Question

For the interaction to be tested in a two-factor randomized block design, it is required that which one of the following occurs?

a. both factors be fixed

b. both factors be random

c. n = 1

d. n > 1

Answer #1

Solution:

For the interaction to be tested in a two-factor randomized block design, it is required to have n > 1.

Therefore, the correct option is:

**d. n > 1**

Explanation:

In a two-factor randomized block design, we have at least two factors at various levels affecting the dependent variable. In such a design, the interaction term which represents the simultaneous effect of two or more variables on the dependent variable can be tested only if we have more than one observation for each combination of the two factors, therefore, for interaction to be tested, we need to at least two replications. Therefore, the correct option is n > 1

For the interaction to be tested in a two-factor randomized
block design, it is required that which one of the following
occurs?
a. both factors be fixed
b. both factors be random
c. n = 1
d. n > 1

A randomized block design was used to study the amount of grants
awarded to students at a large university. One block consisted of
undergraduate students and the other block consisted of graduate
students. Samples of 30 were taken from each block. Could the
combined sample of 60 be considered a simple random sample from the
population of all students, undergraduate and all graduate, at the
university? Explain.

QUESTION 1
An interaction occurs whenever
a. there is one main effect
b. there are two main effects
c. there is no main effect for either factor
d. the existence of an interaction is independent of the main
effects
QUESTION 2
In a 2 ´ 2 factorial experiment if the effect of one factor is
the same at both levels of the second factor, then
1.
there is an interaction.
2.
the experiment is confounded.
3.
there is no interaction....

Explain why interaction (in a two-way ANOVA model (fixed factor
effects) with alevels of Factor A and b
levels of Factor B and equal sample sizes) has (a
- 1)(b - 1) degrees of freedom. Use the ideas of parameter
estimation in your answer.

Complete the following ANOVA summary table for a two-factor
fixed-effects ANOVA, where there are three levels of factor A
(school) and seven levels of factor B (curriculum design). Each
cell includes 14 students. Use a significance level of α=0.05.
Source
SS
DF
MS
F
p
A
B
10902.6
AxB
15786.8
Error
197379
TOTAL
229475.3
Decision for the main effect of factor A:
reject the null H01
fail to reject the null H01
Decision for the main effect of factor...

Consider the experimental results for the following randomized
block design. Make the calculations necessary to set up the
analysis of variance table.
Treatments
A
B
C
Blocks
1
10
9
8
2
12
6
5
3
19
15
14
4
20
18
18
5
8
7
8
Use α = 0.05 to test for any significant differences.
a) Find the value of the test statistic. (Round your answer to
two decimal places.)
b) Find the p-value. (Round your answer to...

A factorial experiment involving two levels of factor A and
three levels of factor B resulted in the following data.
Factor B
Level 1
Level 2
Level 3
Factor A
Level 1
135
90
75
165
66
93
Level 2
125
127
120
95
105
136
Test for any significant main effects and any interaction. Use
α = 0.05.
Find the value of the test statistic for factor A. (Round your
answer to two decimal places.)
Find the p-value for...

Examine the following two-factor analysis of variance table
(shown below). Determine if interaction exists between factor A and
factor B. Use alpha = 0.05.
Source
SS
df
MS
F-Ratio
Factor A
162.79
4
Factor B
28.12
AB Interaction
262.31
12
Error
________
___
Total
1,298.74
84

A factorial experiment involving two levels of factor A and
three levels of factor B resulted in the following data.
Factor B
Level 1
Level 2
Level 3
Factor A
Level 1
137
88
75
167
64
93
Level 2
123
129
120
93
107
136
a) Test for any significant main effects and any interaction.
Use α = 0.05.
Find the value of the test statistic for factor A. (Round your
answer to two decimal places.)
Find the p-value...

Consider the experimental results for the following randomized
block design. Make the calculations necessary to set up the
analysis of variance table.
Treatment A B C
1 11 10 9
Blocks 2 12 6 6
3 18 16 14
4 21 18 19
5 8 8 9
Use = .05 to test for any significant differences. Show entries
to 2 decimals, if necessary. Round p-value to four decimal places.
If your answer is zero enter "0". Source of Variation Sum...

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