366 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



a large extent, of the schooling habits of the fish. 

 These schools are particularly noticeable when 

 the migration intensity is low, but even during a 

 heavy run wide fluctuations in numbers continue 

 to occur. 



Table 6. — Determination of possible error from omitting 

 all night counts from tower No. 1, 1951 and 1959 



The width of the confidence intervals associated 

 with a point estimate is influenced directly by the 

 fluctuations in numbers of fish. The width of such 

 intervals can be decreased by an increase in sam- 

 pling time, especially by increasing the number of 

 samples but also by expanding the length of the 

 sample unit. 



Confidence Limits of the 1959 Escapement 



Confidence limits were determined for point 

 estimates of the annual red salmon escapements.^ 

 The method was applied to the 1959 counts to illus- 

 trate the procedures and to point out the accuracy 

 achieved by the present sampling methods. The 

 counts were of 15 minutes' duration and were taken 

 every 4 hours early in the season. A change to 

 10-minute counts taken hourly was made on June 

 29 as the migration increased. Daytime counts 

 were increased to 15 minutes, some to 30 minutes 

 or more each hour, near the peaks of the escape- 

 ment. Then all counts were reduced to 10 minutes 

 and taken every 4 hours near the end of the run. 



Before confidence limits can be calculated, the 

 season must first be stratified, since the variance 

 in the counts is associated with the mean numbers 

 of fish for each segment of the escapement (table 

 7). The total migration season from which the 



' The principal procedures have been used previously by O. A. 

 Mathisen In analysis of Wood River escapement estimates ; A 

 Stratifled Sampling Program for Visual Tower Counting, 1957. 

 University of Washington, Fisheries Research Institute, Seattle 

 (Wash.). Manuscript Modifications in this procedure for ap- 

 plication to Kvlchak River data were made with the assistance 

 of C. O. Junge, ,Tr., of the Fisheries Research Institute. 



four strata were drawn extended from noon, June 

 21 to August 1, a total of 39.5 days. This is equiva- 

 lent to 79 days of total counting for the two towers. 

 As intended by the sampling plan, an increase in 

 the percentage of sampling time occurred with 

 each strata in proportion to its numerical impor- 

 tance; 7.8, 14.1, 22.1, and 24.8 percent with strata 

 I to IV, respectively. 



It is assumed that the sample counts were taken 

 randomly throughout each stratum regardless of 

 some extended coimts or occasional gaps and were, 

 therefore, representative of the stratum from 

 which they were taken. The preliminary calcula- 

 tions for the determination of the confidence limits 

 are summarized in tables 7 and 8, where — 



A^= total number of sampling units (10- 

 minute counts). 

 P = total fish passage (population). 

 ^^ = total number of sampling units in the i"" 



stratum. 

 n= total number of samples (10-minute 



counts) obtained. 

 nt = total number of samples obtained in i"" 



stratum. 

 X,-, = number of fish in ]'" sample in i'" 



stratum. 

 lY7=mean number of fish per sample in i'" 



stratum from — 



z=^ — 



nt 

 S'5=variance of the samples in i"" stratum from— 



s?=-* 



rii 



m-l 



Ni 



Each stratum is weighted by Wi= -^- The 

 weighted mean (X) and the associated variance 

 5==) are then calculated from — 



X=Z1X, • Wi=60.62, also 



i = l 





