Chapter 7: Tables
1.
a.
0.406
b.
0.046
c.
0.125
d.
0.019
a.
7.779
b.
9.488
c.
16.919
d.
21.666
2.
3.
False. The χ2 test only measures the significance of the association, not the degree of the association.
4.
The p-value from the test is 0.041576 which would cause us to reject the hypothesis that this data comes
from a fair die.
5.
The Pearson Chi-Square test assumes nominal data and thus is not as powerful when testing ordinal data.
To test ordinal data you should use a test like the Goodman-Kruskal Gamma, Kendall's tau-b, Stuarts tau-c,
and Somers' D.
6.
a.
The pivot table appears as:
Count of Dept
Dept
Percentage of Dept
Total
Dept
Total
Bus,Econ
91
Bus,Econ
HealthSc
25
HealthSc
26.38%
7.25%
MathSci
128
MathSci
37.10%
Soc Sci
101
Soc Sci
Grand Total
345
Grand Total
29.28%
100.00%
1
Chapter 7: Tables
The pie chart and bar chart appear as:
b.
Total
Count of Dept
Bus,Econ
26%
Soc Sci
29%
Dept
Bus,Econ
HealthSc
MathSci
Soc Sci
HealthSc
7%
MathSci
38%
Total
140
Count of Dept
120
100
80
Total
128
60
101
91
40
20
25
0
Bus,Econ
HealthSc
MathSci
Soc Sci
Dept
The bar chart gives the best indication of comparative group size. The pie chart is better for
comparing the size of each group to the whole.
c.
The initial pivot table appear as:
Computer
Not req
Prereq
Grand Total
PC
106
18
124
Mac
16
7
23
Main
43
12
55
Mini
Grand Total
3
1
4
168
38
206
2
Chapter 7: Tables
However since the Mini category contains sparse data, we'll combine the Main and Mini
categories as follows:
Not req
Observed Counts
Prereq
PC
106
Mac
16
18
7
Main/Mini
46
13
The test statistics for the table are:
Not req
Expected Counts
Prereq
PC
101.13
Mac
18.76
22.87
4.24
Main/Mini
48.12
10.88
Not req
Std. Residuals
Prereq
PC
0.48
-1.02
Mac
-0.64
1.34
Main/Mini
-0.31
0.64
Value
Test Statistics
df
p-value
Pearson Chi-Square
3.975
2
0.137
Continuity Adjusted Chi-Square
2.793
2
0.248
Likelihood Ratio Chi-Square
3.756
2
0.153
Value
Measures of Association
Std. Error
p-value
Phi
0.139
Contigency
0.138
Cramer's V
0.139
Goodman-Kruskal Gamma
0.236
0.144
0.101
Kendalls tau-b
0.104
0.068
0.125
Stuart's tau-c
0.084
0.055
0.129
Somer's D (C|R)
0.077
0.051
0.129
Somer's D (R|C)
0.139
0.091
0.123
The Pearson Chi-Square does not indicate a significant relationship at the 5% level. There is a
hint of a relationship since 18.4% of the calculus prerequisite classes (7 of 38) use the Macintosh,
but only about 9.5% (16 of 168) of the other classes use the Macintosh. Perhaps a larger sample
would show significance. In any case, it would not be appropriate to declare that Computer and
Calculus are independent. There is not sufficient evidence to indicate a definitive relationship.
d.
The pivot table of enrollment versus computer type appears as follows:
Count of Computer
Computer Group
Enrollment
PC's
Non PC's
Grand Total
001-050
15
21
36
051-100
27
18
45
101-150
16
11
27
151-200
16
8
24
201-500
28
11
39
501-
18
8
26
120
77
197
Grand Total
3
Chapter 7: Tables
The table statistics are:
PC's
Expected Counts
Non PC's
001-050
21.93
14.07
051-100
27.41
17.59
101-150
16.45
10.55
151-200
14.62
9.38
201-500
23.76
15.24
501-
15.84
10.16
PC's
Std. Residuals
Non PC's
001-050
-1.48
1.85
051-100
-0.08
0.10
101-150
-0.11
0.14
151-200
0.36
-0.45
201-500
0.87
-1.09
501-
0.54
-0.68
Value
Test Statistics
df
p-value
Pearson Chi-Square
8.677
5
0.123
Continuity Adjusted Chi-Square
6.914
5
0.227
Likelihood Ratio Chi-Square
8.617
5
0.125
Value
Measures of Association
Std. Error
Phi
0.210
Contigency
0.205
Cramer's V
p-value
0.210
Goodman-Kruskal Gamma
-0.264
0.097
0.006
Kendalls tau-b
-0.167
0.062
0.007
Stuart's tau-c
-0.209
0.078
0.007
Somer's D (C|R)
-0.127
0.047
0.007
Somer's D (R|C)
-0.220
0.081
0.007
The ordinal tests are all statisticall significant, indicating that a relationship between enrollment
and computer type exists. As the enrollment increases, it is more likely that the course uses a PC
rather than a non-PC computer. However this could be due to other factors besides class size.
