CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
SCHOOL OF BUSINESS AND PUBLIC ADMINISTRATION
Department of Public Policy and Administration
PPA 415 – Research Methods in Public Administration
Exercise 6 - Answers
Question
1
2
3
4
5
Total
Analysis
4
4
12
16
4
40
Interpretation
6
6
18
24
6
60
1. Do problem 9.4 in Healey (p. 222). Do calculations by hand (10 points – 4 analysis, 6
interpretation).
9.4 CJ The city of Shinbone has implemented two separate crime prevention programs.
One involves a neighborhood watch program with citizens actively involved in crime
prevention. The second involves officers patrolling the neighborhoods on food rather
than in patrol cars. In terms of the percentage reduction in crimes reported to the police
over a one-year period, were the programs successful? The results are for random
samples of 18 neighborhoods drawn from the entire city.
Step 1: Making the Assumptions and Meeting Test Requirements
Model: Independent random samples
Interval-ratio measurement of the dependent variable.
Normally distributed populations
Equal population variances
Step 2: Stating the Null Hypothesis
H0: 1 = μ2 = μ3
H1: At least one mean is significantly different
Step 3: Selecting the Sampling Distribution and Establishing the Critical Region.
Sampling distribution = F distribution
 = 0.05
Degrees of freedom (within) = N – k = 18 – 3 = 15
Degrees of freedom (between) = k – 1 = 3 – 1 = 2
F(critical) = 3.68
Step 4: Computing the Test Statistic
Table 1. Analysis of Variance of Crime Prevention Strategy Outcomes
Anova: Single Factor
SUMMARY
Groups
Neighborhood Watch
Foot Patrol
No Program
Count
Sum
6
6
6
ANOVA
Source of Variation
Between Groups
Within Groups
SS
10208.44444
15973.33333
Total
26181.77778
Average
Variance
80 13.33333333 986.6666667
-186
-31
800
144
24
1408
df
MS
F
P-value
F crit
2 5104.222222 4.793196995 0.024573848 3.682320344
15 1064.888889
17
Step 5: Making a Decision and Interpreting the Results of the Test
F(obtained) of 4.79 is higher than F(critical) of 3.68. We can reject the null hypothesis that
the three approaches to crime reduction have the same effect on crime. The data suggest that
foot patrol has the strongest impact on reducing crime, whereas current practices have
actually coincided with an increase in crime.
2. Do problem 9.7 in Healey (p. 223). Do problem in SPSS (10 points – 4 analysis, 6
interpretation).
9.7 GER Do older citizens lose interest in politics and current affairs? A brief quiz on recent
headline stories was administered to random samples of respondents from each of four
different age groups. Is there a significant difference? The data below represent numbers of
correct responses.
Table 2. The Influence of Age on Interest in Politics
High
Young
Middle
Retired
School
Adult
Aged
(15-18)
(21-30)
(30-55)
(65+)
0
0
2
5
1
0
3
6
1
2
3
6
2
2
4
6
2
4
4
7
2
4
5
7
3
4
6
8
5
6
7
10
5
7
7
10
7
7
8
10
7
7
8
10
9
10
10
10
Step 1: Making the Assumptions and Meeting Test Requirements
Model: Independent random samples
Interval-ratio measurement of the dependent variable.
Normally distributed populations
Equal population variances
Step 2: Stating the Null Hypothesis
H0: 1 = μ2 = μ3 = μ4
H1: At least one mean is significantly different
Step 3: Selecting the Sampling Distribution and Establishing the Critical Region.
Sampling distribution = F distribution
 = 0.05
Degrees of freedom (within) = N – k = 48 – 4 = 44
Degrees of freedom (between) = k – 1 = 4 – 1 = 3
F(critical) = 2.816465827.
