Question

Case Problem A Bipartisan Agenda for Change

In a study conducted by Zogby International for the Demaocrat and Chronicile, more than 700 New Yorkrs were polled to dtermine whether the New York state government works. Respondent survyed were asked questions involving pay cuts for state legislators, restrictions on lobbyists, term limits for legislators, and whethr stat citizens should be able to put matters directly on the state ballot for a vote.The results regarding several proposed reforms had broad support, crossing all demographic and political lines.

Suppose that a follow-up survey of 100 individuals who live in the western region of New York was conducted. The party affiliation (emocrat, Independent, Republican) of each individual surveyed was recored, as well as their responses to the following three questions.

1. Should legislative pay be cut for every day the state budget is late? (Yes / No)

     2. Should there be more restrictions on lobbyists? (Yes / No)

     3. Should there be term limits requiring that legislators serve a fixed number of years? (Yes / No)

The responses were coded using 1 for a Yes response and 2 for a No response. The complete

data set is available in the file named NYReform.

Managerial Report

1. Use descriptive statistics to summarize the data from this study. What are your preliminary

conclusions about the independence of the response (Yes or No) and party

affiliation for each of the three questions in the survey?

2. With regard to question 1, test for the independence of the response (Yes and No)

and party affiliation. Use α _ .05.

3. With regard to question 2, test for the independence of the response (Yes and No)

and party affiliation. Use α _ .05.

4. With regard to question 3, test for the independence of the response (Yes and No)

and party affiliation. Use α _ .05.

5. Does it appear that there is broad support for change across all political lines? Explain.

Observation Party Pay Cut? Lobbyists? Term Limits?
1 Democrat 1 2 2
2 Democrat 1 1 2
3 Democrat 2 1 2
4 Democrat 1 2 1
5 Democrat 2 2 2
6 Democrat 2 1 1
7 Democrat 1 2 2
8 Democrat 2 1 2
9 Democrat 1 1 2
10 Democrat 1 2 1
11 Democrat 1 2 1
12 Democrat 1 2 1
13 Democrat 2 2 1
14 Democrat 1 2 1
15 Democrat 1 1 1
16 Democrat 1 2 2
17 Democrat 1 1 2
18 Democrat 1 2 1
19 Democrat 1 1 2
20 Democrat 1 1 1
21 Democrat 2 2 1
22 Democrat 1 2 2
23 Democrat 2 1 2
24 Democrat 2 1 1
25 Democrat 2 1 1
26 Democrat 1 1 1
27 Democrat 1 1 2
28 Democrat 2 1 1
29 Democrat 2 2 2
30 Democrat 1 1 2
31 Democrat 1 2 2
32 Democrat 2 1 1
33 Democrat 1 1 2
34 Democrat 2 1 1
35 Democrat 2 1 2
36 Democrat 1 1 2
37 Independent 2 2 1
38 Independent 2 2 1
39 Independent 1 1 1
40 Independent 1 1 2
41 Independent 2 1 2
42 Independent 2 2 1
43 Independent 1 1 2
44 Independent 2 1 1
45 Independent 1 1 1
46 Independent 2 1 2
47 Independent 1 1 1
48 Independent 1 1 1
49 Independent 2 1 2
50 Independent 2 2 1
51 Independent 1 1 2
52 Independent 1 1 1
53 Independent 1 1 2
54 Independent 1 1 2
55 Independent 2 1 2
56 Republican 1 1 1
57 Republican 1 2 1
58 Republican 1 1 2
59 Republican 1 1 1
60 Republican 2 1 2
61 Republican 1 1 2
62 Republican 1 1 2
63 Republican 1 1 1
64 Republican 1 1 1
65 Republican 1 1 1
66 Republican 1 1 2
67 Republican 1 1 2
68 Republican 1 2 1
69 Republican 1 2 1
70 Republican 1 1 1
71 Republican 2 2 1
72 Republican 2 1 1
73 Republican 1 1 1
74 Republican 2 2 1
75 Republican 2 1 1
76 Republican 1 2 1
77 Republican 1 2 1
78 Republican 1 1 2
79 Republican 1 1 1
80 Republican 1 1 1
81 Republican 1 2 1
82 Republican 1 2 2
83 Republican 2 1 2
84 Republican 1 1 1
85 Republican 1 1 2
86 Republican 1 1 1
87 Republican 1 1 2
88 Republican 1 1 2
89 Republican 1 1 1
90 Republican 1 1 1
91 Republican 1 1 1
92 Republican 1 1 1
93 Republican 1 1 1
94 Republican 1 1 1
95 Republican 1 1 1
96 Republican 1 2 1
97 Republican 1 1 1
98 Republican 1 1 1
99 Republican 1 2 2
100 Republican 1 1 1

