CALIFORNIA STATE UNIVERSITY, BAKERSFIELD
SCHOOL OF BUSINESS AND PUBLIC ADMINISTRATION
Department of Public Policy and Administration
PPA 415 – Research Methods in Public Administration
Exercise 8
Question
1
2
3
4
Total
Analysis
6
12
6
16
40
Interpretation
9
18
9
24
60
All answers must include all inferential steps in narrative form. All answers must be
presented in professional format as though being presented to an evaluation sponsor.
1. Do problem 11.5 in Healey (p. 272) – (15 points, 6 – analysis, 9 –
interpretation).
As the state director of mental health programs, you note that some local
mental health facilities have very high rates of staff turnover. You believe
that part of this problem stems from the fact that some of the local directors
have scant training in administration and poorly developed leadership skills.
Before implementing a program to address this problem, you collect some
data to make sure that your beliefs are supported by the facts. Is there a
relationship between staff turnover and the administrative experience of the
directors? Use column percentages, the maximum difference, and measures
of association to describe the strength and direction of the association. Write
a few sentences describing the relationship.
1
Table 1. Mental health staff turnover by director's level of experience
Staff Turnover * Director Experienced? Crosstabulation
Staff
Turnover
Low
Moderate
High
Total
Count
% within Director
Experienced?
Count
% within Director
Experienced?
Count
% within Director
Experienced?
Count
% within Director
Experienced?
Director Experienced?
No
Yes
4
9
Total
13
14.3%
40.9%
26.0%
9
8
17
32.1%
36.4%
34.0%
15
5
20
53.6%
22.7%
40.0%
28
22
50
100.0%
100.0%
100.0%
Assuming a random sample and nominal or ordinal measure for both variables,
Table 1 assesses the impact of mental health directors’ experience on staff
turnover. The null hypothesis suggests that experience has no effect on turnover.
However, the state director believes that directorial experience reduces staff
turnover. He evaluates the table above using the chi-square distribution with two
degrees of freedom (χ2 critical = 5.991). Chi-square obtained is 6.35 (from the
SPSS run). We can reject the null hypothesis of no difference; experience does
reduce turnover. The maximum difference is 30.9 percent, a fairly strong
relationship. If we predict using the largest category, we can reduce our error in
prediction by 13.3 percent knowing the level of experience. If we predict using
the actual distribution, we reduce our error by 6.3 percent. In general, we can
conclude that the state mental health director may well reduce turnover by
promoting local directors with more experience.
2. Do problem 11.8 in Healey (p. 273) – (30 points, 12 – analysis, 18 –
interpretation).
A researcher has conducted a survey on sexual attitudes for a sample of 317
teenagers. The respondents were asked whether they considered premarital
sex to be "always wrong" or "OK under certain circumstances." The tables
below summarize the relationship between responses to this item and several
other variables. For each table, assess the strength and pattern of the
relationship and write a paragraph interpreting these results.
2
a. Attitudes toward premarital sex by gender:
Table 2. The effect of gender on attitudes toward premarital sex
Premarital Sex * Gender Crosstabulation
Premarital
Sex
Always wrong
Not always wrong
Total
Count
% within Gender
Count
% within Gender
Count
% within Gender
Gender
Female
Male
90
105
58.1%
64.8%
65
57
41.9%
35.2%
155
162
100.0%
100.0%
Total
195
61.5%
122
38.5%
317
100.0%
α = .05.
Df = 1.
χ2 critical = 3.841.
χ2 obtained = 1.525.
λ = 0.
b. Attitudes toward premarital sex by courtship status:
Table 3. The effect of courtship status on attitudes toward premarital sex.
Premarital Sex * Ever "Gone Steady" Crosstabulation
Premarital
Sex
Always wrong
Not always wrong
Total
Count
% within Ever
"Gone Steady"
Count
% within Ever
"Gone Steady"
Count
% within Ever
"Gone Steady"
α = .05.