Step 4: Computing the Test Statistic
Table 3. Descriptive Statistics on Age and Political Interest
Descriptives
Correct res ponses on headline quiz
N
High School (15-18)
Young Adult (21-30)
Middle Aged (30-55)
Retired (65+)
Total
12
12
12
12
48
Mean
3.67
4.42
5.58
7.92
5.40
Std. Deviation
2.871
3.088
2.466
1.975
3.023
Std. Error
.829
.892
.712
.570
.436
95% Confidence Interval for
Mean
Lower Bound Upper Bound
1.84
5.49
2.45
6.38
4.02
7.15
6.66
9.17
4.52
6.27
Minimum
0
0
2
5
0
Table 4. Analysis of Variance of Age and Political Interest
ANOVA
Correct res ponses on headline quiz
Between Groups
Within Groups
Total
Sum of
Squares
124.063
305.417
429.479
df
3
44
47
Mean Square
41.354
6.941
F
5.958
Sig.
.002
Maximum
9
10
10
10
10
Mean Number of Correct responses on headline quiz
10
9
8
7
6
5
4
3
2
1
0
High School (15-18)
Young Adult (21-30)
Middle Aged (30-55)
Retired (65+)
Age level
Figure 1. Mean Political Interest by Age
Step 5: Making a Decision and Interpreting the Results of the Test
F(obtained) of 5.958 exceeds the F(critical) of 2.82. We can reject the null hypothesis
that age has no influence on political interest. The researcher anticipated that political
interest would decline with age; however, political interest appears to increase with age,
although it is difficult to determine from a cross-sectional survey whether this is an aging
or a generational effect.
3. Path-Goal Theory attempts to link leadership style to the characteristics of the
subordinate and the type of work being conducted. Generally, the theory suggests
the following patterns (30 points – 12 points analysis, 18 points interpretation).
Table 5. Path-Goal Theory: How It Works
Using the Path-Goal Leadership data set, determine whether the four leadership styles
(directive, supportive, participative, participative, and achievement oriented) vary
significantly by the type of organization (public, private, nonprofit) that the members of
the class worked for. HINT: Be sure to use the variables with the full scores and not the
ranked variables).
Step 1: Making the Assumptions and Meeting Test Requirements
Model: Independent random samples
Interval-ratio measurement of the dependent variable.
Normally distributed populations
Equal population variances
Step 2: Stating the Null Hypothesis
H0: 1 = μ2 = μ3
H1: At least one mean is significantly different
Step 3: Selecting the Sampling Distribution and Establishing the Critical Region.
Sampling distribution = F distribution
 = 0.05
Degrees of freedom (within) = N – k = 39 – 3 = 36
Degrees of freedom (between) = k – 1 = 3 – 1 = 2
F(critical) = 3.259446306
Step 4: Computing the Test Statistic
Table 6. Four Leadership Styles by Type of Organization
Descriptives
N
Directive Style
Supportive Style
Participative Style
Achievement-Oriented
Style
Public
Private
Nonprofit
Total
Public
Private
Nonprofit
Total
Public
Private
Nonprofit
Total
Public
Private
Nonprofit
Total
17
17
5
39
17
17
5
39
17
17
5
39
17
17
5
Mean
28.65
28.94
29.00
28.82
28.18
29.94
32.00
29.44
25.35
24.59
25.80
25.08
27.12
27.18
26.60
Std. Deviation
4.256
4.841
4.359
4.418
3.167
3.152
1.581
3.218
2.957
3.203
2.775
3.003
4.923
4.447
2.510
Std. Error
1.032
1.174
1.949
.707
.768
.764
.707
.515
.717
.777
1.241
.481
1.194
1.079
1.122
39
27.08
4.385
.702
95% Confidence Interval for
Mean
Lower Bound Upper Bound
26.46
30.84
26.45
31.43
23.59
34.41
27.39
30.25
26.55
29.80
28.32
31.56
30.04
33.96
28.39
30.48
23.83
26.87
22.94
26.23
22.35
29.25
24.10
26.05
24.59
29.65
24.89
29.46
23.48
29.72
25.66
Minimum
20
18
22
18
22
23
30
22
18
19
21
18
18
15
23
Maximum
35
35
33
35
34
35
34
35
29
31
28
31
35
33
29
15
35
28.50
Table 7. Analysis of Variance of Path-Goal Leadership Style by Type of Organization
ANOVA
Directive Style
Supportive Style
Participative Style
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
35
35
30
30
25
Mean of Supportive Style
Mean of Directive Style
Achievement-Oriented
Style
Sum of
Squares
.920
740.824
741.744
64.178
329.412
393.590
7.969
334.800
342.769
1.334
729.435
730.769
20
15
10
5
df
2
36
38
2
36
38
2
36
38
2
36
38
Mean Square
.460
20.578
F
.022
Sig.