More advanced classes tend to be smaller and might therefore be using non-PC computers (such
as mainframes and workstations.)
7.
a.
Use the Sort command on the Excel menu bar.
b.
The pivot table appears as:
Rank Hired
F
M
Grand Total
instructor
20
17
37
asst prof
17
15
32
assoc prof
0
9
9
full prof
0
3
3
37
44
81
Grand Total
4
Chapter 7: Tables
c.
The table statistics are:
Expected Counts
F
M
instructor
16.90
20.10
asst prof
14.62
17.38
assoc prof
4.11
4.89
full prof
1.37
1.63
Std. Residuals
F
M
instructor
0.75
-0.69
asst prof
0.62
-0.57
assoc prof
-2.03
1.86
full prof
-1.17
1.07
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Measures of Association
Value
df
p-value
11.852
3
0.008
8.039
3
0.045
16.398
3
0.001
Value
Std. Error
p-value
Phi
0.383
Contigency
0.357
Cramer's V
0.383
Goodman-Kruskal Gamma
0.440
0.160
0.006
Kendalls tau-b
0.250
0.095
0.009
Stuart's tau-c
0.277
0.109
0.011
Somer's D (C|R)
0.223
0.083
0.007
Somer's D (R|C)
0.279
0.110
0.011
Warning: More than 1/5 of Fitted Cells are Sparse
Because the rank hired data is ordinal, we should use one of the ordinal statistics. However some
of the table cells are sparse, leaving some question as to the validity of the statistical results. We
should either remove some of the sparse cells or combine them.
5
Chapter 7: Tables
d.
The revised table appears as:
Observed Counts
F
M
Instructors
20
17
asst prof
17
15
0
12
Full and Assoc
The table statistics are:
Expected Counts
F
M
Instructors
16.90
20.10
asst prof
14.62
17.38
5.48
6.52
Full and Assoc
Std. Residuals
Instructors
asst prof
Full and Assoc
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Measures of Association
F
M
0.75
-0.69
0.62
-0.57
-2.34
2.15
Value
df
p-value
11.852
2
0.003
9.516
2
0.009
16.398
2
0.000
Value
Std. Error
p-value
Phi
0.383
Contigency
0.357
Cramer's V
0.383
Goodman-Kruskal Gamma
0.440
0.160
0.006
Kendalls tau-b
0.251
0.097
0.009
Stuart's tau-c
0.277
0.109
0.011
Somer's D (C|R)
0.226
0.085
0.008
Somer's D (R|C)
0.279
0.110
0.011
Once again, the table statistics indicate a relationship between rank hired and gender. This time
there is no problem with sparse cells.
6
Chapter 7: Tables
e.
Grouping the data into professors and non-professors yields:
Observed Counts
F
M
Instructors
20
17
Professors
17
27
The table statistics are:
Expected Counts
F
M
Instructors
16.90
20.10
Professors
20.10
23.90
Std. Residuals
F
M
Instructors
0.75
-0.69
Professors
-0.69
0.63
Test Statistics
Value
df
p-value
Pearson Chi-Square
1.925
1
0.165
Continuity Adjusted Chi-Square
1.354
1
0.245
Likelihood Ratio Chi-Square
1.931
1
0.165
Measures of Association
Value
Std. Error
p-value
Phi
0.154
Contigency
0.152
Cramer's V
0.154
Goodman-Kruskal Gamma
0.303
0.205
0.141
Kendalls tau-b
0.154
0.110
0.161
Stuart's tau-c
0.153
0.109
0.161
Somer's D (C|R)
0.154
0.110
0.161
Somer's D (R|C)
0.154
0.110
0.161
After grouping the Rank Hired variable this way, the relationship between rank and gender is no
longer significant. The three p-values for the ordinal statistics are now 0.14, 0.16, and 0.16, so we
can no longer reject the null hypothesis at the 5% level. The two top levels of professorship might
be grouped together, preserving the conclusion and not losing all of the distinction between
different ranks.
f.
