THE STATISTICAL STUDY OF VARIATION 
53 
moment, and the summation of all the product-moments divided by n 
is the average product-moment. 
expressed by the formula 
This measure of absolute correlation is 
dz dy) 
Av. prod.-mom. = BMY — 
n 
No. of culms per plant———> x 
Gr = 4 
Oe oe de be bireyi ody f.aty fd DS taled’s) 
, 0-1 3 3 —3| -9| 27 18 —3(—6) 
& 1-2) 28] 19) 3 50| —2| —100| 200 150 —2[-56+(—19)] 
q 
an 2-3] =1|) =106 -1[- 
2 18| 66} 20 1] 1/106 1] —106] 106 98 1[—36+(—66) +1+ 3] 
B34 1! 42] 58] 7] 1] |109 0 o| 60 | 
_ | 
as 
Zg 49 7| 59/11} 3] | 80 1 80/80 10 1(—7+114+6) 
Ey ee 
a 546 26/14] 2 | 42 2) s4) 164 36 2(14+4) 
5 Vb esis Bali | 
il | | | | : 
3 6-7] } 4] 3] | 7 3] 21) 68 30 3(4+6) 
i —_— —— — -|--— 
| 
|: 7-3 le 2 4 3 32 | 4 4(1) 
a cence aemar | | 
3-9 T | tet 5 S|) 28 | 10 5(2) 
> | — ee eal sal a 
os 134/167 38/10|1/400 mae GEE 200 seo 
Wy = —— awe ——=, 
Fz | ¥ "400 400 | 400 
| mae ella lie =—.0425 | 1.7425 | w,wy=.0184 
aie pasate —1| of 1) 2/3} Jwy= .0018 .0018 8716 
= eae aarlta 1.7407 | Sa 
ones 
fd’z|—100/—134| 0/38/20/3) 400. "|g 1.323 
= w2z= 1871 = 
.8716 
421 Tey = 
| fies (1.323) (.9303) 
farz,| 200) 134| 038/409 18h fit EI 
8654 Vn 
.6745(1 — 5013) 
ox = .9303 eile = .0168 
| sie 20 
| Try =. 708+ .017. 
Fic. 26.—Calculation of coefficient of correlation (r) for total yield of plant in grams and 
number of culms per plant for Sixty Day oats grown at Ithaca, N. Y., in 1910. 
But we cannot compare such a number as derived for instance from 
size of potatoes and starch content with size of beets and sugar content 
without reducing them to a relative basis. 
Pearson suggested the product 
of the two standard deviations as the best index of variability by which to 
divide the average product-moment so as to reduce it to a relative basis. 
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