DISCUSSION OF RESULTS 



355 



Table 8.6 shows the results of the significance tests on the slopes of the 

 various experimental and theoretical (predicted) regression lines. The 

 number of pieces of data is shown in the first column, the observed slope 

 b and theoretical slope /3 in the second and third columns, the autocorrela- 

 tion coefficient for lag of one time unit in the fourth column, and the 

 weighted mean r' as defined in (8.28) in the fifth column. In column 6 

 the effective number of independent pieces of data, j, is shown, while in 

 column 7 the value of tj^o is shown for the difference between b and /S. 

 The next column shows the value of ^_,_2, 0.5, the value for the 50 percent 

 significance level for j — 2 degrees of freedom. 



Only one of the t values turns out to be significant at the 50 percent 

 level, which means that there was a better than even chance that such 

 differences would have occurred by chance in the other cases. In the case 

 of the Colhns data at ^0 = 8°, the value of t = 1.01 would not be significant 

 at the 25 percent level; the value ^46 = 1.01 corresponds to a = 0.34, or 

 a 34 percent chance that the observed deviation |6 — /3| is of a random 

 nature, and thus not significant. 



Table 8.6. Experimental versus theoretical slopes 



From the point of view of a statistician, the results of these tests are 

 such that no significance can be attached to any of the apparent discrep- 

 ancies between theory and observation, and given reason to believe that 

 the values of /3 are theoretically sound, one could say that the results are 

 significantly positive in nature. The significance of the differences be- 

 tween the predicted and observed slopes of the regression lines for ^0 = 

 20 mrad for the independent data check of subsection 8.3.4 were tested 

 using the same method as the preceding tests, except that the six observa- 

 tions in each case were assumed to be independent. The results are 

 summarized in table 8.7 and confirm the general use of the Standard 

 Sample for do > 20 mrad. 



