required to obtain a minimum desired accuracy of ± 15% about the 

 mean expansion estimate (total catch in numbers, total number of 

 digging hours dug, etc.) at the 90% confidence level. The results of 

 these analyses on both bloodworms and sandworms are shown in 

 Tables 29 and 30. respectively. In most cases (using both optimum 

 and proportional allocation), the number of sampling daylight low 

 tides required to obtain the desired accuracy exceeds the number of 

 tides which could reasonably be sampled. Furthermore, to make 

 use of optima] allocation, one must be able to reliably predict the 

 relative variability which occurs in each stratum (month), but the 4 

 yr of data do not demonstrate consistent monthly variability from 

 year to year. Because of these problems, we chose to sample six 

 daylight low tide periods per month, and accept the large standard 

 errors about the mean estimates for probability expansion esti- 

 mates. 



We applied the combined methodology of Gulland (1966), Pope 

 (1956), and Snedecor and Cochran (1967) to determine whether 

 satisfactory estimates of mean length in a future commercial marine 

 worm sampling program could be obtained with less sampling of 

 worms/digger, diggers/dealer, and dealers/month. The results of 

 this analysis indicate that variability of no more than +15% of the 

 estimated mean at the 95 % confidence level could be obtained for 

 bloodworm lengths by sampling approximately 10 measurable 

 worms/digger 6 diggers/dealer, and 2 dealers/mo (if only 1 mo was 

 sampled). Similar data could be collected for sandworms by sam- 

 pling approximately 14 measurable worms/digger, 5 diggers/ 

 dealer, and 1 dealer/mo (Creaser footnote 37). Obviously, the 



desire to obtain a variability of no more than 5 or 10% of the esti- 

 mated mean at the 95% confidence level would be obtained by 

 increasing the sample size. Since we sampled approximately 20 

 measurable bloodworms/digger and approximately 7 bloodworm 

 diggers/dealer from an average of 3 bloodworm dealers/mo, and 

 approximately 18 measurable sandworms/digger, and approxi- 

 mately 6 sand worm diggers/dealer from an average of nearly 3 

 sandworm dealers/mo between 1973 and 1976, we have sampled 

 more than what was required to obtain the minimum desired degree 

 of accuracy. The magnitude of the standard errors about the 6-mo 

 mean lengths (Tables 10, 1 1) also demonstrates this point. 



Considering that 1) probability expansion estimates could be 

 improved (smaller standard errors obtained) by sampling more fre- 

 quently each month, and 2) satisfactory monthly estimates of 

 marine worm length could be obtained with fewer length samples, 

 it would probably the possible to sample more frequently each 

 month and improve the probability estimates if fewer worms were 

 being obtained for length processing. Although it is not possible to 

 increase sampling to the point at which we could attain the accuracy 

 expressed in Tables 29 and 30, it would probably be possible to 

 increase the amount of sampling to 8 or 10 daylight low tides per 

 month. Sampling could furthermore be stratified so that each of 4 

 or 5 bloodworm and 4 or 5 sandworm shippers could be randomly 

 sampled each month. Both worm species would be sampled at 

 those shippers selected who purchase both species of worms. 



Despite the decreased sampling required to estimate worm 

 length, it might still be desirable to collect some length samples 



Table 29. — Calculations of the desired frequency of monthly samplings 

 for bloodworms to obtain a minimum accuracy of + 15% about the 

 mean estimate for 1) total catch in numbers and 2) total number of dig- 

 ger hours dug, at the 90% confidence level. 



Table 30.— Calculation of the desired frequency of monthly samplings 

 for sandworms to obtain a minimum accuracy of + 15% about the mean 

 estimate for 1) total catch in numbers and 2) total number of digger 

 hours dug, at the 90% confidence level. 





1973 



1974 



1975 



1976 





1973 



1974 



1975 



1976 









Total catch in numbers (bloodworms, 













Total catch in numbers (sandworms) 













Optimum allocation 













I 



Dptimum allocation 







A 



'(36) 



2 8.72 



(36) 



15.15 



(38) 



2.75 



(36) 



24.20 



A 



'(36) 



218.57 



(36) 



13.30 



(38) 



4.04 



(36) 



2.90 



M 



(42) 



16.81 



(40) 



31.65 



(41) 



19.03 



(25) 



8.17 



M 



(42, 



25.61 



(40) 



18.17 



(41, 



40.46 



(25) 



11.41 



J 



(42) 



25.01 



(41) 



21.69 



(42) 



17.09 



(39) 



30.81 



J 



(42) 



23.01 



(41) 



24.64 



(42) 



16.60 



(39) 



18.32 



J 



(44) 



19.76 



(42) 



25.88 



(41) 



27.70 



(42) 



20.47 



J 



(44) 



7.62 



(42) 



27.90 



(41) 



28.01 



(42) 



33.05 



A 



(40) 



