BTM8106-8-3 Jackson, Even-Numbered Chapter Exercises
Exercises covering statistical and research methods in business.
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BTM8106-8-3 1
BTM8106-8-3 JACKSON, EVEN-NUMBERED CHAPTER EXERCISES, PP. 308-310.
2. What is the difference between a randomized ANOVA and a repeated measures ANOVA?
What does the term one-way mean with respect to an ANOVA?
A one-way randomized ANOVA is an inferential statistical test used to compare the
means of three or more groups using a between-subjects design and one independent variable
(Jackson, 2012). A one-way repeated measures ANOVA is an inferential statistical test that
compares the means of three or more groups using a correlated groups design and one
independent variable (Jackson, 2012): a test to detect any overall differences between related
means. The participants are either the same individuals tested on three or more occasions on the
same dependent variable or the same individuals tested under three or more different conditions
on the same dependent variable (Laerd, 2015). However, randomized ANOVA’s indicate that
subjects are randomly assigned to conditions (Jackson, 2012).
The one-way ANOVA compares the means between the groups and determines whether
any of those means are significantly different from each other. Specifically, it tests the null
hypothesis. The one-way ANOVA cannot tell which specific groups were significantly different
from each other, only that at least two groups were (Laerd, 2015).
4. If a researcher decides to use multiple comparisons in a study with three conditions, what is
the probability of a Type I error across these comparisons? Use the Bonferroni adjustment to
determine the suggested alpha level.
The formula 1 - (1 - .05) / 3 is used to determine the probability of a Type I error when
making multiple comparisons: there is a 14% chance of a Type I error. Using the Bonferroni
adjustment, the suggested alpha level is .05 / 3. The suggested alpha level is .017.
6. When should post hoc comparisons be performed?
Post hoc tests should be performed when there are three or more groups being compared,
and the F-ratio is significant (Jackson, 2012). Post-hoc tests are used to control the error rate
BTM8106-8-3 JACKSON, EVEN-NUMBERED CHAPTER EXERCISES, PP. 308-310.
2. What is the difference between a randomized ANOVA and a repeated measures ANOVA?
What does the term one-way mean with respect to an ANOVA?
A one-way randomized ANOVA is an inferential statistical test used to compare the
means of three or more groups using a between-subjects design and one independent variable
(Jackson, 2012). A one-way repeated measures ANOVA is an inferential statistical test that
compares the means of three or more groups using a correlated groups design and one
independent variable (Jackson, 2012): a test to detect any overall differences between related
means. The participants are either the same individuals tested on three or more occasions on the
same dependent variable or the same individuals tested under three or more different conditions
on the same dependent variable (Laerd, 2015). However, randomized ANOVA’s indicate that
subjects are randomly assigned to conditions (Jackson, 2012).
The one-way ANOVA compares the means between the groups and determines whether
any of those means are significantly different from each other. Specifically, it tests the null
hypothesis. The one-way ANOVA cannot tell which specific groups were significantly different
from each other, only that at least two groups were (Laerd, 2015).
4. If a researcher decides to use multiple comparisons in a study with three conditions, what is
the probability of a Type I error across these comparisons? Use the Bonferroni adjustment to
determine the suggested alpha level.
The formula 1 - (1 - .05) / 3 is used to determine the probability of a Type I error when
making multiple comparisons: there is a 14% chance of a Type I error. Using the Bonferroni
adjustment, the suggested alpha level is .05 / 3. The suggested alpha level is .017.
6. When should post hoc comparisons be performed?
Post hoc tests should be performed when there are three or more groups being compared,
and the F-ratio is significant (Jackson, 2012). Post-hoc tests are used to control the error rate
BTM8106-8-3 2
(alpha = 0.05), similarly the one-way ANOVA’s are used, and usually after the study has been
conducted.
8. Why is a repeated measures ANOVA statistically more powerful than a randomized
ANOVA?
When the same participants are used in all conditions, their individual differences; factors
contributing to error variance, are removed. Because error variance represents the denominator in
the F-ratio, a smaller number is used in dividing and the answer results in a larger final F-ratio
(Jackson, 2012). Therefore, repeated-measures ANOVA’s are more sensitive to negligible
differences between groups than randomized ANOVA’s (Jackson, 2012).
10. In a study of the effects of stress on illness, a researcher tallied the number of colds people
contracted during a 6-month period as a function of the amount of stress they reported during
that same time period. There were three stress levels: minimum, moderate, and high stress.
The sums of squares appear in the following ANOVA summary table. The mean for ach
condition and the number of subjects per condition are also noted.
Source df SS MS F
Between groups 22.167
Within groups 14.750
Total 36.917
Stress Level Mean N
Minimal 3 4
Moderate 4 4
High 6 4
10a. Complete the ANOVA summary table.
Source df SS MS F
Between groups 2 22.167 11.08 6.76
Within groups 9 14.750 1.64
Total 11 36.917
10b. Is Fobt significant at α = .05; at α = .01?
Yes, F (2, 9) = 6.76, p < .05.
(alpha = 0.05), similarly the one-way ANOVA’s are used, and usually after the study has been
conducted.
8. Why is a repeated measures ANOVA statistically more powerful than a randomized
ANOVA?
When the same participants are used in all conditions, their individual differences; factors
contributing to error variance, are removed. Because error variance represents the denominator in
the F-ratio, a smaller number is used in dividing and the answer results in a larger final F-ratio
(Jackson, 2012). Therefore, repeated-measures ANOVA’s are more sensitive to negligible
differences between groups than randomized ANOVA’s (Jackson, 2012).
10. In a study of the effects of stress on illness, a researcher tallied the number of colds people
contracted during a 6-month period as a function of the amount of stress they reported during
that same time period. There were three stress levels: minimum, moderate, and high stress.
The sums of squares appear in the following ANOVA summary table. The mean for ach
condition and the number of subjects per condition are also noted.
Source df SS MS F
Between groups 22.167
Within groups 14.750
Total 36.917
Stress Level Mean N
Minimal 3 4
Moderate 4 4
High 6 4
10a. Complete the ANOVA summary table.
Source df SS MS F
Between groups 2 22.167 11.08 6.76
Within groups 9 14.750 1.64
Total 11 36.917
10b. Is Fobt significant at α = .05; at α = .01?
Yes, F (2, 9) = 6.76, p < .05.
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University
Northcentral University
Subject
Business Management