be equal, and yet the estimates obtained from the samples are not. The vari- 



■ 

 ance of the stereo data is 1.54 times the estimated variance of the wave pole 



data and 1.48 times the upper confidence bound of the estimated variance of 



the wave pole data. 



This result is not necessarily highly improbable. If the number of effective 

 degrees of freedom of the 10,800 points in the stereo data is very low due to 

 their correlation with each other, the result would be possible. Thus it is neces- 

 sary to obtain an estimate of the degrees of freedom of the estimated variances 

 of the stereo data. 



This can be done by applying a formula similar to the one used on the wave 

 pole spectrum in Part 10 except that now every fourth point is truly independent 

 and there are 16 degrees of freedom per point for each of the original spectra 

 and 32 degrees of freedom per point for the average spectrum. 



The total variance was found to have at least 800 degrees of freedom by 

 means of a computation using the average spectrum and grouping data so as al- 

 ways to decrease the computed degrees of freedom. The variances of the indi- 

 vidual data sets as a consequence have about 400 degrees of freedom. Additional 

 entries in Table 11.1 give the upper 95 percent and lower 5 percent confidence 

 bounds on the estimates of the variance based on the above degrees of freedom. 



The lower 5 percent confidence bounds for the stereo data are greater 

 than the upper 95 percent confidence bounds for the wave pole data. The hypo- 

 thesis that the wave pole data and the stereo data are samples (free from any 



sources of additional error) from, the population with the same variance must 



171 