Since the first statistics had a serious sparseness problem, no conclusive results could come from
the analysis. Grouping the data solved the sparseness problem, but if we grouped the data too much,
we lost important information. Grouping the associate and full professors together seemed to
preserve most of the important information, while at the same time resolving the sparseness issue.
Our tentative conclusion is that rank and gender are related with a higher percentage of males hired
for the upper-level positions. Several important factors are not considered in this analysis, such as
the number of applicants for the positions, their qualifications, the gender of the applicants, and
their previous experience. All of these could be relevant to the study.
7
Chapter 7: Tables
g.
Grouping the full and associate professors together creates the following table:
Observed Counts
F
M
instructor
15
11
asst prof
11
8
0
8
Assoc/Full Prof
The table statistics are:
Expected Counts
F
M
instructor
12.75
13.25
asst prof
9.32
9.68
Assoc/Full Prof
3.92
4.08
Std. Residuals
instructor
asst prof
Assoc/Full Prof
Test Statistics
F
M
0.63
-0.62
0.55
-0.54
-1.98
1.94
Value
df
p-value
Pearson Chi-Square
9.073
2
0.011
Continuity Adjusted Chi-Square
6.627
2
0.036
12.165
2
0.002
Likelihood Ratio Chi-Square
Measures of Association
Value
Std. Error
p-value
Phi
0.414
Contigency
0.382
Cramer's V
0.414
Goodman-Kruskal Gamma
0.461
0.194
0.017
Kendalls tau-b
0.267
0.121
0.027
Stuart's tau-c
0.295
0.137
0.031
Somer's D (C|R)
0.242
0.107
0.023
Somer's D (R|C)
0.295
0.137
0.031
For employees with a Master's degree when hired, there still appears to be a relationship between
gender and rank. Once again, women are hired at a lower-than-expected rate for the upper-level
positions.
8.
a.
The hypotheses are:
H0: The incidence of colds will be the same in both groups.
Ha: The incidence of colds will be different.
8
Chapter 7: Tables
b.
The table statistics are:
Observed Counts
Cold
No Cold
Placebo
31
109
Ascorbic Acid
17
122
Expected Counts
Cold
No Cold
Placebo
24.09
115.91
Ascorbic Acid
23.91
115.09
Std. Residuals
Placebo
Ascorbic Acid
Test Statistics
Cold
No Cold
1.41
-0.64
-1.41
0.64
Value
pvalue
df
Pearson Chi-Square
4.811
1
0.028
Continuity Adjusted Chi-Square
4.141
1
0.042
Likelihood Ratio Chi-Square
4.872
1
0.027
Measures of Association
Std.
Error
Value
pvalue
Phi
0.131
Contigency
0.130
Cramer's V
0.131
Goodman-Kruskal Gamma
0.342
0.145
0.019
Kendalls tau-b
0.131
0.058
0.024
Stuart's tau-c
0.099
0.045
0.027
Somer's D (C|R)
0.099
0.045
0.027
Somer's D (R|C)
0.174
0.076
0.023
Based on the table statistics, we reject the null hypothesis with a p-value of 0.028, concluding that
group is related to the incidence of the common cold. In this case, taking ascorbic acid apparently
reduces the incidence of colds.
9.
a.
The hypotheses are:
H0: The heights of husbands and wives are the same.
Ha: The heights are different.
9
Chapter 7: Tables
b.
