Question

A two-factor factorial design has 5 degrees of freedom for factor A variation, 3 degrees of freedom for factor B variation, 15 degrees of freedom for interaction variation, 96 degrees of freedom for random variation, and 119 degrees of freedom for total variation. Suppose also that SSA=50,SSB=60,SSAB=1,050,SSE=480, SST=1,640,MSA=10,MSB=20,MSAB=70, and MSE=5. Complete parts (a) through (d).

a. What is the value of the FsTAT test statistic for the interaction effect?
b. What is the value of the F STAT test statistic for the factor A effect? F STAT =2 (Simplify your answer.)
c. What is the value of the F STAT test statistic for the factor B effect? F STAT = (Simplify your answer.)

Answer 1

The value of the FsTAT test statistic for the interaction effect is 14. The value of the F STAT test statistic for the factor A effect is 2. The value of the F STAT test statistic for the factor B effect is 4.

Step-by-step explanation:

a. The value of the FsTAT test statistic for the interaction effect can be calculated by dividing the mean square for the interaction (MSAB) by the mean square error (MSE).

Therefore, FsTAT = MSAB/MSE = 70/5 = 14.

b. The value of the F STAT test statistic for the factor A effect can be calculated by dividing the mean square for factor A (MSA) by the mean square error (MSE).

Therefore, F STAT = MSA/MSE = 10/5 = 2.

c. The value of the F STAT test statistic for the factor B effect can be calculated by dividing the mean square for factor B (MSB) by the mean square error (MSE).

Therefore, F STAT = MSB/MSE = 20/5 = 4.