11.1.
While a t test is used to compare two means, the one-way ANOVA can be used to
simultaneously compare ____ groups.
11.2.
An ANOV A is considered to be an extension of the t test for independent samples
because both investigate differences between ______.
11.3.
By conducting a one-way ANOVA test to compare multiple (more than 2) group
means simultaneously instead of conducting a series of t tests to compare these
means, the potential level of ____ is reduced.
11.4. In order to apply the ANOV A test, the data should be measured on a(n)
_____ or ______scale .
•
11.5.
The one-way ANOV A is used when there is/are ____
independent variable(s).
11.6. With 3 groups, the null hypothesis (Ho) in ANOVA is: __________.
11.7. The total (or grand) mean in ANOV A can be thought of as the mean of ____.
11.8. The SSw (within-groups sum of squares) and the SSg (between-groups
sum of squares) are equal to the
sum of squares.
11.9. To find the MSg, we divide the SSg by _________.
11.10. To compute the F ratio, we divide the ______ mean square by the
_________ mean square.
11.11. Factorial ANOVA is commonly used when there are at least ______ independent
variables.
Circle the correct answer:
11.12. The following is an example of a(n) null/alternative hypothesis in ANOVA:
Mean one does not equal mean 2 and/or mean one does not equal mean 2 and/or
mean 2 does not equal mean 3
11.13. Post hoc comparisons should be conducted in cases where the F ratio is/is not
statistically significant.
11.14. The F ratio is likely to be statistically significant when the differences between
the group means are small/large.
.
11.15. The F ratio is more likely to be statistically significant when it is used to
analyze scores from groups that are homogenous/heterogeneous in regard to the
characteristic or behavior being measured.
11.16. An ANOVA procedure is used to analyze data from a study comparing scores of
three groups. Following are the obtained mean squares and the appropriate critical
values for the F ratio at p=.05 and p=.01
Fcrit(.05,2,20) = 3.49 and Fcrit(.O1,2,20) = 5.85
a.
b.
c.
Compute the obtained F ratio.
Determine whether the results are statistically significant.
Report your conclusions.
11.17. Three different age groups of consumers (ages 18-25, 26-35, 36-45) in two different
regions of the country (Midwest, South) were surveyed about their likelihood of
buying a new product. Following are the means and standard deviations obtained by
the three age groups in each of the two regions:
Means
Standard Deviations
Ages
Ages
Ages
Ages
Ages
Ages
Region
18-25
26-35
36-45
18-25
26-35
Midwest
50.2
52.8
53.3
2.5
3.1
3645
2.7
South
41.0
48.5
55.9
2.7
3.2
2.8
Two separate one-way ANOVA procedures are conducted to test whether the
differences between the three means of the three age groups in each of the two
regions are statistically significant. Estimate which F ratio would be larger: The one
resulting from analyzing the survey results obtained from the three age groups in the
Midwest or the one from analyzing the survey results obtained by the three age
groups in the South explain your answer.
11.18. Three statistics classes at University A took the same test as did 3 other statistics
classes at College B. Following are the means and standard deviations of the 3
classes in each of the two schools:
Means
SCHOOL
Standard Deviations
Stats
Stats
Stats
Stats
Stats
Stats
Class I
Class 2
Class 3
Class I
Class 2
Class 3
University A
71.4
78.8
90.2
3.2
4.3
4.8
College B
72.1
78.6
89.3
9.3
6.6
8.7
Two separate one-way ANOVA procedures are used to test whether the differences
between the means in each of the two schools are statistically significant. Estimate
which F ratio would be larger: the one resulting from analyzing the test scores
obtained by the three groups at University A or the one resulting from analyzing the
test scores of the three groups at College B. Explain your answer.
11.19. Each of the two figures below (Figure A and Figure B) depicts a set of 3
distributions. Two separate one-way AN OVA analyses are performed to test
whether there are statistically significant differences between the three means in
each set and two F ratios are computed. Estimate which of the two F ratios is likely
to be higher and explain your answer.
11.20. In a study comparing means of 4 groups, the F ratio was significant at the p<.05 level. The 4
means are Mean 1=13.12; Mean 2=9.31; Mean 3=13.65; and Mean 4=11.34. Tukey's post
hoc comparison is used to test which means statistically differ from each other. The
obtained HSD value at the p=.05 level is 3.74. Which means are statistically significantly
different from each other? Explain.
11.21. A pilot-test marketing research study comparing two new models of widgets was conducted
in two companies (Company A and Company B). In each of the two companies, one
manufacturing plant used one new widget and the other plant used the other new widget. At
the end of the year, the employees using the new widgets in their jobs completed a
questionnaire assessing their satisfaction with the widgets. Following is a table listing the
mean scores of the two plants questionnaire scores for each of the two companies (those that
used new widget 1 and those that used new widget 2). Study the data in the table. (Note: Do
not attempt to compute the F ratios or the exact level of significance in order to answer the
questions below.)
Means of
Means of
Employees Using
Employees Using
Widget 1
Widget 2
Company A
55
53
Company B
50
48
Company
a. Are there differences in questionnaire scores as a result of the using the two
widgets? Explain.
b. Are there differences in questionnaire scores between the two companies?
Explain.