Answer following questions.

a) First, we will look at potential differences in political affiliation when it comes to the topic of pay cut for late budgets. For this, look at the answers for question 1 (refers to question 1 out of 3 in the problem description) depending on the political affiliation. Specifically, fill in the following contingency table based on the data in the csv.

b) Now, we’re interested in potential differences across the three political affiliations with respect to the percentage of people answering ‘Yes’. What type of test would you run for this, and why?

c) What are the hypotheses for this test? Specify them here, and describe their meaning for this problem.

d) Conduct the test suggested in part b and c, using alpha = 0.05 and the table created in part a (note: you can create the table in Excel, save it as csv, read it into R, and run the test in R). Show the test statistic and the corresponding p-value. What is your conclusion?

e) Now, to identify which political affiliations might be different from each other, run the multiple comparison Marascuilo test. Which political affiliations differ from each other in their answers to question 1 (refers to question 1 out of 3 in the problem description)?

f) Finally, with regard to question 2 (lobbying) in the problem description, test for the independence of the response (Yes and No) and party affiliation at the level alpha = 0.05. What is your conclusion?

Answer 1

Chi square output for each question is shown below:

Chi-Square Test: CUT PAY FOR LATE BUDGET
Observed Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	22	14	36
Independent	10	9	19
Republican	39	6	45
Total	71	29	100
Expected Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	25.56	10.44	36
Independent	13.49	5.51	19
Republican	31.95	13.05	45
Total	71	29	100
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	10.18748
p-Value	0.006135
Reject the null hypothesis
Expected frequency assumption
is met.

Chi-Square Test: RESTRICTIONS ON LOBBYISTS?
Observed Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	21	15	36
Independent	15	4	19
Republican	34	11	45
Total	70	30	100
Expected Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	25.2	10.8	36
Independent	13.3	5.7	19
Republican	31.5	13.5	45
Total	70	30	100
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	3.71902
p-Value	0.155749
Do not reject the null hypothesis
Expected frequency assumption
is met.

Chi-Square Test: SUPPORT TERM LIMITS?
Observed Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	17	19	36
Independent	10	9	19
Republican	32	13	45
Total	59	41	100
Expected Frequencies
	Column variable
Row variable	Yes	No	Total
Democrat	21.24	14.76	36
Independent	11.21	7.79	19
Republican	26.55	18.45	45
Total	59	41	100
Data
Level of Significance	0.05
Number of Rows	3
Number of Columns	2
Degrees of Freedom	2
Results
Critical Value	5.991465
Chi-Square Test Statistic	5.11158
p-Value	0.077631
Do not reject the null hypothesis
Expected frequency assumption
is met.

#1: "Support Congressional Team Limits?" because for question 3, the test statistic is 5.1 (yellow line).

#2. ?² = 10.19, Reject H₀; ?² = 3.72, Fail to Reject H₀; ?² = 5.11, Fail to Reject H₀

#3 Since the proportion of each party answering "Yes" for each question is not consistent across all three political parties, it must indicate that support for the reforms is not independent of political party.

#4 The best way to compare these charts visually is to break up each political party bar into two pieces, one for "Yes" and one for "No" creating six pieces for each chart. Then compare the size of the corresponding piece on the observed side to its corresponding piece on the expected side. If the corresponding pieces are very different in size, then it indicates the variables are not independent of each other.

#5 The distribution is not applicable to any of the three chi-square tests.