cxxx Tables for Statisticians and Biometricians [XXV 



The correlation is '390 and the size of the sample 19. The distribution curve 



will then be 



2/ = 2/ (l-r 2 r 5 , 



and m z = 7'5 =%(n 3), or n=I8, 



Turning to our Table XXV : 



U Q = -949,3160, B z u = - 7531, 

 w t = -955,1406, 8% = -6616, 

 6 = -21, < = '79, 00 = -02765, 

 and the use of S 4 is unnecessary. Accordingly 



u 9 = -950,5392 + -000,0594 

 = -950,5986. 



The chance is therefore 1-2 ('950,5986 - '5) = '098,8028 that a sample of 19 

 from a population of zero correlation would show a correlation numerically greater 

 than '390. Thus such a correlation will occur in samples of this size about once in 

 10 trials. 



It will be clear from the results in this illustration : 



(a) That the introduction of the observed standard deviations into the sample 

 (i.e. using pu r O-\<TZ instead of r) lessens the probability of the parent population 

 being one of zero correlation. 



(b) That very little of definite value can be learnt as to correlation from small 

 samples, i.e. in the above illustrations the sample might have been easily obtained 

 from a parent population of correlation = '00 or '45 *. 



Illustration (vi). In the long series of observations referred to in Illustration (iv) 

 the mean spans of Fathers and of Sons were 68"'67 and 69" '94 respectively. Hence 

 the regression line of Son's span on Father's span is 



y = 39"-06 + 0"-44966#. 



If y x be the value of y found in a particular sample from the regression line of 

 that sample, the standard deviation of y x 's for numerous samples is 

 v 2 /i n z\ i 9 



o ^2 I 1 P I 1 1 ^ 



r_, __ I f J I 



?/- K T -I- ~ ' 



= (3-ll) 2 (l-(-454) 2 ) f _ 2 (x-mtf ) 

 n-3 \ n + (314) 2 j 



7-678,5254 f 2 (#-68"-67) 2 ) 



~ 



9-8596 j ' 



* Inferences like these in character may easily be drawn by looking at Table XXV for n = 19 and 

 examining the entries above + -39 and below - '39 in the column with p = 0, -4 and -5. 



