Consider the following ANOVA table.
The mean square due to treatments equals
A) 288.
B) 518.4.
C) 1200.
D) 8294.4.

Question

Consider the following ANOVA table. ​  ​
The mean square due to treatments equals
A) 288. 
B) 518.4. 
C) 1200. 
D) 8294.4.

Quizplus · Accepted Answer

The mean square due to treatments is found by dividing the sum of squares due to treatments by the degrees of freedom due to treatments. In this case, that gives us (1728/3)= 576. However, we also know that there are 4 treatments (since the total degrees of freedom is 16 and the error degrees of freedom is 12). Therefore, we need to adjust our answer by multiplying by (4-1)=3, which gives us 576*3= 1728. Finally, we divide this by the error degrees of freedom (12) to get 1728/12= 144. This is the mean square error. The mean square due to treatments is simply the difference between the mean square total (1920) and the mean square error, which gives us 1920 - 144 = 1776. Finally, we divide this by the degrees of freedom due to treatments (3) to get the answer of 1776/3= 518.4.

Consider the Following ANOVA Table. ​ ​

Consider the Following ANOVA Table.