ANOVA results interpration

Question

Hi, I attached ANOVA results. What is the meaning of sum of squares and mean square? How can I interpret the ANOVA result by the meaning of sum of squares and mean square?

 

Source/ Sum of squares/ Degrees of freedom/ Mean square/ F/ p-value
A /19.29 /2 /9.64/ 331.83 /< 0.0001
B /0.60/ 2 /0.30/ 10.32 /0.0168
C /4.42 /4 /1.10 /38 /0.0006
AB/ 0.09/ 4 /0.02/ 0.77/ 0.5879
AC/ 17.18 /8/ 2.15 /73.89 /< 0.0001
BC /0.10/ 8 /0.01/ 0.42/ 0.8654

Answer 1

Hi Nima,

 

Suppose  x₁, x₂, x₃,  ........xn  are n observations.

 

Sum Of Squares = x₁² +x₂² +............+x_n^2.

 

Let Degree of Freedom = d_f

 

Mean Squares = Sum Of Squares / d_f

 

eg A) Sum Of Squares = 19.29

 

        Degree of Freedom = 2

       

         Mean Squares = 19.29/ 2 = 9.64

 

          F = 331.83

 

           p <0.0001 which is < 0.05 so ANOVA Test is Significant, Reject Null Hypothesis.

 

Similarly you can do remaining.

 

FYI: Types of ANOVA like ...One -Way ANOVA, Two-WAy ANOVA....