Chapter 13

One-way ANOVA

1.A researcher conducts an experiment comparing four treatment conditions with a separate sample of n=5 in each treatment.An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the table below.Complete all missing values in the table.


 
Source
SS
df
MS
F
Between
12
3
4
2.0
Within
32
16
2
Total
44
19

2.Use an ANOVA with a = .05 to determine whether the following data provide evidence of any significant differences among the three treatments.If significant differences are found, test the differences using Tukey’s HSD.


 
Treatment 1
Treatment 2
Treatment 3
0
4
1
2
6
0
G=30
2
1
3
0
5
1
SX2=114
1
4
0
T=5
T=20
T=5
SS=4
SS=14
SS=6

Ho: m1 = m 2 = m 3

Ha: At least one of the population means is different.


 
Source
SS
Df
MS
F
F (2, 12) = 3.88
Between
30
2
15
7.5
Reject Ho:At least 1 of the pop means is sig diff.
Within
24
12
2
Total
54
14

Tukey’s HSD = 2.38

Treatment 1 is significantly different from Treatment 2.

Treatment 2 is significantly different from Treatment 3

3.A researcher uses an analysis of variance to test for mean differences among three treatment conditions using a sample n=10 subjects in each treatment.The F-ratio from this analysis would have

a.df = 29

b.df = 2, 29

c.df = 3, 27

d.df = 2, 27

4.In general, the largest F-ratio will be obtained when the differences between sample means are __________ and the magnitudes of the sample variances are __________.

a.small, small

b.small, large

c.large, small

d.large, large

5.A research study compares three treatment conditions using a sample of n=5 in each treatment.For this study, the three sample totals are T1=5, T2=10, and T3=15.What value would be obtained for SS Between?

a.1

b.5

c.10

d.15

6.The purpose for post hoc tests is

a.to determine whether or not a Type I error was committed

b.to determine how much difference exists between the treatments

c.to determine which treatments are significantly different

d.none of the above

Chapter 15

Two-way ANOVA

1.Use a two-way ANOVA to evaluate the following data from an experimental design using n=5 subjects for each treatment condition.Use a = .05 for all tests.


 
Treatment
B1
B2

B3

A1
Mean = 1

T = 5

SS = 15
Mean = 1

T = 5

SS = 15
Mean = 4

T = 20

SS = 25
A2
Mean = 1

T = 5

SS = 15
Mean = 3

T = 15

SS = 25
Mean = 8

T = 40

SS = 25

N = 30

G = 90

SX2 = 580

Ho: mA1 = mA2 

Ha: mA1 does not equal mA2

Ho: mB1 = mB2 =mB3

Ha: At least one of the population means is different

Ho: There is not an interaction.The effects of factor A do not depend on factor B.

Ha: There is an interaction.The effects of factor A do depend on factor B.


 
Source
SS
df
MS
F
F critical
Decision
Between
190
5
A
30
1
30
6
F(1, 24) = 4.26 
Reject
B 
140
2
70
14
F(2, 24) = 3.40
Reject
Intx
20
2
10
2
F(2, 24) = 3.40
FTR
Within
120
24
5
Total
310
29

There is a main effect for factor A: Treatment A1 is significantly different from A2.

There is a main effect for factor B: At least one of the treatments is significantly different.

There is not an interaction.The effects of factor A do not depend on factor B.

2.The results from a two-factor research study with 2 levels of factor A, 3 levels of factor B, and n=5 subjects in each treatment condition were evaluated with an ANOVA.The results are summarized in the following table.Fill in all missing values.


 
Source
SS
df
MS
F
Between
35
5
A
5
1
5
2.5
B
20
2
10
5
Intx
10
2
5
2.5
Within
48
24
2
Total
83
29

3.For an experiment involving three levels of factor A and 4 levels of factor B with a sample of n = 5 in each treatment condition, what is the value for df within?

a.12

b.24

c.48

d.60

4.The results from a two-factor ANOVA show a significant main effect for factor A and a significant main effect for factor B.Based on this information, you can conclude that

a.There must be a significant interaction.

b.The interaction cannot significant

c.You cannot make any conclusion about the significance of the interaction.

5.The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no main effect for factor A?

 

B1
B2
A1
40
30
A2
30
?

a.10

b.20

c.30

d.40

6.A two-factor research study is used to evaluate the effectiveness of a new blood pressure medication.In this two-factor study, factor A is medication versus no medication and factor B is male versus female.The medicine is expected to reduce blood pressure for both males and females, but it is expected to have a much greater effect for males.This expectation should result in

a.a significant main effect for medication.

b.a significant interaction.

c.a significant main effect for gender

d.all of the above

Chapter 16

Correlation and Regression

1.For the following set of scores

 

X
Y
0
16
1
6
2
9
3
0
4
9

a.Compute the Pearson correlation.

SSx = 10 

Ssy = 134

SP = -20

r = -0.546

b.Find the regression equation for predicting Y from X.

Y = 12 – 2X

c.Calculate the standard error of the estimate.

Standard error = 6.00

2.In general, the more square-footage a person’s home has, the greater the value of the car he/she drives.This demonstrates

a.a positive correlation

b.a negative correlation

c.a curvilinear correlation

d.none of the above

3.Which of the following Pearson correlations shows the largest magnitude of relationship?

a.–0.90

b.+0.74

c.+0.85

d.–0.33

4.A correlation is computed for a sample of n=15 pairs of X and Y values.How large a correlation is necessary to be statistically significant at the .05 level assuming a two-tailed test?

a.0.468

b.0.482

c.0.497

d.0.514