238 



Fishery Bulletin 100(2) 



30- 



20- 



10- 



30- 



20- 



_g 10- 



E 



30- 



20- 



10- 



June 

 n=47 

 Mean=56 



Ma 



20 40 60 80 100 



July 



n=74 



IVIean=46 



n 



n 



n 



n II n 



20 40 60 80 100 



August 



n=68 



Mean=52 



n 



nn 



30-1 



20- 



10- 



September 



n=63 



Mean=45 



n n 



80-1 

 60- 

 40- 

 20- 

 



20 40 60 80 100 



Total 



n=252 



IVlean=49 



_IZL 



M 



JTL 



20 40 60 80 100 



20 40 60 80 100 



Body weight (g) 



Figure 6 



Distributions of body weight by month foi' ayu caught in the Nakagawa River- 



can be obtained by the equations derived in our study. 

 In such repeated measure designs, the most precise esti- 

 mates of annual catch are obtained by method 2. On the 

 other hand, stratified surveys, or successive independent 

 sui-veys between time intervals based on random samples 

 of anglers or boats, are better than longitudinal surveys if 

 the designer's goal is to obtain precise estimates of total 

 effort, or catch (or total effort and catch), over the entire 

 season. Stratification by month would improve the preci- 

 sion of annual estimates even more if estimates varied 

 greatly across months. Stratified sampling allows inde- 

 pendent monthly estimates, and monthly estimates can 

 be summed to produce precise estimates over time. In the 

 absence of correlations between monthly sample obser- 

 vations, the estimated variance of annual estimates can 

 be obtained simply by adding the estimated variances of 

 the monthly estimates. The estimated variances of annual 

 estimates stratified by month would be considerably less 

 than those of annual estimates based on repeated monthly 

 observations of a one-time annual sample. 



If method 2 is used to analyze data obtained by such in- 

 dependent surveys, how would the precision of the estima- 



tor compare with the precision of a stratified estimator? 

 For simplicity, we consider a population that is divided 

 into two subpopulations of A^,, N., units, respectively. The 

 stratified estimator of the population total and the respec- 

 tive variance are 



V{Y} = N^^V{y,) + N'^V{y,), 



where Vj and y-, are the sample means for sample sizes 

 of «, and /!2. On the other hand, those obtained by method 

 2 are 



- TV, + N.-, _ 

 r, = — ' =- 1 " i.v, + n.,y.:, ), 



^,^., J ..(7V..N,, ]-y, j ,MiV, + 7V,, -^,-^, 



«] +n., 



n, + n.. 



Subtracting i' from Y. we have 



