APPENDIX 

 STATISTICAL TESTS 



1. Chi-square Test . 



The chi-square test is a nonparametric test used to determine the 

 significance of differences between two sets of data which consist 

 primarily of frequencies. This includes "goodness-of-fit" tests 

 concerned with testing whether observed sample frequencies fit a theore- 

 tical or hypothetical frequency. In this report all uses of chi square 

 have been for goodness-of-fit. 



The variance to mean ratio (s^/x) should be one for a random distribu- 

 tion, less than one for a regular distribution, and greater than one for 

 a clumped distribution. The formula for testing the variance to mean 

 ratio is: 



^2 ^ s2(n-l) 



X 



where: s^ = variance 



n = number of observations. 



Significant deviation from a random distribution is determined from a 

 nomogram in Elliott (1971) . 



Chi square was also used in a second test to determine if the clam sex 

 ratios differed from a theoretical frequency of one to one or 50 percent 

 males and 50 percent females. In this case the formula for chi square is: 



.2 = zi^^^ 



where: o = observed frequency 



e = expected frequency 



The chi square is then compared to a table for one degree of freedom at 

 the selected level of rejection (usually 5 percent). A value of chi square 

 exceeding the tabled value is evidence of a significant deviation from the 

 theoretical value. 



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