122 



Pearl and Surface. 



Table 9. 



Series C. 

 Showing the number and percent of the measurements falling 

 in the several quintiles for plants starting in a given quintile. 



B^rom these tal)les it is clear that there is, in most instances, a 

 tendency for the largei- proportion of the observations to fall in or near 

 the particular quintile in -which the plant started. Tliis tendencj' is 

 to be expected on general grounds. However, it is well worth while 

 to obtain a measure of it and to study its changes in the several cases. 



In order to obtain such a measure it is necessary to consider 

 certain aspects of the theory of probability. Let us take first the 

 simplest case which is nearly realized in series C (Table 9). Here it 

 will be remembered there were 55 plants thus making 11 in each 

 quintile^). Each plant was measured 14 times, but since the plants 

 have been grouped according to the quintile in which they started, we 

 must exclude this initial measurement if we wish to preserve an analogy 

 with the conditions of simple sampling. Consequently there are for 

 consideration 13 measurements of each plant, or a total of 143 measure- 

 ments for the 11 plants stai-ting in each quintile (Tal)le 9). Now if 

 there were no influence except that of chance acting upon these corn 

 plants it is clear that the obsei-vations would tend to fall in equal 



') In one distribution of the series tliere were 12 plants in quintile IV and 1(1 iu 

 quintile V so that there is a slight irregularity in these two quintiles. 



