220 EXPERIMENTAL DESIGN 



is used for computing variance, and the various parts of this calculation 

 are also included in the table. The value, Xx- — (J^x^'/n, will be called 

 the "sum of squares." 



In this experiment there are three ways of estimating the variance of 

 the population. The first is the variance s^ computed over the entire ex- 

 periment of twelve plants. The second consists of the variance within 

 each of the treatments; for example, the four S plants have a variance. 

 The third estimate is derived from the differences among the various 

 treatments, S, V, and L. Ultimately, if the variability among treatments 

 is greater than the variability which can be attributed to chance, we must 

 conclude that the treatments had some effect. 



Table 16-2. Results of a Randomized Block Experiment 



Referring to Table 16-2, an estimate of variance is obtained from the 

 individuals in each treatment. The sums of squares are pooled, or added 

 together, to yield a "total sum of squares." The variance of each treatment 

 would be 



s2 = 



^x^'-Qlxy/n 



n — 1 

 and the pooled value becomes 



the sum of the three "sums of squares" 



^ ^ (WS - 1) -f (WV - 1) + (WL - 1) 



The sum (ws — 1) + (wf — 1) + (wl — 1) is the number of degrees of 

 freedom assigned to the individuals within treatments. 



The means of the three treatments form another estimate of the popu- 

 lation variance. The variance of this distribution of means is an estimate 



