APPENDIX A 



The following formulas were used to calculate the means, vari- 

 ances, and standard errors for length and weight data and the per- 

 cent males, females, broken, regenerated, and punctured 

 individuals collected during each dealer daylight low tide period 

 sampled. 



where X,, = expanded estimate for the /?th month, 

 X h = mean for the hth month (Equation (4)), 

 N,, = number of daylight low tides in the hth month, 

 D h = number of qualified dealer locations open during the 



/jth month, 

 n,, = number of daylight low tides sampled in the hth 



month. 



Y, = LN;Y/LN t 



var (F,) = E(F, - Y,y/(m(m - 1) ) 



Yj= ZYjJnj 



(1) 

 (2) 

 (3) 



Formulas used to calculate probability expansions and their 

 standard errors for the entire 6-mo sampling period include the 

 following: 



X SI = EX„ 



h 



var (XJ = E var (X) 



(10) 

 (ID 



where F, = mean for the /th dealer daylight low tide, 

 Yj= mean for the jth digger sampled, 

 Nj = number worms landed by the/th digger sampled, 

 m = number of diggers sampled, 

 Y Jt = measurement for the kth worm from the jth digger 



sampled, 

 tij = number of worms measured from the jth digger 

 sampled. 



Formulas used to calculate the monthly means, variances, and 

 standard errors for the same parameters above include the 

 following: 



Y„ = EF,// 

 var(F„)= E(F,-?,,) 2 /(/(Z-l)) 



(4) 

 (5) 



where Y h = mean for the hth month. 



F, = mean for the ith dealer daylight low tide (Equation ( 1 )). 

 / = number of dealer daylight low tides sampled. 



Formulas used to calculate the 6-mo means and standard errors 

 for the same parameters above include the following: 



F^EA^F/EN, 



I, h 



var ( F„) = E(/V„--var ( ?„) ) / (Efy,)- 



(6) 



(7) 



where X sl = 6-mo stratified total, 



X h = total for the hth month (Equation (8)). 



Ratios of two variables (catch/effort data) have been calculated 

 for the following marine worm sampling data: numbers dug/digger 

 tide, numbers dug/digger hour, pounds dug/digger tide, and pounds 

 dug/digger hour. The formulas used in calculating these ratios of 

 two variables, their variances, and standard errors on a monthly 

 basis, conform to the methodology of Cochran (1963) and are pre- 

 sented as follows: 



r, = j:yji:x, 



var (R,)=n h 'j:(Y-R,:Xy/ ( (n„- 1)(EX,)-) 



(12) 

 (13) 



where R,, = ratio estimate for the hth month . 



F, = some measure of catch sold to the /th dealer daylight 



low tide sampled, 

 X, = some measure of effort for diggers selling to the ith 



dealer daylight low tide sampled, 

 n h = number of dealer daylight low tides sampled. 



Formulas used to calculate the ratios of two variables and their 

 standard errors for the entire 6-mo sampling period include the 

 following: 



fl„ = E/vvfl,/EyV, 



(14) 



where F„ = 6-mo stratified mean, 



?,, = mean for the /?th month (Equation (4)), 



N k = number of daylight low tides in the hth month. 



Probability expansions have been calculated for the following 

 marine worm sampling data: total catch in numbers, total number 

 of diggerhours dug, total value of the catch, total number of digger 

 tides dug, and total catch in pounds. The formulas used in calculat- 

 ing these expanded estimates, their variances, and standard errors 

 on a monthly basis, conform to the methodology of Gulland (1966) 

 and Snedecor and Cochran ( 1967) and are presented as follows: 



X„ = N„-D,:X„ 

 var (X h ) = N, (N„ - «„)•£»,-• var {X„) 



(8) 

 (9) 



var (/?„) = E(AV-var (#,) )/(ENJ- 



(15) 



where R h = ratio estimate for the hth month (Equation (12)). 

 N t , = number of daylight low tides in the hth month. 



Estimates for the number of dealers that should be sampled each 

 month, the number of diggers that should be sampled per dealer, 

 and the number of worms that should be sampled from each digger, 

 conform to the methodology of Snedecor and Cochran (1967). 

 Information on the use of their methods may be found in Creaser 

 (text footnote 29). 



The relationship of worm weight to worm length was calculated 

 using a logarithmic transformation of the basic equation W=aL h . 



56 



