368 Distribution of Correlation Coeficient in Small Samples 
Fig. 2. Mode (Antimode) and Mean Curves for ?i = 3, and for values of p from 0 to +1. 
1-C 
■9 
•8 
-I -7 
£ -6 
5 
^ -4 
■2 
7 
1 
r 
1 o 
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y 
a, 
ti 
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\b 
\c 
. 
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4 
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-1-0-9 -8 -7 "6 -5 -4 -3 -2 -1 0 0 -2 -3 -4 
Vnhie of Corrdaiioii in Sample. 
■9 1-0 
between p = -95 and p = 1-00. The curve is shown in Fig. 2, and both antimodal 
and mean hnes on the photograph of the model of the frequency surface. 
The distributions are after p= '2 very skew U-shaped frequency curves, whose 
^1, ^2 lis ^h*^ U-area of Pearson's skew curves, which, however, do not 
reproduce the antimode very closely. The ordinates are given in Table A (p. 379). 
TABLE II. Samples of Three. 
p, value of 
correlation 
in sampled 
population 
r, moan cor- 
relation of 
samp] es 
r, antimode 
of samples 
/3i 
^■2 
Number of 
positive 
correla- 
tions per 
1000 
samples 
Numberof 
negative 
correla- 
tions per 
1000 
samples 
0-0 
•0000,0000 
•000,0000 
•707,1068 
•000,0000 
1-500,0000 
500 
500 
0-1 
•0786,3836 
-•151,2541 
•704,5029 
•028,0136 
1 •532,3082 
550 
450 
0-2 
•1578,7706 
-•275,5141 
•696,5708 
•115,2406 
b632,9424 
600 
400 
0-3 
■2383,6407 
- •367,9037 
•682,9273 
•272,2374 
1-814,1763 
650 
350 
0-4 
•3208,5431 
- •435,4082 
•662,8536 
•520,5707 
2-101,1480 
700 
300 
0-5 
•4062,9889 
-•485,5321 
•635,1363 
•901,7817 
2-542,3242 
750 
250 
0-6 
•4960,0160 
-•523,8811 
•597,7313 
r500,1840 
3-236,2938 
800 
200 
0-7 
•5919,.3885 
-•553,8751 
•546,9866 
2^510,5375 
4-411,4204 
850 
150 
0-8 
•6975,5118 
-•577,9216 
•475,4818 
4^503,0667 
6-738,8238 
900 
100 
0-9 
•8204,3635 
-•597,5916 
•363,4654 
10222,6204 
13-467,2160 
950 
50 
0-95 
•8742,5455 
-•606,1358 
•268,4676 
21-078,0376 
26-340,9890 
975 
25 
1-00 
1^0000,0000 
-•613,9616 
•000,0000 
00 
00 
1,000 