.978
32.089
9.150
3.507
.041
3.985
9.300
.428
.655
.667
20.262
.033
.968
25
20
15
10
5
0
0
Public
Private
Nonprofit
Type of Organization
Figure 2. Directive Style by Type of Organization
Public
Private
Nonprofit
Type of Organization
Figure 3. Supportive Style of Organization
35
30
30
Mean of Achievement-Oriented Style
Mean of Participative Style
35
25
20
15
10
5
25
20
15
10
5
0
0
Public
Private
Nonprofit
Type of Organization
Figure 4. Participative Style by Type of Organization
Public
Private
Nonprofit
Type of Organization
Figure 5. Achievement-Oriented Style by Type of Organization
Step 5: Making a Decision and Interpreting the Results of the Test
For three of the analyses (Directive, Participative, and Achievement-Oriented Styles), Fobtained is less than F-critical (.022, .438, .033 versus 3.26). We cannot reject the null
hypothesis that type of organization has no impact on across these three leadership styles.
For the supportive style, F-obtained of 3.507 exceeds the F-critical of 3.26. We can
reject the null hypothesis that organization has no impact on supportive leadership. In
fact, students in the leadership class who served in nonprofit organizations had higher
average supportive leadership scores than private sector students. Public sector students
had the lowest averages, about 12 percent less than nonprofit students.
4. The second round of the CSUB Policy Delphi asked faculty, administrators,
students, staff, and community members to rank ten learning outcomes (critical
speaking, critical reading, ethical framework, working independently, critical
writing, technology applications to problem solving, application of discipline to realworld, critical thinking, diversity and cultural understanding, basic understanding
of a discipline [Speaking to Undertanding]) from first to tenth most important. The
most important was given a score of ten and the least important a score of one. Does
the mean ranking of each learning outcome vary significantly by the respondent’s
relationship to the university? Use the .10 level of significance (alpha). HINT: Use
the recoded relationship variable (30 points – 12 points analysis, 18 interpretation).
Step 1: Making the Assumptions and Meeting Test Requirements
Model: Independent random samples
Interval-ratio measurement of the dependent variable.
Normally distributed populations
Equal population variances
Step 2: Stating the Null Hypothesis
H0: 1 = μ2 = μ3
H1: At least one mean is significantly different
Step 3: Selecting the Sampling Distribution and Establishing the Critical Region.
Sampling distribution = F distribution
 = 0.10
Dfw (critical speaking) = N – k = 237 – 3 = 234
Dfw (critical reading) = N – k = 238 – 3 = 235
Dfw (ethical framework) = N – k = 233 – 3 = 230
Dfw (working independently) = N – k = 232 – 3 = 229
Dfw (critical writing) = N – k = 235 – 3 = 232
Dfw (technology applications to problem solving) = N – k = 237 – 3 = 234
Dfw (application of discipline to real world) = N – k = 237 – 3 = 234
Dfw (critical thinking) = N – k = 241 – 3 = 238
Dfw (diversity and cultural understanding) = N – k = 237 – 3 = 234
Dfw (basic understanding of a discipline) = N – k = 240 – 3 = 237
Dfb = k – 1 = 3 – 1 = 2
F-critical (critical speaking) = 2.325
F-critical (critical reading) = 2.325
F-critical (ethical framework) = 2.326
F-critical (working independently) = 2.326
F-critical (critical writing) = 2.326
F-critical (technology applications to problem solving) = 2.325
F-critical (application of discipline to real world) = 2.325
F-critical (critical thinking) = 2.325
F-critical (diversity and cultural understanding) = 2.325
F-critical (basic understanding of a discipline) = 2.325
Step 4: Computing the Test Statistic
Table 8. Student Learning Outcome Ranking by Role at University
Descriptives
N
Critical s peaking.
Critical reading.
Ethical framework.
Work Independently
Critical writing.
Technology applications to
problem s olving.
