FISHERY BULLETIN: VOL. 74. NO. 4 



these distribution functions. Using winter sam- 

 ples only, the test failed to reject Hq; thus, the data 

 from each A and B subarea pair were combined 

 and considered to be one subarea for comparison to 

 the subareas sampled in the spring and summer. 

 Hence, all data were analyzed as if they had been 

 collected from four equal sized subareas, of 

 dimensions 45 m by 7 m, during each season, using 

 a sample of size four on each stratum. 



The empirical cumulative distribution functions 

 were constructed from the data by defining a 

 random variable X as the sum of the percent of the 

 total sediment weights retained in the sieve sizes 

 <0.063, 0.063, and 0.124 mm. The random variable 

 X takes a value of each sample, in each subarea, on 

 each stratum. Thus, the empirical distribution 

 functions constructed from this data characterized 

 the sum of the weights of three finest sediment 

 grades (and by subtraction from 100%, the three 

 coarsest grades as well) for each stratum in each 

 subarea. These three sieve sizes were grouped 

 together because they constitute what may be 

 called the finer grades of sediment and they 

 probably have the greatest biological impact 

 (Newell 1965). If the grain size which is of prin- 

 cipal importance to the organisms is known, then 

 the random variable could be chosen accordingly. 

 There is much evidence that grain size is impor- 

 tant to the organisms (e.g., see Loosanoff and 

 Tommers 1948; Sanders 1958; Wieser 1959; Gray 

 1974). Subject to this limitation of comparing only 

 the finer sediment groups, the sediment data may 

 be statistically compared stratum to stratum in 

 any one subarea, between subareas, or in combi- 

 nations of these, both within or between seasons. 



In each case, the null hypothesis for the K-S test 

 on sediment was 



species types with entries in the expected value 

 table which were either greater than unity, or at 

 least, not far below unity. All species identified are 

 listed, but, in certain cases, some species were 

 grouped into families for the analysis; these are 

 noted in the tables of data. Grouping of data is 

 often advisable on statistical or biological grounds 

 depending upon the objectives of the study. When 

 data were grouped in this study, the grouping was 

 dictated by sample sizes and was consistent with 

 biological facts such as where the organisms occur 

 in Garrison Bay, their modes of feeding, and their 

 taxonomy. 



The data were organized into contingency 

 tables for a multinomial distribution. We denote 

 the probability of a randomly selected value from 

 the /th population as being classified in the jth 

 class by P,,. The columns of the table represent 

 species (classes) while the rows represent popula- 

 tions, i.e., a particular stratum in a given subarea 

 during a specific season. The null hypothesis may 

 be stated as: 



Ho: Pi, =P^,= ... = P,, for alii; i = 



l,2,...,c, (2) 



and the alternative 



H^: there is at least one P^j "/ P^j for some 

 j and pair i, k where r equals the number of rows 

 and c equals the number of columns. Under Hq, 



P 11 — P2I = . . • = Prl = Pi 



Plr — P2C — 



= P = P 



Ro.FAx) = FAx) = ... = F,{x) (1) 



and the alternative 



H^: there is at least one inequality where 

 Fj (x) is the cumulative distribution function of the 

 random variable A" corresponding to area J. 



The statistical analysis of the distribution of 

 animal populations was based upon standard 

 chi-square procedures (Conover 1971). Let the 

 random variable Z have a multinomial distribution 

 where the number of classes corresponds to the 

 number of species types used, and the number of 

 trials is the total number of individuals of all 

 species. The chi-square test was applied to those 



where Pj = Q /N; Q = sum of observations in 

 column j; N = total number of observations from 

 all samples; and P, estimates P^. When a row or 

 column of a particular contingency table equalled 

 zero, it was not possible to reach a decision about 

 the chi-square null hypothesis. To maintain con- 

 sistent comparisons, no alteration of the contin- 

 gency tables was made in such cases. The results of 

 some of these tests of homogeneity are summa- 

 rized in the next section. 



RESULTS 



The sampling data and the estimates of the 

 variances of the sample means appear in Tables 



940 



