As the boom, shipboard, and rawinsonde temperatures were recorded by in- 

 dependent systems, the data samples were assumed to be independent, although 

 they may be correlated. It was further initially assumed that the data were 

 drawn from normally distributed populations. Plots of sample data from the 

 Oaeanographer seem to support this assumption (fig. 6). The F test was applied 

 to the null hypothesis that the sample variances in question are equally good 

 estimates of the same population, i.e., that they are not significantly dif- 

 ferent. The F statistic for sample variances can be calculated from 



(ni s 2/ (ni-D) 



F= i , 



(n2 S22/ Cn2-1]] 



or, if n-^= n2, 



F=si2/S22 , 



? 2 



where s^ and S2 are the sample estimates of the population variances for 



the two groups, n-i and n2 are the number of independent elements in the sam- 

 ples, and n^-l and n2-l are the degrees of freedom. In working with time- 

 sequenced temperature observations, one cannot assume these observations to 

 be independent of each other. Brooks and Carruthers (1953) calculated this 

 dependency or persistence by using an autocorrelation function, i.e., any 

 correlation within a series in which the correlated values are a constant 

 time interval apart. Almazan (1970) suggests the use of the sample autocor- 

 relation function R(k), where k is the lag, to obtain an estimate of the 

 number of independent observations in a sample N. This can be found by deter- 

 mining the lag k where R(k) = 0; thus. 



Number of independent observations n 



The sample autocorrelation function is given by 



n - k 



N 



1 \ 



R(k) = y (zi) . (Z(i+k)) k=0,l,2,...,M, (1) 



i = 1 

 where M is the maximum lag, and z^ and zrj+k) ^^^ '^^^ ^^" sample data points 



after normalizing by 



(Xi - X ; 



z. = 



1 



where s^^ is the sample standard deviation. 