Application of dis cipline to
real-world.
Critical thinking.
Divers ity and cultural
understanding.
Bas ic unders tanding of a
discipline.
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
Faculty, staff, or adminis trator
Student
Alumni or community member
Total
58
118
61
237
58
119
61
238
58
114
61
233
57
115
60
232
57
119
59
235
55
121
61
237
58
118
61
237
58
120
63
241
58
119
60
237
58
120
62
240
Mean
4.88
5.42
5.95
5.42
6.81
6.18
6.57
6.43
6.38
5.32
5.89
5.73
4.42
5.01
4.27
4.67
6.25
6.18
6.17
6.20
3.36
3.64
3.97
3.66
5.43
6.52
6.41
6.22
8.76
8.23
8.22
8.36
3.71
3.97
3.00
3.66
5.00
5.15
4.98
5.07
Std. Deviation
2.541
2.684
2.533
2.628
2.131
2.466
2.239
2.337
2.621
2.652
2.409
2.610
2.291
2.799
2.524
2.623
2.132
2.361
2.245
2.269
2.189
2.221
2.429
2.269
2.555
2.819
2.710
2.755
1.848
2.028
2.413
2.099
2.656
2.911
2.636
2.799
3.340
3.020
3.257
3.149
Std. Error
.334
.247
.324
.171
.280
.226
.287
.151
.344
.248
.308
.171
.303
.261
.326
.172
.282
.216
.292
.148
.295
.202
.311
.147
.336
.259
.347
.179
.243
.185
.304
.135
.349
.267
.340
.182
.439
.276
.414
.203
Table 9. Analysis of Variance of Student Learning Outcome Rankings by Role at University
ANOVA
Critical s peaking.
Critical reading.
Ethical framework.
Work Independently
Critical writing.
Technology applications to problem s olving.
Application of dis cipline to real-world.
Critical thinking.
Divers ity and cultural unders tanding.
Bas ic unders tanding of a dis cipline.
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Between Groups
Within Groups
Total
Sum of
Squares
34.146
1595.660
1629.806
17.298
1277.126
1294.424
45.482
1534.483
1579.966
26.484
1562.619
1589.103
.196
1204.799
1204.996
10.655
1204.662
1215.316
48.703
1742.444
1791.148
12.335
1044.976
1057.311
37.434
1811.883
1849.316
1.512
2368.284
2369.796
df
2
234
236
2
235
237
2
230
232
2
229
231
2
232
234
2
234
236
2
234
236
2
238
240
2
234
236
2
237
239
Mean Square
17.073
6.819
F
2.504
Sig.
.084
8.649
5.435
1.592
.206
22.741
6.672
3.409
.035
13.242
6.824
1.941
.146
.098
5.193
.019
.981
5.327
5.148
1.035
.357
24.352
7.446
3.270
.040
6.167
4.391
1.405
.247
18.717
7.743
2.417
.091
.756
9.993
.076
.927
Step 5: Making a Decision and Interpreting the Results of the Test
For six of the analyses (critical reading, working independently, critical writing,
technology applications, critical thinking, diversity, and disciplinary understanding), Fobtained is less than F-critical (.019 to 1.942 versus 2.33). We cannot reject the null
hypothesis that role at the university has no impact on these six learning outcomes. For
four of the learning outcomes (critical speaking, ethical framework, application of
discipline to the real world, and diversity), F-obtained of 2.417 to 3.409 exceeds the Fcritical of 2.33. We can reject the null hypothesis that university role has no impact on
these four learning outcomes. In general, alumni and community members rate critical
speaking highest, whereas faculty members rate it lowest. Faculty members rate ethics
highest, and students rate it lowest. Students rate application of disciplines to the real
world highest and faculty rate it lowest. Students also rate diversity and cultural
understanding highest, while community members rate it lowest.
5. Several authors have suggested that some regions of the country are more likely to
receive disaster declarations than other regions of the country. Does the probability
of a major disaster declaration (if SBA declarations are treated as turndowns
[ActionType2]) vary significantly by FEMA region (10 points – 4 points analysis, 6
points interpretation)?
