July 1. 1920 Universality of Field Heterogeneity 285 



The data given by Stewart are number of tubers and total weight of 

 tubers per plant. These two characters permit the determinations of 

 the average weight per tuber. 



When all the pairs are omitted which have been omitted by Stewart^ 

 or have been designated as affected by leaf roll, there remain 139 quad- 

 ruplets. Determining the correlations between the yield of the two 

 plants derived from different tubers but exposed to the same conditions 

 for growth, we have the following correlations: 



For number of tubers per hill — 



rab =o.3i8±o.o5i, r/E,= 6.19. 



^ab = -isSi .056, r/E^^^ 2.46. 



ra'b = -ssoi .054, r/E^= 4.26. 



ra'b' = .220 ± .054, r/E,= 4.04. 



For total weight of tubers per hill — 



rab = 0.457 ± 0.045, r/Er= 10.10. 



rab = •3i2± .052,r/Er= 6.00. 



rab = •427± .047, r/E^= 9.09. 



ra'b = •290± .052, r/E,= 5.53. 



For average weight of tubers — 



rab = 0.237 ± 0.054, r/Er= 4-39- 



rab' = •i04± •057»»'/£^r= 1-82. 



rab = •054± -057. ^-/^r^ -QS- 



ra'b' = •ii7± .056, r/Er= 2.07. 



The correlations are positive throughout and generally statistically 

 significant with regard to their probable errors. They show, therefore, 

 that this experimental plot was heterogeneous to an extent that influ. 

 enced in a very measurable degree the number of tubers, the total 

 weight of tubers, and the average weight of tubers of neighboring hills. 

 For all four measures of interdependence the coefficients are lowest for 

 average weight of tubers and highest for total weight of tubers, while 

 the correlations for number of tubers produced are intermediate in 

 value. 



The values of rab are consistently higher than those for ra'b', notwith- 

 standing the fact that a' and b' are more closely associated than a and 6. 

 The measures of interrelationship between the yields of pairs of plants, 

 one of which occupies an inside and the other an outside position in 

 the quadruplet, are sometimes intermediate between Vab and ra'b' and 

 sometimes less than ra'b'- On the assumption that the correlation is 

 due solely to environmental influence one would expect the highest 



' Records have been abstracted from Stewart's Table I. Prof. Stewart has kindly furnished some 

 additional information in regard to certain entries in this table. 



