Question

consider a two-factor factorial design with three levels for facts a, three levels for factor b, and four replicates in each of the nine cells

a. how many degrees of freedom are there in determining the A variation and the factor B variation

b. how many degrees of freedom are there in dreaming the interaction variation

c. how many degrees of freedom are there in determining the random variation

d. how many degrees of freedom are there in determining the total variation

Answer 1

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

What is a two-factorial design?

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

Learn more about using a two-factor factorial design for determining the degree of freedom here:

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