As already mentioned the parameters a, g and S used to construct the limit curve are only a function of N and of the assumption that the population can or cannot be concave. Thus when the size of a target finite population is known, a random sample of size n will correspond to a predicted pessimistic accuracy computed by means of the function as defined in (7.5). Alternatively, if the population is of infinite size, predicted pessimistic accuracy values will be obtained through the use of the model described by (8.3).
The question arising here is whether the size of a finite population can be known to a reasonable degree of certainty. In most samplebased fishery surveys the population under study is finite and of known size as is, for instance, the case of total number of fishing craft operating from homeports. When the population size varies, then a maximum must be assumed.
The described model also provides information regarding critical sample size and breakpoints in the accuracy growth. As stated in Section 6.2 the critical sample size is when x=0.5 or sample size . It is clear that by simply computing a researcher can immediately determine at which sampling level the accuracy will start a steady increasing process towards 1. However, fixing a sample size by only considering the critical level does not always constitute an optimal approach for the following two reasons:
(a) For small populations the critical sample size and the predicted pessimistic accuracy at critical sample size will not necessarily indicate an expected accuracy of much higher level. This is particularly true in concave populations, such as the total set of recordings of fishing unit activities.
(b) Conversely, and particularly in large populations, an arbitrary selection of a very large sample size well beyond the critical point, may not prove a very costeffective approach and the user may miss the opportunity of achieving about the same accuracy by using considerably smaller samples.
For these two reasons it is suggested that a table be constructed illustrating the predicted pessimistic accuracy for several sample sizes, so as to obtain more flexibility in the evaluation process of alternative sampling schemes. Table 9.1 and Figure 9.1 give an example of such a tabular approach using a simple electronic worksheet. The tabular data and the diagram refer to a concave population of size N=10 000. The worksheet was programmed to also include the intermediate computational steps and the resulting primary and secondary parameters used for the construction of the pessimistic accuracy curve A_(x).
The presented method also suggests that sampling criteria and practices should be reviewed and adjusted when the original target population is stratified into more homogeneous subpopulations. For instance, if a sample size is known to be effective when applied to a population before stratification, its effectiveness would be reduced if divided proportionally to the size of each of the stratified populations.
Table 9.1
PESSIMISTIC ACCURACY MODEL FOR FINITE POPULATIONS
INPUTTING PARAMETERS
Please indicate if the population can be concave 
(=0) 
or that concave populations should be excluded 
(=1) 
CONCAVE/NON CONCAVE 
0 
POPULATION SIZE 
10000 
Computed model parameters
Primary parameter W (concave) 
0.594501557 
Primary parameter W (non concave) 
0.749925 
Resulting W 
0.594501557 
Intercept a 
0.189040931 
Intercept g 
0.189122027 
Area S 
0.087958861 
Curvature k 
0.457405054 
Coefficient a2 
0.823062612 
Intercept a1 
1.012184639 
x=logn/logN 
Sample size 
Proportion % 
ACCURACY (Lower limit) 
0 
1 
0.01 
0.189 
0.01 
1 
0.01 
0.223 
0.02 
1 
0.01 
0.256 
0.03 
1 
0.01 
0.287 
0.04 
1 
0.01 
0.317 
0.05 
1 
0.01 
0.345 
0.06 
1 
0.01 
0.373 
0.07 
1 
0.01 
0.399 
0.08 
2 
0.02 
0.425 
0.09 
2 
0.02 
0.449 
0.1 
2 
0.02 
0.472 
0.11 
2 
0.02 
0.494 
0.12 
3 
0.03 
0.516 
0.13 
3 
0.03 
0.536 
0.14 
3 
0.03 
0.556 
0.15 
3 
0.03 
0.575 
0.16 
4 
0.04 
0.593 
0.17 
4 
0.04 
0.610 
0.18 
5 
0.05 
0.627 
0.19 
5 
0.05 
0.643 
0.2 
6 
0.06 
0.658 
0.21 
6 
0.06 
0.672 
0.22 
7 
0.07 
0.686 
0.23 
8 
0.08 
0.700 
0.24 
9 
0.09 
0.713 
0.25 
10 
0.1 
0.725 
0.26 
10 
0.1 
0.737 
0.27 
12 
0.12 
0.748 
0.28 
13 
0.13 
0.759 
0.29 
14 
0.14 
0.770 
0.3 
15 
0.15 
0.780 
0.31 
17 
0.17 
0.789 
0.32 
19 
0.19 
0.798 
0.33 
20 
0.2 
0.807 
0.34 
22 
0.22 
0.816 
0.35 
25 
0.25 
0.824 
0.36 
27 
0.27 
0.832 
0.37 
30 
0.3 
0.839 
0.38 
33 
0.33 
0.846 
0.39 
36 
0.36 
0.853 
0.4 
39 
0.39 
0.860 
0.41 
43 
0.43 
0.866 
0.42 
47 
0.47 
0.872 
0.43 
52 
0.52 
0.878 
0.44 
57 
0.57 
0.883 
0.45 
63 
0.63 
0.889 
0.46 
69 
0.69 
0.894 
0.47 
75 
0.75 
0.899 
0.48 
83 
0.83 
0.903 
0.49 
91 
0.91 
0.908 





Critical 
Sample 
Size 
0.5 
100 
1 
0.912 
0.51 
109 
1.09 
0.916 
0.52 
120 
1.2 
0.920 
0.53 
131 
1.31 
0.924 
0.54 
144 
1.44 
0.928 
0.55 
158 
1.58 
0.931 
0.56 
173 
1.73 
0.934 
0.57 
190 
1.9 
0.938 
0.58 
208 
2.08 
0.941 
0.59 
229 
2.29 
0.944 
0.6 
251 
2.51 
0.946 
0.61 
275 
2.75 
0.949 
0.62 
301 
3.01 
0.952 
0.63 
331 
3.31 
0.954 
0.64 
363 
3.63 
0.957 
0.65 
398 
3.98 
0.959 
0.66 
436 
4.36 
0.961 
0.67 
478 
4.78 
0.963 
0.68 
524 
5.24 
0.965 
0.69 
575 
5.75 
0.967 
0.7 
630 
6.3 
0.969 
0.71 
691 
6.91 
0.971 
0.72 
758 
7.58 
0.973 
0.73 
831 
8.31 
0.974 
0.74 
912 
9.12 
0.976 
0.75 
1000 
10 
0.977 
0.76 
1096 
10.96 
0.979 
0.77 
1202 
12.02 
0.980 
0.78 
1318 
13.18 
0.981 
0.79 
1445 
14.45 
0.983 
0.8 
1584 
15.84 
0.984 
0.81 
1737 
17.37 
0.985 
0.82 
1905 
19.05 
0.986 
0.83 
2089 
20.89 
0.987 
0.84 
2290 
22.9 
0.988 
0.85 
2511 
25.11 
0.989 
0.86 
2754 
27.54 
0.990 
0.87 
3019 
30.19 
0.991 
0.88 
3311 
33.11 
0.992 
0.89 
3630 
36.3 
0.993 
0.9 
3981 
39.81 
0.994 
0.91 
4365 
43.65 
0.994 
0.92 
4786 
47.86 
0.995 
0.93 
5248 
52.48 
0.996 
0.94 
5754 
57.54 
0.996 
0.95 
6309 
63.09 
0.997 
0.96 
6918 
69.18 
0.998 
0.97 
7585 
75.85 
0.998 
0.98 
8317 
83.17 
0.999 
0.99 
9120 
91.2 
0.999 
1 
10000 
100 
1.000 
Fig. 9.1 Pessimistic accuracy level