Question

1. Complete the ANOVA summary table and answer the questions that follow.

Source SS df MS F

A 127.44 2

B .222 1

A X B 110.778 2

Within 166.00 12

Total 404.444 17

What are the F critical values for A effect, B effect, and the interaction?

Which effects are significant? Write the results statistically.

Answer #1

Ans:

SS | df | MS | F | F critical | |

A | 127.44 | 2 | 63.72 |
4.61 |
3.885 |

B | 0.222 | 1 | 0.222 |
0.02 |
4.747 |

A*B | 110.778 | 2 | 55.389 |
4.00 |
3.885 |

Within | 166 | 12 | 13.833 |
||

Total | 404.44 | 17 |

MS=SS/df

F=MS(between)/MS(within)

For A,F=63.72/13.833=4.61

For B,F=0.222/13.833=0.02

For A*B,F=55.389/13.833=4.00

Assume significance level=0.05

For,A and A*B,critical value F=FINV(0.05,2,12)=3.885

For,B,critical value F=FINV(0.05,1,12)=4.747

**Effect A and A*B are significant** as F statistic
is greater than F critical value.

Complete the ANOVA
summary table below. In addition, answer the following questions
for the ANOVA summary table.
a. What is the
factorial notation?
b. How many conditions
were in the study?
c. How many subjects
were in the study?
d. Identify
significant main effects and interaction effects.
Source
df SS MS F
A 2 40
B 3 60
A x B 6 150
Error 72
Total 83 400

6. (36 pts) The following is an incomplete
ANOVA summary table:
Source
df
SS
MS
F
Among Groups
3
63
Within Groups
16
97
Total
(a) Complete the ANOVA summary table.
(b) Determine the number of groups.
(b) At the α = 0.05 level of significance, determine whether
there is evidence of difference in the population means.

Consider the partially completed one-way ANOVA summary
table.
Source
SS
df
MS
F
Treatment
150
Error
17
Total
840
21
Using α = 0.05, the critical F-score for this ANOVA procedure
is ________.

Answer the following questions based on the summary table
below
Source
SS
df
MS
F
Subjects
850
13
Time
204
2
102
3.4
Error
780
26
30
1. How many people were in the study?
2. How many times was the dependent variable measured in each
person?
3. What should be concluded about the effect of time on the
dependent variable? Justify your answer by providing the
appropriate critical value, assuming alpha = 0.05.

ANOVA
Source of Variation
SS
df
MS
F
p-value
Factor A
31,313.49
3
10,437.83
Factor B
23,456.13
2
11,728.07
Interaction
163,204.45
6
27,200.74
Error
90,156.59
36
2,504.35
Total
308,130.66
47
(a) What kind of ANOVA is this?
One-factor ANOVA
Two-factor ANOVA with replication
Two-factor ANOVA without replication
(b) Calculate each F test statistic and the
p-value for each F test using Excel's function
=F.DIST.RT(F,DF1,DF2). (Round your
Fcalc values to 3 decimal places and
p-values to 4 decimal places.)
Source of...

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...

Complete the following ANOVA table to answer the
question
Source
df
MS
f
F CRIT
City_Size (A)
2
380
Gender (B)
1
20
AxB
70
Error
100
Total
59
The partial eta-squared due to interaction
is
A..583
B. Insufficient data. It cannot be estimated from the
data
C. .206
D. .185

10a
The following is an incomplete ANOVA table.
Source of Variation
SS
df
MS
F
Between groups
2
11.7
Within groups
Total
90
10
The value of the test statistic is
Multiple Choice
11.7
90
8.325
1.405

Fill in the rest of the table below and calculate F.
Source
SS
DF
MS
F
Between
2
35
Within
30
16
Total
100
Would the result above be significant if the critical value was
2.75?
What would eta2 be in the example above?

The results of a one-way ANOVA are reported below.
Source of variation
SS
df
MS
F
Between groups
7.18
3
2.39
21.73
Within groups
48.07
453
0.11
Total
55.25
456
How many treatments are there in the study?
What is the total sample size?
What is the critical value of F if p = 0.05?
Write out the null hypothesis and the alternate
hypothesis.
What is your decision regarding the null hypothesis?
Can we conclude any of the treatment means...

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