Df = 1.
χ2 critical = 3.841.
χ2 obtained = 53.751.
λ = .270.
3
Ever "Gone Steady"
No
Yes
148
47
Total
195
77.9%
37.0%
61.5%
42
80
122
22.1%
63.0%
38.5%
190
127
317
100.0%
100.0%
100.0%
c. Attitudes toward premarital sex by social class:
Table 4. The effect of social class on attitudes toward premarital sex.
Premarital Sex * Social Class Crosstabulation
Premarital
Sex
Always wrong
Not always wrong
Total
Count
% within Social Class
Count
% within Social Class
Count
% within Social Class
Social Class
Blue Collar White Collar
72
123
60.5%
62.1%
47
75
39.5%
37.9%
119
198
100.0%
100.0%
Total
195
61.5%
122
38.5%
317
100.0%
α = .05.
Df = 1.
χ2 critical = 3.841.
χ2 obtained = 0.082.
λ = 0.
The three analyses assume random sampling and nominal association. The
null hypotheses for three tables suggest that gender, courtship status, and
social class bear no relationship to attitudes toward premarital sex. Using chisquare and alpha=.05, the critical value is 3.841 for all three tables. Only for
courtship status can we reject the null hypothesis. If we know the courtship
status of the teenager, we can reduce the error in predicting attitudes toward
premarital sex by 27 percent over not knowing whether they have “gone
steady.” In general, teenagers who have “gone steady” have more lenient
attitudes toward premarital sex.
3. Do problem 12.5 in Healey (p. 295) – (15 points, 6 – analysis, 9 –
interpretation).
All applicants for municipal jobs in Shinbone, Kansas, are given an aptitude
test, but the test has never been evaluated to see if test scores are in any way
related to job performance. The following table reports aptitude test scores
and job performance ratings for a random sample of 75 city employees.
a. Are the two variables associated? Describe the strength and direction
of the relationship in a sentence or two.
4
Table 5. The relationship between aptitude tests and job performance in
Shinbone, Kansas
Efficiency Ratings * Test Scores Crosstabulation
Low
Efficiency
Ratings
Low
Moderate
High
Total
Count
% within Tes t Scores
Count
% within Tes t Scores
Count
% within Tes t Scores
Count
% within Tes t Scores
11
44.0%
9
36.0%
5
20.0%
25
100.0%
Tes t Scores
Moderate
6
24.0%
10
40.0%
9
36.0%
25
100.0%
High
7
28.0%
9
36.0%
9
36.0%
25
100.0%
Total
24
32.0%
28
37.3%
23
30.7%
75
100.0%
α = .05.
Z critical = 1.65.
Z obtained = 1.443.
Somer’s dyx = .147.
Assuming random sampling and ordinal measurement, Table 5 tests the
ability of Shinbone’s employment aptitude test to predict job performance.
The ordinal association model assumes no relationship (Somer’s dyx = 0).
The City of Shinbone clearly assumes that the test positively predicts
performance. For the test to be significant, Z obtained must exceed 1.65.
The Z score for the ordinal table is only 1.443. I cannot reject the null
hypothesis. The aptitude test appears to be a poor predictor of
performance. Substantively, Somer’s d suggests that we can only improve
our prediction of a positive relationship by 15 percent by knowing the
applicants score on the aptitude test.
b. Should the aptitude test continue to be administered? Why or why
not?
Given the insignificant relationship and the weak association, the current
aptitude test should be discontinued. The test is a poor predictor of
performance. The city needs to adopt or develop a more focused and valid
test of job performance for new applicants.
4. A researcher at the University of Delaware Disaster Research Center believes
that the probability of a major disaster declaration (with SBA declarations
treated as turndowns) varies by FEMA region, primary type of disaster,
intensity scale, and number of deaths (recoded to zero for no deaths and one
for one or more deaths). In particular, she is interested in four hypotheses:
a. The probability of a major disaster declaration varies across the 10
FEMA regions.
b. The probability of a major disaster declaration increases significantly
across the five levels of disaster intensity.
