STEPS FOR CONDUCTING AN ANOVA FOR A TWO-FACTOR FACTORIAL EXPERIMENT (PART II)

1. Create an ANOVA table for the treatments (only for the main effects)

 

2. Use the F-ratio to test the hypothesis that the treatment means are equal

 

3. Create an ANOVA table for the main and interaction effects

 

4. Use the F-ratio to test the hypothesis that the factors do not interact

5.Use the F-ratio to test the two hypotheses that the mean response is the same at each level of factor A and factor B.

 6. Compare the means (multiple comparison)

ACTIVITY

Suppose that USGA tests four different brands (A, B, C, D) of galf balls and two different clubs (driver, five-iron) in a completely randomized design. Each of the eight Brand-Club combinations (treatments) is randomly and independently assigned to four experimental units, each experimental unit consisting of a specific position in the sequence of hits by Iron Byron. The distance response is recorded for each of the 32 hits and the results are shown below.

 
Brand
Club
A
B
C
D
Driver
226.4
238.3
240.5
219.8
232.6
231.7
246.9
228.7
234.0
227.7
240.3
232.9
220.7
237.2
244.7
237.6
Five-iron
163.8
184.4
179.0
157.8
179.4
180.6
168.0
161.8
168.6
179.5
165.2
162.1
173.4
186.2
156.5
160.3

Use the following steps and Statlets window given above, to carry out ANOVA procedure to appropriate for this two-factor factorial experiment.

Next we will carry out two-way ANOVA.