10 15 



5 10 15 



CRAB CATCH (10^ lb) 



Figure 6. — Scatter diagrams of upwelling and crab catch 

 for various lag times, for Oregon. The median values of 

 upwelling index and crab catch divide each scatter diagram 

 into quadrants. 



The null hyphothesis of independence cannot 

 be rejected for lag times of from IVa to 4V2 yr 

 in Washington, SV2 and AV2 yr in Oregon, and 

 3V2 yr in northern California. Nonsignificance 

 at lag times of 4V2 yr in Washington and Ore- 

 gon and 31/2 yr in northern California implies 

 that the crab fishery is not strongly dependent 

 upon the survival or growth of recently meta- 

 morphosed crabs, or upon the survival of crab 

 larvae. Thus, even if abundance and survival 

 of crab larvae in one year are important to a 

 successful crab fishery some years later, up- 

 welling has no strong influence upon these 

 factors. 



Another statistical test lends stronger sup- 

 port for this conclusion. Contingency tables 

 (2 X 2) were set up from each scatter diagram. 

 The tables were defined by the number of data 

 points in each quadrant. For example, the IV2- 

 yr lag scatter diagram for Oregon (see Figure 

 6) reduces to a 



9 



median value of 

 >c crab catch 



Table 1. — Results of certain statistical tests performed 

 upon scatter diagrams of upwelling index vs. crab catch 

 in Washington, Oregon, and northern California. The 

 Corner Test was performed on the scatter alone, while 

 the absolute probabilities were calculated from 2x2 

 contingency tables set up from each scatter diagram. Qua- 

 drants were defined by the median value of the upwelling 

 index and crab catch. The number of data points in each 

 quadrant were the frequencies entered in each cell of 

 the contingency table. The null hypothesis tested was 

 independence of crab catch from the upwelling index. The 

 absolute probability calculations indicate rejection of this 

 hypothesis for the Wi-yx lag periods in Oregon and 

 northern California, and the 1/2-yr lag period for Wash- 

 ington; i.e., crab catch and upwelling index are related 

 at these lag times. 



contingency table, symbolically represented by 



C 



B 



D 



median value of 

 upwelling index 



Where N = A + B +C + D. 



The chi-square test can be applied to contin- 

 gency tables but the results tend to be unre- 

 liable when N is less than about 40 (N = 24 in 

 my examples). In such cases, if reliable results 

 are desired, the exact probability of a particular 

 contingency table given the null hypothesis can 

 be calculated from 



Po = (A + B)\{C + D)l(A + OUB + D)\^ 

 N\A\B\C\D\ 



(Tate and Clelland, 1957:73). To obtain a two- 



907 



