FISHERY BULLETIN: VOL. 71, NO. 4 



Table 19. — An example of the calculation of rank- 

 correlation coefficients. 



Food item 

 category 



10 stickleback 

 rank 



10 trout- 

 perch rank 



Difference 

 d 



rf2 



a tie in importance of any two categories, the 

 larger item was ranked first. An r^ value of 

 + 1.0 indicates that the various food categories 

 were eaten in the same order of preference, and 

 as r approaches - 1.0, there is no agreement 

 in order of occurrence. 



To test the hypothesis that fish of the same 

 species eat the same things in different areas, 

 10 randomly selected fish caught from one sta- 

 tion within 3 days were compared. In interspe- 

 cific tests, 10 fish of each species taken at the 

 same station on the same day were used. Except 



for smelt, only adults were used in the tests 

 because juveniles of other species were not com- 

 pletely available to the gear and not taken in 

 large enough quantities to test. 



Analyses of individual tests were not made; 

 instead the results from several comparisons 

 (N in Table 20) were combined and a test made 

 using the combination of probabilities discussed 

 by Snedecor (1956:216). The sum of the natural 

 logarithms of the probabilities associated with 

 each of several comparisons is multiplied by 

 — 2, and the resulting values have a chi-square 

 distribution with two degrees of freedom for 

 each comparison. Pearson (1924) presents a 

 figure which allows graphical calculation of 

 probabilities associated with r^. 



Intraspecific correlations were significant 

 for all comparisons (Table 20). Indications are 

 that food habits among individuals of the same 

 species were almost identical within the Apostle 

 Islands. 



Significant interspecific correlations were 

 found between sticklebacks and slimy sculpins 

 in spring and summer and sticklebacks and 



Table 20. — Food composition similarity measured by rank-correlation coefficients (r^) between stickle- 

 backs and other Apostle Islands species. (N equals the number of individual tests for each comparison, 

 and n equals the number of food categories in each comparison.) 



Comparison 



N 



Mean r^ 



Chi-square 



1. Between adult sticklebacks 



of stations 2 and 3 



2. Between adult trout -perch 



5. 



+ 0.94 



36.89*' 



* Significant at the 0.01 level. 

 ** Significant at the 0.005 level. 



1056 