5
c. The probability of a major disaster declaration varies significantly
across primary type of disaster.
d. The probability of a major disaster declaration increases significantly
as the number of deaths increases.
Run the appropriate cross-tabulations to test these four hypotheses, and
prepare a one-page report (with tables) summarizing and interpreting the
results. HINT: two of the cross-tabulations involve nominal association and
two involve ordinal association. (40 points, 16 – analysis, 24 – interpretation).
Table 6. The effect of region on major disaster declarations, 1953 - 1973
Crosstab
FEMA Region
Presidential Disaster
Decis ion (SBA as
Turndowns)
.0 Turndown,
Withdrawn, SBA
1.0 Major Disaster
Total
1
Connecticut,
Maine,
Mas sachusett
s , New
Hampshire,
Rhode Island,
Vermont
4
17.4%
19
82.6%
23
100.0%
2 New
Jers ey, New
York, Puerto
Rico, and the
Virgin Is lands
3
15.0%
17
85.0%
20
100.0%
3 Delaware,
Dis trict of
Columbia,
Maryland,
Penns ylvania,
Virginia and
W. Virginia
9
20.9%
34
79.1%
43
100.0%
4 Alabama,
Florida,
Georgia,
Kentucky,
Mis sis s ippi,
N. Carolina, S.
Carolina and
Tenness ee
47
45.2%
57
54.8%
104
100.0%
5 Illinois ,
Indiana,
Michigan,
Minnesota,
Ohio and
Wis cons in
26
36.1%
46
63.9%
72
100.0%
6 Arkansas,
Louis iana,
New Mexico,
Oklahoma
and Texas
29
33.3%
58
66.7%
87
100.0%
7 Iowa,
Kansas ,
Mis souri and
Nebraska
16
30.8%
36
69.2%
52
100.0%
8 Colorado,
Montana, N.
Dakota, S.
Dakota, Utah
and Wyoming
13
36.1%
23
63.9%
36
100.0%
9 Arizona,
California,
Hawaii,
Nevada,
American
Samoa,
Guam,
Northern
Mariana
Is lands,
Marshall
Is lands,
Micronesia
26
39.4%
40
60.6%
66
100.0%
10 Alas ka,
Idaho,
Oregon and
Was hington
6
16.7%
30
83.3%
36
100.0%
Total
179
33.2%
360
66.8%
539
100.0%
α = .05.
Df = 9.
χ2 critical = 16.919.
χ2 obtained =21.370 (from SPSS).
G&K τb = .04.
Table 7. The effect of type of disaster on major disaster declarations, 1953 – 1973.
Crosstab
Presidential Disas ter
Decis ion (SBA as
Turndowns)
.0 Turndown,
Withdrawn, SBA
1.0 Major Disaster
Total
1 Earthquake
0
.0%
5
100.0%
5
100.0%
2 Winds ,
Tornadoes
and Flooding
3
10.3%
26
89.7%
29
100.0%
3 Flooding,
Storm Surge,
Tsunamis ,
Lands lides
83
25.8%
239
74.2%
322
100.0%
Primary Disas ter Type
5
4
Commercial
Winds torms ,
Failures
Hurricanes,
Caus ed by
6 Fores t Fire,
and
Climate and
Brush Fire,
Tornadoes
Environment
Wildfire, Fire
39
4
10
35.5%
66.7%
62.5%
71
2
6
64.5%
33.3%
37.5%
110
6
16
100.0%
100.0%
100.0%
α = .05.
Df = 8.
χ2 critical = 15.507.
χ2 obtained =75.214 (from SPSS).
G&K τb = .140.
