Figure Ik shows variance plotted against arithmetic mean for frequency 

 of number of clams per bottom sample grouped in classes of two for each 

 sampling series shown in Table ^. Slope of trend line indicates need for 

 transformation to make variances independent of the means in order that 

 methods for analysis of variance become applicable (Beall, 19U2 and Barnes, 

 1952 J Barlett,1936 and 19U7 and Snedecor, I9U0) . 



Table 6 shows transformation of data from Table 5 by grouping number 

 of clams per sample into classes of two, adding 3/8 to midpoint of each 

 class as per Anscombe (19U8) and Quenouille (1950), and taking the square 

 root. 



Arithmetic means and variances for untrans formed and for transformed 

 values which are plotted in Figures lU and 15 are shown at the bottom of 

 Table 6. Also shown are derived arithmetic means, standard deviations 

 and standard error in number of clams computed from the transformed \alueQ. 



Derived arithmetic means were determined by squaring the transformed 

 mean, subtracting 3/8 and adding the Variance as per Quenouille (1950). 



Derived standard deviations v.'ere determined by the following formula: 

 Derived s " [Trans x + trans s) — 3/8] — derived x. 



Derived standard errors were computed by the following formula: 

 Derived s * ■ Derived s 



Figure 15 sh ows varia nce plotted against arithmetic means for counts 

 transformed by /x + 3/b 



Figures I6 and 1? show untransformed and transformed frequencies of 

 number of clams per sample for all series 19U9 and 1950. The square root 

 transformation has changed the distribution to approximate normality and 

 has made the variance independent of the mean as shown by the fact that 

 the trend line in Figure 1$ has practically no slope. 



Therefore statistical methods designed for normal distributions can 

 be applied to these transformed values. The mean number of clams, stand- 

 ard deviation and standard error computed from transformed values and 

 shown in the last three lines of Table 6 can then be considered reliable. 



Sampling reliability was estimated by computing standard error of 

 the difference of means and normal deviates for each pair of series in 

 I95O0 Results are shown in Table ?• 



3U 



