (with a power of 80%) is reduced as the number of
replications increases (Fig. 2) and it is reduced by a third when the number of
replications is increased from two to three. The effect size is not significantly reduced
when the N is increased above 100.