The partially complete ANOVA table given here is for a

Chapter 9, Problem 66E

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QUESTION:

The partially complete ANOVA table given here is for a two-factor factorial experiment.

a. Give the number of levels for each factor.

b. How many observations were collected for each factor level combination?

c. Complete the ANOVA table.

d. Test to determine whether the treatment means differ. Use \(\alpha\ =\ .10\).

e. Conduct the tests of factor interaction and main effects, each at the \(\alpha\ =\ .10\) level of significance. Which of the tests are warranted as part of the factorial analysis? Explain.

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QUESTION:

The partially complete ANOVA table given here is for a two-factor factorial experiment.

a. Give the number of levels for each factor.

b. How many observations were collected for each factor level combination?

c. Complete the ANOVA table.

d. Test to determine whether the treatment means differ. Use \(\alpha\ =\ .10\).

e. Conduct the tests of factor interaction and main effects, each at the \(\alpha\ =\ .10\) level of significance. Which of the tests are warranted as part of the factorial analysis? Explain.

ANSWER:

Step 1 of 5

b) The number of observations were collected for each factor level combination is  

 

c) Using the formulae shown in the general summary table of two-factor ANOVA, the missing entries are filled in as specified in the following table.

   

The degrees of freedom for AB is  

 

                          =  3

The degrees of freedom for Error is

   

    = (8)(2)

    = 16

Sum of Squares:

From the given table we have

 

We have

 

Similarly we find SSE = 2.4

   

   

   

Source

df

SS

MS

F

Treatments

7

4.1

0.5857

3.90

A

3

2.25

0.75

5.00

B

1

0.95

0.95

6.33

AB

3

0.9

0.3

2.00

Error

16

2.4

0.15

Total

23

6.5

 

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