J. A. Harris 75 
TABLE II. 
Tests for Linearity of Regression. 
Series 
Correlation, r, 
and 
Probable Eiror 
Correlation'Ratio, 
■q, and 
Probable Error 
Regression 
Straight Line 
Ec[uatioii 
Blakeman's 
Criterion, 
J. I ^1 
Blakeman's 
Criterion, 
Test B 

For Ovules : 
uss 
•0232 + -0083 
•0657 + ^0083 
5^4230+ ^0074 
3-720 
1-688 
DHH 
■0445 ± -0095 
•0788 + •oogs 
4^9385 + -0257 iv 
3-431 
1-151 
USDD 
•2381 + •0218 
■2978+ -0211 
3 6886 + 1001 IV 
1 1 '096 
GGD2 
•0442+ -0192 
•1276+ ^0189 
4-7224 + ^0137 w 
3-152 
1-907 
FSS 
•0209 + -0076 
•0403+ -0076 
5^5606+-0153?<; 
2^263 
•754 
HH 
•0098 ± ^005 7 
•0661 ± ^0057 
5-3600 + -0056 iv 
5^159 
1-678 
For Seeds : 
USS 
•0407 + -0083 
■0946 + -0082 
3-5870 + -0206 w 
5-182 
2-351 
DHH 
•0111 + -0095 
■0541 + -0095 
4-1521 + -0106 w 
5-573 
1-869 
USDD 
•1313 ± -0227 
■1932± ^0223 
2-1840+ -0940 m) 
8-712 
1-650 
GGD'2 
•0794+ -0191 
■1760 ± ^0187 
2-4735 + -0346 w 
4-181 
2-529 
FSS 
•0261 + ^0076 
■0499 ± ^0076 
3-0712 + -0269 if 
2-793 
-931 
HH 
•0068 + -0057 
■0953 + ^0057 
4 2119 + -0058 lu 
8-421 
2-739 
Blakeman's criterion has been applied in two ways, A and B. In the first the 
actual number of pods examined has been taken as N. In test B the number of 
seeds planted (not the weighted number) has been used in obtaining p^^j. If the 
first test be accepted as the proper one, it follows that regression cannot safely be 
regarded as linear. But there are two important points to be taken into account. 
The correlation ratio r] depends upon the squares of the differences in means, hence 
it has always a positive value, which may be very substantial because of the errors 
of sampling when the number of individuals per ai'ray is small. Thus when r 
approaches zero 77 is limited by 7), the mean values of rj for zero correlation*. 
Hence a test for linearity based on a comparison of t) with a very low value of r 
may be misleading. Again, as pointed out above, the significance of both r and t] 
should perhaps be tested on the basis of the lowest number of measurements. If 
this be done, as it is in test B, there is found very little evidence for non-linear 
regression. Certainly, one cannot possibly assert that the low values of r, which 
is seen throughout these experiments, is due to the number of ovules (seeds) per 
pod at first becoming larger and then decreasing after a maximum is reached as 
one passes from the lowest to the highest grade of seed weight. 
The results of Table I are also shown graphically in Diagram 2. Here the 
relationships for weight of seed planted and number of pods on the plant developing 
are also indicated as a basis of comparison. The values of both r,„o and r.i^g are in 
general conspicuously lower than the low values of But very few of them 
drop below the zero bar; one is forced to the conclusion that there is a distinct 
though very slight correlation between weight and ovules and between weight 
and seeds. 
* See K. Pearson, Biometril;a, Vol. viii. pp. 254 — 2.5G, 1911. 
10—2 
