372 Distribution of Correlation Coefficient in Small Sam2)les 
TABLE V. Values of the Freq^uency Constants for the Correlation in 
Samples of 50. 
p 
V 
Actual T 
r from 
Pearson's 
formula* 
Actual a 
^ P 
Vn - 1 
Pi 
P-2 
00 
0 
0 
0 
•142,857 
•142,857 
0 
2-88236 
01 
•098,995 
•1054 
•1053 
•141,505 
•141,429 
•00666 
2-89184 
0-2 
•198,047 
•2104 
•2102 
•137,439 
•137,143 
•02683 
2^93350 
0-3 
•297,218 
•3147 
•3144 
•130,634 
•130,000 
•06107 
2^99909 
0-4 
•396,565 
•4180 
•4177 
•121,049 
•120,000 
•11041 
309417 
0-5 
•496,150 
•5198 
•5196 
•108,620 
•107,143 
•17635 
322240 
0-6 
•596,038 
•6201 
•6199 
•093,260 
•091,429 
•26110 
3 38912 
0-7 
•696,295 
•7184 
•7183 
•074,878 
■072,857 
•36774 
3 60222 
0-8 
•796,989 
•8146 
•8146 
•053,324 
•051,429 
•50037 
3^87312 
0-9 
■898.198 
•9085 
•9085 
•028,434 
•027,143 
•66608 
4^22186 
10 
1 
1 
1 
0 
0 
00 
00 
TABLE VL Values of the Frequency Constants for the Correlation in 
Samples of 100. 
p 
/• 
mean 
Actual f 
mode 
f from 
Pearson's 
formula* 
Actual cr 
1 - p2 
Vn - 1 
^1 
P-2 
00 
0 
0 
0 
■100,5038 
•100,5038 
0 
2^94060 
01 
•099,5016 
•10258 
•10255 
•099,5260 
•099,4987 
•00346 
2^94736 
02 
•199,0319 
•20499 
•20494 
•096,5887 
•096,4836 
•01390 
2^96774 
0-3 
•298,6219 
•30708 
•30701 
•091,6832 
•091,4584 
•03147 
300213 
0^4 
•398,3013 
•40868 
•40860 
•084,7934 
•084,4232 
•05644 
3^05118 
05 
•498,1002 
•50964 
•50957 
•075,8968 
•075,3778 
•08919 
311583 
06 
•598,0498 
•60982 
•60976 
•064,9640 
•064,3224 
•13025 
3 19739 
0^7 
•698,1815 
•70907 
•70903 
•051,9577 
•051,2569 
•18031 
3^29767 
0^8 
•798,5279 
•80726 
■80724 
•036,8329 
•036,1814 
•24027 
3^41896 
0^9 
•899,1225 
•90427 
•90423 
•019,5352 
•019,0957 
•31148 
3^57898 
10 
1 
1 
1 
0 
00 
00 
TABLE VIL Values of the Frequency Constants for the Correlation in 
Samples of 400. 
p 
r 
mean 
Actual r 
mode 
?■ from 
Pearson's 
formula* 
Actual (7 
I- 
Vn - 1 
Pi 
^2 
0-0 
0 
0 
0 
■0500,626 
•0500,626 
0 
2^9850 
0^1 
•0998,760 
•1006,250 
•1006,232 
■0495,654 
■0495,620 
•00089 
2^9868 
0^2 
•1997,595 
•2012,116 
•2012,082 
•0480,733 
•0480,601 
•00357 
29921 
03 
•2996,579 
•3017,217 
•3017,171 
•0455,851 
•0455,570 
•00804 
30010 
0-4 
•3995,788 
•4021,171 
•4021,115 
■0420,988 
•0420,526 
•01433 
3^0138 
0^5 
•4995,297 
•5023,602 
•5023,584 
•0376,115 
•0375,470 
•02250 
3^0297 
0-6 
•5995,181 
•6024,134 
•6024,089 
■0321,195 
•0320,401 
•03245 
3-0498 
0^7 
•6995,517 
•7022,401 
■7022,386 
■0256,183 
•0255,319 
•04435 
30725 
0^8 
•7996,380 
•8018,037 
■8018,013 
•0181,023 
•0180,255 
•05820 
3-1017 
0^9 
•8997,849 
■9010,725 
•9010,668 
•0095,653 
•0095,119 
•07402 
3-1342 
1^0 
1 
1 
1 
0 
0 
00 
00 
* r-=f+ /J., (/3, + 3)/{mo (lOft - 12/3i - 18)}. 
