376 Prof. Karl Pearson on Testing the 



The "theoretical"''' tables in this case are those with 

 independent variates, i. e., 



(i.) 



483373 



19-6627 



68 



10-6627 



4-3373 



15 



(ii.) 



59 



24 



83 



385-018 



233982 



619 



236-982 



144-018 



381 



622 



378 



1000 



The % 2 are 



(i.) % 2 = -7080, 



(ii.) % 2 = 133-3265. 



The reciprocals o£ ns are to be found from the " theo- 

 retical " tables. But if we have a fourfold table : 



a-\-b 



c-\-d 



a+c b+d 



a little consideration shows that 



8 



\n s J (a + 



W 



b)(c + d)(a + c)(b + dy 



if the condition oi zero contingency be satisfied. 

 Hence we Hnd 



^ = sQ-) = -395,8866 for (i.), 

 = '018,0344 for (ii.) ; 

 2(? — 1) = 6 for both ; 



2-^^ = -096,3855 for (i.), 



= -008 for (ii.). 

 Accordingly, 



<r x » = J 6-492,2721}* = 2*5480 for (i ), 



= {6-026,0344}*= 2-4548 for (ii.). 



It is clear that a 2 depends chiefly on the term 2(q— 1) — 6, 

 and will be generally for fourfold tables very near 



V6 = 2-4495. 

 Thus we have 



% 2 = -7080 + 1-7186 for (i.), 



X 2 = 133-3265+1-6557 for (ii.); 



