Question

How is the total variation in the dependent variable broken down in analysis of variance? 2. What does the total sum of squares describe? What are its degrees of freedom? 3. What is the mathematical expression for the sum of squares for treatments? 4. What is the grand mean? How is it calculated? 5. What is the mean square for treatments? 6. What is the relationship between TSS, SST, and SSE? Explain why this relationship makes sense..

Answer 1

1. The total variation in the dependent variable is broken down into two components: i. Between variation (i.e. explained by the model) ii: Within variation (i.e. unexplained by the model).

2. Total sum of squares describes total variation in a sample of the dependent variable and its degrees of freedom=n-1 where,

n=total no. of observations.

3.

4. Grand mean is overall mean and it is calculated by

5.

TSS=total variation in a sample of dependent variable which is divided into two parts:

A. SST=sum of squares due to treatments=measure of the variation  in a sample of dependent variable which is explained by the model

B. SSE=sum of squares due to error=measure of the variation  in a sample of dependent variable which is unexplained by the model

and df of SST=n-1=df of SST(=t-1)+df of SSE(=n-t)

where df=degrees of freedom.

Hence this relationship makes sense.