24.75 



(40) 



12.53 



(39, 



29.64 



(38) 



7.76 



A 



(40) 



15.61 



(40) 



17.14 



(39) 



5.81 



(38) 



4.64 



S 



(33) 



13.45 



(35) 



9.85 



(33) 



16.34 



(34) 



10.96 



S 



(33) 



12.19 



(35) 



13.10 



(33) 



4.75 



(34) 



14.86 









Proportional allocation 













Proportional allocation 







A 



(36) 



17.72 



(36) 



20.21 



(38) 



22.05 



(36, 



20.61 



A 



(36, 



17.44 



(36) 



18.51 



(38) 



25.77 



(36) 



19.91 



M 



(42) 



20.67 



(40) 



22.45 



(41) 



23.79 



(25) 



13.17 



M 



(42) 



20.35 



(40, 



20.57 



(41) 



27.81 



(25) 



13.83 



J 



(42) 



20.67 



(41) 



23.02 



(42) 



24.37 



(39) 



22.33 



J 



(42) 



20.35 



(41) 



21.08 



(42) 



28.49 



(39) 



21.57 



J 



(44) 



21.66 



(42) 



23.58 



(41) 



23.79 



(42) 



24.04 



J 



(44, 



21.32 



(42) 



21.60 



(41) 



27.81 



(42) 



23.23 



A 



(40) 



19.69 



(40) 



22.45 



(39) 



22.63 



(38) 



21.75 



A 



(40, 



19.38 



(40) 



20.57 



(39) 



26.45 



(38) 



21.02 



S 



(33) 



16.24 



(35) 



19.65 



(33) 



19.15 



(34) 



19.46 



S 



(33) 



15.99 



(35) 



18.00 



(33) 



22.38 



(34) 



18.81 







Total number of digger 



hours dug (bloodwor 



ms) 









Total number of digger 



hours dui 



; (sandworms) 











Optimum 



allocation 













Optimum 



allocation 







A 



(36) 



11.21 



(36) 



17.87 



(38) 



1.55 



(36) 



22.91 



A 



(36, 



14.94 



(36) 



13.17 



(38) 



5.62 



(36) 



3.41 



M 



(42) 



24.71 



(40) 



29.90 



(41) 



14.59 



(25) 



8.73 



M 



(42) 



23.11 



(40) 



15.61 



(41) 



39.20 



(25) 



9.38 



J 



(42) 



24.33 



(41) 



20.80 



(42) 



20.91 



(39) 



29.67 



J 



(42) 



22.93 



(41) 



17.39 



(42) 



12.53 



(39) 



15.40 



J 



(44 1 



17.85 



(42) 



27.49 



(41) 



26.95 



(42) 



21.46 



J 



(44) 



6.56 



(42) 



32.45 



(41) 



32.23 



(42) 



31.51 



A 



(40) 



16.33 



(40) 



19.65 



(39) 



31.40 



(38) 



9.67 



A 



(40) 



16.48 



(40) 



19.10 



(39) 



7.99 



(38) 



8.32 



S 



(33) 



8.15 



(35) 



11.42 



(33) 



12.11 



(34) 



10.70 



S 



(33) 



16.40 



(35) 



9.17 



(33) 



7.00 



(34) 



15.40 









Proportional allocation 













Proportional allocation 







A 



(36) 



16.86 



(36) 



20.71 



(38) 



22.34 



(36) 



19.98 



A 



(36) 



16.98 



(36) 



18.48 



(38) 



25.62 



(36) 



18.28 



M 



(42) 



19.67 



(40) 



23.01 



(41) 



24.07 



(25) 



12.77 



M 



(42) 



19.81 



(40) 



20.54 



(41) 



27.65 



(25) 



12.69 



J 



(42, 



19.67 



(41) 



23.59 



(42) 



24.65 



(39) 



21.65 



J 



(42) 



19.81 



(41) 



21.05 



(42) 



28.32 



(39) 



19.80 



J 



(44) 



20.61 



(42) 



24.16 



(41) 



24.07 



(42) 



23.32 



J 



(44) 



20.75 



(42) 



21.56 



(41) 



27.65 



(42) 



21.33 



A 



(40) 



18.73 



(40) 



23.01 



(39) 



22.89 



(38) 



21.10 



A 



(40) 



18.86 



(40) 



20.54 



(39) 



26.30 



(38) 



19.30 



S 



(33) 



15.46 



(35) 



20.14 



(33) 



19.37 



(34) 



18.88 



S 



(33) 



15.56 



(35) 



17.97 



(33) 



22.25 



(34) 



17.27 



'( } = The total number of daylight low tides in the month. 

 2 The calculated number of sampling tides required to obtain the desired 

 accuracy. 



'( ) = The total number of daylight low tides in the month. 

 2 The calculated number of sampling tides required to obtain the desired 

 accuracy. 



53 



