Given the results from Problems 1 through 3,
a. at the 0.05 level of significance, is there an effect due to factor A?
b. at the 0.05 level of significance, is there an effect due to factor B?
c. at the 0.05 level of significance, is there an interaction effect?
Problem 1: Consider a two-factor factorial design with three levels for factor 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 factor A variation and the factor B variation?
b. How many degrees of freedom are there in determining 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?
Problem 2: Assume that you are working with the results from Problem 1, and SSA = 120, SSB = 110, SSE = 270, and SST = 540.
a. What is SSAB?
b. What are MSA and MSB?
c. What is MSAB?
d. What is MSE?
Problem 3: Assume that you are working with the results from Problems 1 and 2.
a. What is the value of the FSTAT test statistic for the interaction effect?
b. What is the value of the FSTAT test statistic for the factor A effect?
c. What is the value of the FSTAT test statistic for the factor B effect?
d. Form the ANOVA summary table and fill in all values in the body of the table.
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