to be 0.30 millimeter by the retaining sieve definition would be about 

 0.35 millimeter by the geometric mean definition. 



5. . Comparison of RSA and Sieve Analyses . 



The mean RSA and dry sieve sizes of the 30 samples from sample set A 

 processed by both methods are listed in Table 1 and compared in Figure 

 14. There is a well-defined shift to the right in Figure 14 which shows 

 that the processed RSA data usually indicate coarser means than those 

 calculated from dry sieve data. A visual fit line (solid line) drawn 

 through the data has an average shift of 0.33 phi. Therefore, RSA means 

 of all samples in sample set A were corrected using the following formula: 



SAMPLE MEAN = RSA MEAN + 0.33 PHI . (2) 



Hereafter, for data in sample set A, the term, "sample mean," is defined 

 by this equation. Sample means allow a reasonable comparison of CERC's 

 settling tube data to McMaster's (1954) sieve data. However, since sample 

 mean and RSA mean differ by only a constant additive factor when working 

 in phi units, relative changes will be the same whether sample means or 

 RSA means are used; i.e., the trends which show up in Figures 15, 16, 17, 

 and 18 are really trends in the fall velocities of the particles making 

 up the particular samples and not necessarily trends in the geometric size 

 of the particles. 



The sample correlation coefficient (Natrella, 1966) for Figure 14 was 

 0.90. Assuming a perfectly random selection procedure was used to choose 

 the 30 samples, there is a 95-percent probability that the correlation 

 coefficient for the entire population (469 samples) is between 0.81 and 

 0.95. The sample correlation coefficient improves to 0.92 if the extrap- 

 olated sample (consecutive number 59) is ignored, giving a 95-percent 

 confidence interval of 0.85 and 0.96. 



The solid curve in Figure 14 was visually fit to the data. Linear 

 regression yields the equation; 



y = 0.68 X +0.25 (3) 



for all data points and 



y = 0.84 X -0.06 , (4) 



when consecutive number 59 was ignored. Confidence intervals (Guttman 

 and Wilks, 1965) for equation (4) were computed to be: 



for the slope and 



[0.84 ± 0.24] „ and [0.84 ± 0.20]or,o 

 y b "^ y (J "6 



[-0.06 ± 0.22]„^„ and [-0.06 ± 0.18]„„<, 

 ■■95% "■ ■'90% 



27 



