The test was used to check groups of stations for differences in mean 

 densities after the analysis of variance had indicated that the stations 

 differed. This test refined the analysis of variance by finding groups 

 of densities which were different from others. This could not be done by 

 the analysis of variance which merely indicated differences among all 

 stations as a group. 



Formulas for this test are: 



S- 



y 



= / 



'Mean square within 

 LSR (for k groups) = Q X S- 



y 



where: mean square within = the mean square from 



analysis of variance and 

 n is the number of 

 replicates per group. 



Q = studentized range taken 

 from a table such as U 

 in Sokal and Rohlf, 1969. 



It is also necessary to subtract each mean from each other one and 

 compare with LSR figures. Values exceeding the LSR figure are an 

 indication of significant difference. 



4. Mann-lVhitney U Test . 



This is a nonparametric test used to test the differences between two 

 sets of samples, and if two independent samples could have been drawn from 

 the same population. It is the nonparametric alternative to a parametric 

 t test and is used if the data being tested are not from a normally 

 distributed population. 



This test was used in comparing clams on two beaches because it was 

 uncertain the clam populations were normally distributed. 



Formulas for this test are: 



n, (ni+1) 

 U = n^n^ . — ^— - R^ 



where: n = number of observations in group 1 



n = number of observations in group 2 

 R = sum of the ranks assigned in group 1 



63 



