Andrew and Chen: Estimating size structure and mean size of Haliotis rubra 
409 
Number of abalone sampled 
Figure 5 
Errors in size composition and estimated mean size of abalone caught in 
different sizes of the “fishery” with sampling scenario 2. 
3 was scaled up to a larger number of 
diver-days per year. In 1994, there was 
a total of 3,129 diver-days in the fish- 
ery. We simulated the efficiency of mea- 
suring 50 abalone per day in 100 diver- 
days in a fishery of 4,000 diver-days. At 
this sampling intensity, the estimated 
error index for the size structure and 
average difference in estimated mean 
size of abalone were 0.018 and 1.5 mm 
respectively. 
The cumulative frequency distribu- 
tion (Fig. 8) presents the probability of 
correctly rejecting the hypothesis of no 
difference under two scenarios. In the 
first, the probability of detecting a “real” 
difference between an estimated mean 
size and a nominated size is given. This 
nominated size may be a management 
benchmark, significant deviation from 
which will cause a change in manage- 
ment, such as a quota reduction. If, for 
example, the difference between a man- 
agement threshold and an estimated 
mean size is 3 mm, there is an 85% 
chance that the observed difference is 
“real” and not sampling error (Fig. 8, 
line b). If the observed difference is 
greater than 3 mm, then the probabil- 
ity of this being due to sampling error 
is less than 15%. 
In the second scenario, this logic is 
extended to situations in which differ- 
ences among years are considered. In 
this instance, both estimates of mean 
size are measured with error. If, for ex- 
ample, there is a 3-mm difference in 
mean size between two years, the probability of in- 
correctly interpreting this as a real difference among 
years, i.e. more than sampling error, is 0.85 x 0.85 = 
0.72 (Fig. 8, line a). 
Discussion 
Many stock assessment methods rely on reconstruc- 
tions of the demography of exploited populations, 
using age-structured information (e.g. Fournier and 
Archibald, 1982; Deriso et ah, 1985; Megrey, 1989; 
Kimura, 1990; Terceiro et al., 1992). Stock assess- 
ment methods available for species that cannot be 
aged are more limited, although recent development 
in size-based analogues of age-structured models 
have expanded the range of methods available (e.g. 
Sullivan et al., 1990). Size-based methods have tra- 
ditionally relied on reducing size-frequency distri- 
butions into cohorts (e.g. Bhattacharya, 1967; 
Schnute and Fournier, 1980; Grant et al., 1987; 
Castro and Erzini, 1988). The reliability of these 
methods depends in large part on the representa- 
tiveness of the sample distributions and the shape 
of the size-frequency distribution (e.g. Smith and 
Maguire, 1983; Chen, 1996). 
The sampling scheme described in this study is 
essentially a stratified random design, with diver- 
day being the intermediate stratified factor (see also 
Sen, 1986; Kitada et al., 1992; Crone, 1995). An al- 
ternative approach used in sample-size determina- 
tion for estimating age composition has been de- 
scribed by Schweigert and Sibert (1983). Their ap- 
proach was to determine sample-size requirements 
for each size and age class separately and to develop 
an overall sampling scheme as a compromise solu- 
