^\V] Introduction cxxix 



We compute . : . . . - , / - . "(MOW*)) 



:mx.TH 9-7054 



= 7-213,3187, 



then the problem reduces to determining the chance that values of v will differ 

 from zero by an amount as great as or greater than this. The distribution of v in 

 given by 



VTT ( _ 1) T (J (n + 3)) ( l _^_\ 



\ n-i; 



where ?> = i -*L . 



*'"* 4 ' ' 



and <TI, (r a are the standard deviations in the parent population. The curve 

 falls under our Type (iii) above. 



We write y = . 7/n = 



We have accordingly to take 7W 8 = 11'5, and a a a = 360, which gives 

 n = 23, 



52-031,967 



~ 360 + 52-031,967 

 Hence from column for n= 23 of Table XXV we find 



UQ = -951,3679, 8 2 wo = - 11583, 5 4 w =-407, 

 wi = -958,2584, S 2 Ml = - 9804, 8 4 1 = -310, 

 6 = -628,138, <j> = -371,862, tft = '038,9301, 

 u e = -955,6961 + -000,1240 - -000,0008 

 = 955,8193. 



Thus in 884 out of 10,000 samples a v and therefore a pu numerically as large as 

 or larger than the observed product moment coefficient could have arisen from a 

 parent population without correlation. The odds are therefore only about 116 to 

 10 that p n did not arise from a population without correlation. It would occur 

 about once in 11 trials. We cannot therefore assert significance in the observed 



/hi = 3-707,41 80. 

 It is well accordingly to investigate the significance of the observed correlation. 



* This n is that of the Tables, and not the n above which is the size of the sample, the former 



/(tlir latter /< I. 



B. n. r 



