therefore be rejected at least at the 5 percent significance level, and of 

 course the probability that either variance would be obtained, given that the 

 other is correct, is much less than 0,05. 



An application of the F test to the ratio of the two variances, that is, 

 1.54, with 1000 degrees of freedom for the wave pole data and 500 degrees of 

 freedom for the stereo data, yields a rejection of the hypothesis that the vari- 

 ances are from the same population at the 1 percent significance level. 



The directional spectra given in figures 11,9, 11.10, and 11.11 therefore 

 do not have gross properties which agree with independently deternained data 

 from the wave pole. If the wave pole data are assumed to be correct since in 

 the original planning the wave pole data were thought of as a primary source of 

 calibration, it must then be concluded that the directional spectra are in error, 

 Moreover, the directional spectra have negative values which is a definite 

 indication of something wrong. 



Of course, there would be one way to force the two spectra to agree. It 

 would be to assume that the estimate of the white noise error was too low ap- 

 proxinaately by a factor of 4. It would then be necessary to subtract about 

 0,0025 (ft) from each spectra estimate. The effect would be to increase the 

 size of the negative areas. Such a solution would only serve to increase the 

 error in the result due to the negative areas of the spectrum. 



Various attenapts were made to correct the results by making changes in 



the cDvariance surface and calculating their effect on the spectrum and making 



changes in the spectrum and calculating their effect on the covariance surface, 



172 