Step 1: Making the Assumptions and Meeting Test Requirements
Model: Independent random samples
Interval-ratio measurement of the dependent variable.
Normally distributed populations
Equal population variances
Step 2: Stating the Null Hypothesis
H0: 1 = μ2 = μ3 = μ4 = 5 = μ6 = μ7 = μ8 = μ9 = μ10
H1: At least one mean is significantly different
Step 3: Selecting the Sampling Distribution and Establishing the Critical Region.
Sampling distribution = F distribution
 = 0.05
Degrees of freedom (within) = N – k = 539 – 10 = 529
Degrees of freedom (between) = k – 1 = 10 – 1 = 9
F(critical) = 1.897570696.
Step 4: Computing the Test Statistic
Table 10. Disaster Declaration Rates by FEMA Region, 1953 - 1973
Descriptives
Presidential Disaster Decision (SBA as Turndowns)
N
1 Connecticut, Maine, Mas s achusetts , New Hampshire, Rhode Is land, Vermont
2 New Jersey, New York, Puerto Rico, and the Virgin Is lands
3 Delaware, Dis trict of Columbia, Maryland, Penns ylvania, Virginia and W. Virginia
4 Alabama, Florida, Georgia, Kentucky, Miss is sippi, N. Carolina, S. Carolina and Tennes see
5 Illinois , Indiana, Michigan, Minnesota, Ohio and Wisconsin
6 Arkansas, Louisiana, New Mexico, Oklahoma and Texas
7 Iowa, Kansas, Miss ouri and Nebraska
8 Colorado, Montana, N. Dakota, S. Dakota, Utah and Wyoming
9 Arizona, California, Hawaii, Nevada, American Samoa, Guam, Northern Mariana Is lands, Marshall Is lands, Micrones ia
10 Alas ka, Idaho, Oregon and Was hington
Total
23
20
43
104
72
87
52
36
66
36
539
Mean
.826
.850
.791
.548
.639
.667
.692
.639
.606
.833
.668
Std. Deviation
.3876
.3663
.4116
.5001
.4837
.4741
.4660
.4871
.4924
.3780
.4714
Table 11. ANOVA of Disaster Declaration Rates by FEMA Region, 1953 - 1973
ANOVA
Presidential Disaster Decision (SBA as Turndowns )
Between Groups
Within Groups
Total
Sum of
Squares
4.740
114.815
119.555
df
9
529
538
Mean Square
.527
.217
F
2.427
Sig.
.010
Std. Error
.0808
.0819
.0628
.0490
.0570
.0508
.0646
.0812
.0606
.0630
.0203
Mean of Presidential Disaster Decision (SBA
as Turndowns)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Connecticut,
New
Delaware,
Alabama,
Illinois,
Maine,
Jersey,
District of
Florida,
Indiana,
Massachus New York, Columbia,
Georgia,
Michigan,
etts, New Puerto Rico, Maryland,
Kentucky, Minnesota,
Hampshire,
and the
Pennsylvani Mississippi,
Ohio and
Rhode
Virgin
a, Virginia N. Carolina, Wisconsin
Island,
Islands
and W.
S. Carolina
Vermont
Virginia
and
Tennessee
Arkansas,
Louisiana,
New
Mexico,
Oklahoma
and Texas
Iowa,
Kansas,
Missouri
and
Nebraska
Colorado,
Arizona,
Montana, N. California,
Dakota, S.
Hawaii,
Dakota,
Nevada,
Utah and
American
Wyoming
Samoa,
Guam,
Northern
Mariana
Islands,
Marshall
Islands,
Micronesia
Alaska,
Idaho,
Oregon and
Washington
FEMA Region
Figure 6. Disaster Declaration Rates by FEMA Region, 1953 – 1973
Step 5: Making a Decision and Interpreting the Results of the Test
F(obtained) of 2.427 is greater than F(critical) of 1.898. We can reject the null
hypothesis that region does not influence presidential disaster decisions. Generally,
during the period 1953 to 1973, FEMA regions 1, 2, 3, and 10 had higher approval rates
(79% to 85%) and FEMA region 4 had the lowest (55%). The remaining five regions
varied from 61 to 69 percent approval, very close to the overall average of 67 percent.