where C-(r) is the autocorrelation coefficient for lag r of the j-th of 40/L sets, 

 and C (r) is the mean of 40/L coefficients with the same lag r. By analogy with 

 normal distribution theory, the quantity Q (r,L)/<7 2 (r,L) is like a chi-square vari- 

 able with (40/L) - 1 degrees of freedom, where a 1 (r,L) is the variance of C (r) for 

 a sample of length L. Assume the Q(r,L)'s are independent, and that a 2 (r,L) is 

 inversely proportional to sample length and the same for all r. That is, 



ff 2 (r,L) = ka 2 /L where k is any proportionality constant. Then kL \ Q (t,L)/o 2 



7 



is like a chi-square variable with v = 29 [(40/L) - 1] degrees of freedom. For two 

 different values of L, L t and L 2 , the ratio 



-2 



L, > Q^L^/ia 



(4) 



l 2 ^Tq 



(t,L 2 )/v 2 



is like an F-variable with Vi,v 2 degrees of freedom. 



The "mean square," L \ Q(r,L)/i^, and the F-ratios using the mean 



T 



square for 20 years as the denominator, are shown in table 2. Assuming a robust 

 F-test, none of these ratios is significant (though less than 1) and it is concluded 

 that the variability in the autocorrelation functions is about as expected. 



TABLE 2. VARIABILITY IN AUTOCORRELATION FUNCTIONS 



L 



Mean Square 



F-ratio 



5 



0.0994 



0.83 



8 



0.1182 



0.99 



10 



0.0889 



0.74 



20 



0.1195 







13 



