20 On the Probable Error of a Coefficient of Correlation 
The correlation was found to be '6633 + - 0132 ; the probable error from the short 
formula was 0132. 
Illustration V. 
1196 
223 
1419 
318 
1263 
1581 
1514 
1486 
3000 
The correlation was found to be "8464 + '0079 ; the probable error from the short 
formula was '0079. 
These examples will suffice, I think, to give confidence in the formula and in 
the tables accompanying this paper. The absence of probable errors from the 
expressions for fourfold table correlations can no longer be justified on the ground 
of their great laboriousness. 
The following Tables have been calculated by Miss Julia Bell. 
Let X i = -67449/VF. This is given by Miss Gibson's Tables, Biometrika, 
Vol. in. p. 387. Let 
and = ^i(l + «) xi(l -^). 
Then Probable error of r = X\ ■ %>• • X°- s • %«*• 
TABLE I. Values of x>- for Values of r. 
r 
Xr 
r 
Xr 
r 
Xr 
r 
Xr 
r 
Xr 
■00 
1 -oooo 
■20 
•9717 
■40 
•8845 
■60 
•7298 
■80 
•4843 
■01 
•9909 
■21 
•9688 
■41 
■42 
•8785 
■61 
•7200 
■81 
•4687 
■0:2 
•9997 
■22 
•9657 
•8723 
■62 
•7099 
•82 
•4526 
■OS 
•9994 
■23 
■9625 
■43 
•8659 
•63 
■6997 
■83 
•4362 
■oh 
•9989 
■24 
•9591 
■44 
•8594 
■64 
•6892 
■84 
•4192 
■05 
•9982 
■25 
•9556 
■45 
•8527 
■65 
•6785 
•85 
•4018 
■06 
■9975 
■26 
•9520 
■46 
■8458 
■66 
•6675 
■86 
•3838 
■07 
•9966 
■27 
•9482 
■47 
•8388 
■67 
•6563 
■87 
•3652 
■08 
•9955 
•28 
•9442 
•43 
•8315 
■68 
•6448 
■88 
•3461 
■09 
•9943 
■29 
•9401 
■49 
•8241 
■69 
•6331 
■89 
•3262 
■10 
•9930 
■30 
•9358 
■50 
•8165 
•70 
•6211 
•90 
•3057 
■11 
•9915 
■31 
•9314 
•51 
•8087 
■71 
■6088 
■91 
■2843 
■12 
•9899 
■32 
•9268 
■52 
•8007 
■72 
■5962 
■92 
■2620 
■13 
•9881 
■33 
•9221 
■53 
•7926 
'73 
•5834 
■93 
•2387 
■n 
•9862 
■34 
•9172 
■54 
•7842 
■74 
•5702 
■94 
•2142 
■15 
•9841 
■35 
•9122 
■55 
•7756 
■75 
•5568 
•95 
•1882 
■16 
•9819 
■36 
•9070 
•56 
•7669 
■76 
•5430 
■96 
•1605 
■17 
■9796 
■37 
•9016 
'57 
■7579 
'77 
•5288 
■97 
•1305 
■18 
•9771 
■38 
•8961 
•58 
•7488 
•78 
•5144 
■98 
•0972 
■19 
•9745 
■39 
•8904 
■59 
•7394 
■79 
■4995 
■99 
•0585 
1-00 
•0000 
