Question

Consider the following partially completed two-way ANOVA table. Suppose there are 2 levels of Factor A and 3 levels of Factor B. The number of replications per cell is 3. Use the 0.01 significance level. (Hint: estimate the values from the F table.)

1. Complete an ANOVA table. (Round MS and F to 2 decimal places.)

SS df MS F

Factor A 100

Factor B 30

Interaction 250

Error 200

Total 580

2. Find the critical values to test for equal means. (Round your answers to 2 decimal places.)

3. Determine if there is a significant difference in Factor A means, Factor B means.

4. Determine if there is a significant difference in interaction means.

Answer 1

(a)

The ANOVA Table is completed asfollows:

Source of Variation	Sum of Squares	Degrees of freedom	Mean Square	F
Factor A	100	a - 1= 2 - 1 = 1	100/1 = 100	100/16.6667=6.00
Factor B	30	b - 1 = 3 - 1 = 2	30/2 = 15	15/16.6667=0.900
Interaction	250	(a - 1) X (b - 1) = 1 X 2 = 2	250/2 =125	125/16.6667=7.500
Error	200	ab(r-1) = 2 X 3 X 2 = 12	200/12 = 16.6667
Total	580	17

(b)

To find the critical values to test for equal means:

(i)

= 0.01

For Factor A:

Degress of freedom for numerator = 1

Degress of freedom for denominator = 12

From Table:

Critical value of F = 9.33

(ii)

= 0.01

For Factor B:

Degress of freedom for numerator = 2

Degress of freedom for denominator = 12

From Table:

Critical value of F = 6.927

(iii)

= 0.01

For Interaction:

Degress of freedom for numerator = 2

Degress of freedom for denominator = 12

From Table:

Critical value of F = 6.927

(c)

(i)

For Factor A:

Since calculated value of F = 6.00 is less than critical value of F = 9.33, there is no significant difference in Factor A means,

(ii)

For Factor B:

Since calculated value of F = 0.900 is less than critical value of F = 6.927, there is no significant difference in Factor B means,

(d)

For Interaction:

Since calculated value of F = 7.500 is greater than critical value of F = 6.927, there is a significant difference in Interaction means,