1 percent or more in all three areas. Second, the average 

 insurance rate for active-v;ood vessels is higher than the rate 

 for active vessels made of steel by 1»7 percent or more in all 

 three areas. (See table B-7 of this appendix for these two 

 findings.) Third, age of vessel is directly and gross tonnage 

 of vessel inversely correlated with average insxirance rates. 

 Several calctilations confirming this were made by the staff. 

 Correlation in both cases is low because many other factors de- 

 termine insurance rates besides age and gross tonnage. The 

 presence of correlation is better demonstrated by the average 

 insurance rate of vessels distributed in a frequency by age and 

 gross tonnage shown in table B-7 of Section II, Correlation is 

 more pronounced for age. For vessels of less than 86 gross tons, 

 correlation is low in New England and Gulf Area, while direct 

 correlation is evidenced in California. For larger vessels 

 correlation is inverse for all three areas. Inasmuch as a 

 demonstration of the presence of such relationship justifies the 

 use of these variables for stratification purposes no attempt 

 has been made to measure the degree of correlation, 



(c) Second-stage samples . Chi-square analyses of second-stage 

 samples by age and gross tonnage have produced probability values 

 (p) for all areas greater than a 0.01 criterion of significance. 

 These probability values show that the deviations of these samples 

 from the universe with regard to age and gross tonnage of vessels 

 are due to chance error alone (table B-8 of this appendix.) 



(d) Third-stage samples . Chi-square analyses of third-stage 

 samples by age and tonnage has produced probability values for 

 all areas greater than the critical p = 0.01 level. Thus, the 

 null hypothesis has not been impugned and the representativeness 

 of these samples has been demonstrated, (table B-9) 



Conclusion ; The qualitative aspects of insurance experience and the presence 

 of correlation between the stratifying variable and average insurance rates 

 require that Type I errors should be as few as possible. In other words, 

 showing that the difference between the samples and the universe is not 

 significant is more important than showing that this difference is significant. 

 Therefore, P = 0.01 as a criterion of significance may be considered sufficient 

 and we may conclude that all second-stage and third-stage sapiples are reliable 

 representatives of the statistical populations from which th^ have been drawn. 



322 