6
7 Drought
10
66.7%
5
33.3%
15
100.0%
8 Snow
Storm, Ice
Storm, Winter
Weather
18
81.8%
4
18.2%
22
100.0%
9 Riots ,
Chemical
Accidents,
Explosions,
Insect
Infestations
12
85.7%
2
14.3%
14
100.0%
Total
179
33.2%
360
66.8%
539
100.0%
Table 8. The effect of disaster intensity on major disaster declarations, 1953 - 1973.
Crosstab
1
Presidential Disas ter
Decis ion (SBA as
Turndowns)
.0 Turndown,
Withdrawn, SBA
1.0 Major Disaster
Total
Intens ity Scale
3
13
11
46.4%
28.2%
15
28
53.6%
71.8%
28
39
100.0%
100.0%
2
141
34.6%
266
65.4%
407
100.0%
4
12
29.3%
29
70.7%
41
100.0%
5
2
8.3%
22
91.7%
24
100.0%
Total
179
33.2%
360
66.8%
539
100.0%
α = .05.
Z critical = 1.65.
Z obtained (from SPSS) = 1.709.
Somer’s dyx = .069.
Table 9. The effect of number of deaths on major disaster declarations, 1953 - 1973.
Crosstab
Presidential Disaster
Decis ion (SBA as
Turndowns)
.0 Turndown,
Withdrawn, SBA
1.0 Major Disaster
Total
Count
% within Number of
Deaths (Collapsed)
Count
% within Number of
Deaths (Collapsed)
Count
% within Number of
Deaths (Collapsed)
α = .05.
Z critical = 1.65.
Z obtained (from SPSS) = 7.979.
Somer’s dyx = .303.
7
Number of Deaths
(Collaps ed)
0 No deaths 1 Deaths
135
44
Total
179
47.5%
17.3%
33.2%
149
211
360
52.5%
82.7%
66.8%
284
255
539
100.0%
100.0%
100.0%
Assuming random samples and nominal association, the first two tables
test whether FEMA region or primary type of disaster significantly affect
the probability of receiving a major disaster declaration. The null
hypothesis for both tables is that no relationship exists. On the other hand,
I assume that major disaster probabilities vary significantly by region or
type of disaster. If I am willing to tolerate a five percent chance of being
wrong in my predictions, I can reject the null hypothesis in Table 6 if chisquare is greater than 16.9 and in Table 7 if chi-square is greater than 15.5.
The obtained chi-square for both tables exceeds the critical value. I can
reject the null hypothesis and assume that both region and type of disaster
have significant impacts on the probability of receiving a major disaster
declaration. Using Goodman and Kruskal’s tau b to measure the strength
of the association, I can reduce my error in predicting whether a request
receives a declaration by 6.9 percent by knowing FEMA region and by
14.0 percent by knowing type of disaster over simply guessing randomly
that 67 percent receive major disasters and 33 percent are refused.
Substantively, regions 1, 2, 3, and 10 have unusually high rates of
approval (northeast, mid-Atlantic, Pacific Northwest) and region 4 has a
low rate approval (south). Similarly, earthquakes, WTF (wind, tornado,
and flood combination), flooding, and windstorms all have greater than 50
percent probability of receiving a declaration whereas the other five types
have considerable less than 50 percent.
Assuming random samples and ordinal association, the second two tables
test whether disaster intensity and reported deaths have a significant effect
on the probability of a major disaster declaration. The null hypothesis
assumes that no association exists (positive and negative pairs are equal).
The research hypotheses are both one-tailed: increases in intensity and/or
deaths increases the probability of a major disaster declaration. For Tables
8 and 9, this translates into a Z(critical) of 1.65. Z(obtained) for Table 8 is
1.70; Z(obtained) for Table 9 is 7.979. I can reject the null hypothesis for
both tables: intensity and number of deaths are both positively related to
the probability of a major disaster declaration. The Somer’s d coefficients
for both tables suggest that disaster intensity reduces the error in
predicting a positive relationship by about 7 percent, and number of deaths
reduces the error in predicting a positive relationship by about 30 percent.
8