354 REFRACTION AND REFRACTIVE INDEX MODELS 



falling below the 100a = 5 percent level to be not significant, between the 

 5 percent and 1 percent levels to be of questionable significance, and over 

 the 1 percent level to be significant [25]. An observed slope b falling 



Vi:(xi - xY 



would thus be taken to represent a significant departure from the value 

 /So, and would thus imply the possibilities 



(a) j3o does not represent /3, or 



(b) h represents the regression of data from a population different than 

 that used in determining ^So, or 



(c) both. 



Before making the significance tests, however, the value of j, the num.- 

 ber of independent observations going into the determination of h, must 

 be known. In general, data of the type presented here are more or less 

 highly autocorrelated, and hence not all independent. The data pre- 

 sented here, with the possible exception of the Collins data and the 

 Tularosa Basin data for which the calculations could not be performed, 

 have autocorrelation coefficients Vk, for lag k {k = 1, 2, 3 units of time be- 

 tween successive measurements) that can be approximately described by 



and for this type of data the effective number of pieces of independent 

 data, j, is given by [26] 



■fr 



— r 

 J = n 



+ r'J 



(8.27) 



For the data treated here weighted mean values of r' were calculated 

 from 



r. + ^rl-^9rl-+-^.^kM- 

 "^ - 1 + 4 + 9+-.. A;2 ' ^'^■^''^ 



where k was the largest lag for which the autocorrelation coefficient was 

 calculated, usually 4 or 5. No special justification is offered for the use 

 of (8.28) other than the obvious fact that Vk is to be approximated by 

 the kth. power of r', and hence a function of k would seem to be the most 

 logical weighting function to use; the use of k"^ as a weighting function 

 seemed to give the best overall fit to the series of r^ encountered from 

 these data. 



