Question

The results from a two-factor experiment can be presented in a matrix with the levels of one factor forming the rows and the levels of the second factor forming the columns, with a separate sample in each of the matrix cells. Demonstrate this with your own example, and describe what is meant by the main effects for each factor and the interaction between factors based on the numbers that you choose to plug in for each one of the cells.

Answer 1

Answer:-

Given That:-

The results from a two-factor experiment can be presented in a matrix with the levels of one factor forming the rows and the levels of the second factor forming the columns, with a separate sample in each of the matrix cells. Demonstrate this with your own example, and describe what is meant by the main effects for each factor and the interaction between factors based on the numbers that you choose to plug in for each one of the cells.

Main Effect of a factor : Overall difference among levels of the factor that is consistent across another levels.

Interaction of two more factors:- Differences among the lavels of one factor depend on the levels on the other factor.

Let us consider 2 - way levels for main effects and interactions :

Mean =

	factor -	A
factor-B	A=1	A=2
B=1
B=2

main effect of factor A( factor):-Difference between A1 and A2 i.e., in the same direction for both levels of B.

Main effect of factor b( factor):

Difference between B1 and B2 is in the same direction for both levels of A.

Interaction:-

The slopes of the lines are not parallel