# Analysis of Variance for Response Source DF SS MS F P Regression 7 105.4375 15.0625 4.7255 0.0222

## Question:

Analysis of Variance for Response Source DF SS MS F P Regression 7 105.4375 15.0625 4.7255 0.0222 A 1 27.5625 27.5625 8.6471 0.0187 B 3 8.1875 2.7292 0.8562 0.5017 A*B 3 69.6875 23.2292 7.2876 0.0112 Error 8 25.5000 3.1875 Total 15 130.9375 FACTORB1 STATISTICS IN ACTION (continued) REVISITED M09_MCCL3396_14_GE_C09.indd 583 29/09/2021 14:36 584 CHAPTER 9 ● Design of Experiments and Analysis of Variance

a. Identify the treatments for this experiment. Calculate and plot the treatment means, using the response variable as the y-axis and the levels of factor B as the x-axis. Use the levels of factor A as plotting symbols. Do the treatment means appear to differ? Do the factors appear to interact?

b. The Minitab ANOVA printout for this experiment is shown. Sum the appropriate sums of squares and test to determine whether the treatment means differ at the a = .05 level of significance. Does the test support your visual interpretation from part a?

c. Does the result of the test in part b warrant a test for interaction between the two factors? If so, perform it using a = .05.

d. Do the results of the previous tests warrant tests of the two factor main effects? If so, perform them using a = .05.

e. Interpret the results of the tests. Do they support your visual interpretation from part a?