The table statistics are:
Observed Counts
Tall
Medium
Short
Tall
18
28
14
Medium
20
51
28
Short
12
25
9
Expected Counts
Tall
Medium
Short
Tall
14.63
30.44
14.93
Medium
24.15
50.22
24.63
Short
11.22
23.34
11.44
Std. Residuals
Tall
Medium
Short
Test Statistics
Tall
Medium
Short
0.88
-0.44
-0.84
0.11
0.68
0.23
0.34
-0.72
Value
df
-0.24
p-value
Pearson Chi-Square
2.907
4
0.573
Continuity Adjusted Chi-Square
1.979
4
0.740
Likelihood Ratio Chi-Square
2.923
4
0.571
Measures of Association
Value
Std. Error
p-value
Phi
0.119
Contigency
0.118
Cramer's V
0.084
Goodman-Kruskal Gamma
0.019
0.101
0.855
Kendalls tau-b
0.012
0.063
0.855
Stuart's tau-c
0.011
0.060
0.855
Somer's D (C|R)
0.012
0.063
0.855
Somer's D (R|C)
0.012
0.064
0.855
There is no evidence of a relationship between heights of wives and husbands. We fail to reject
the null hypothesis with a p-value of 0.573.
10
Chapter 7: Tables
10.
a.
The table statistics for each question are:
Do you favor or oppose term limits?
Should Federal Spending on Child Care Be Increased?
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Value
2.765
2.570
2.761
df
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.040
0.040
0.040
-0.099
0.059
-0.040
0.024
-0.033
0.020
-0.049
0.030
-0.033
0.020
1
1
1
p-value
0.096
0.109
0.097
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Value
13.641
13.023
13.613
p-value
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.110
0.109
0.110
-0.304
0.078
-0.110
0.030
-0.077
0.021
-0.155
0.042
-0.077
0.021
0.094
0.097
0.097
0.097
0.097
df
1
1
1
p-value
0.000
0.000
0.000
p-value
0.000
0.000
0.000
0.000
0.000
Should Federal Spending on Crime Be Increased?
Should Federal Spending on Welfare Be Increased?
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Value
11.053
10.303
11.095
p-value
0.001
0.001
0.001
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Value
11.053
10.303
11.095
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.089
0.089
0.089
-0.370
0.103
-0.089
0.026
-0.041
0.013
-0.190
0.055
-0.042
0.013
p-value
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.089
0.089
0.089
-0.370
0.103
-0.089
0.026
-0.041
0.013
-0.190
0.055
-0.042
0.013
df
1
1
1
0.000
0.001
0.001
0.001
0.001
df
1
1
1
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Value
0.028
0.010
0.028
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.006
0.006
0.006
0.011
0.067
0.006
0.033
0.005
0.033
0.006
0.033
0.005
0.033
b.
p-value
0.000
0.000
0.000
0.000
0.000
p-value
0.000
0.001
0.001
0.001
0.001
Should Federal Spending on Defense Be Increased?
Should Federal Spending on Social Security Be Increased?
Test Statistics
Value
df
p-value
Pearson Chi-Square
33.848
1
0.000
Continuity Adjusted Chi-Square
32.519
1
0.000
Likelihood Ratio Chi-Square
33.932
1
0.000
Value
Std. Error
0.185
0.182
0.185
-0.601
0.081
-0.185
0.030
-0.102
0.019
-0.328
0.051
-0.105
0.019
p-value
0.001
0.001
0.001
df
1
1
1
p-value
0.867
0.920
0.867
p-value
0.867
0.867
0.867
0.867
0.867
Should Federal Spending on Child Care be Increased?
Should Federal Spending on Crime be Increased?
Should Federal Spending on Welfare be Increased?
Should Federal Spending on Social Security be Increased?
c.
There are no statistically significant differences between men and women involving term limits and
defense spending. The other four issues: child care, welfare, crime, and social security, showed
statistically significant disagreements. In each case, a higher percentage of women than expected
favored increased spending on the problem area. In general, women favor an increased government
role in social issues.
11
Chapter 7: Tables
11.
a.
The table statistics are:
Do you favor or oppose term limits?
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Value
1.459
1.211
1.414
df
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.030
0.030
0.030
0.096
0.083
0.028
0.025
0.016
0.014
0.023
0.021
0.033
0.030
2
2
2
p-value
0.482
0.546
0.493
p-value
0.246
0.268
0.269
0.268
0.268
Should Federal Spending on Crime Be Increased?
Test Statistics
Pearson Chi-Square
Continuity Adjusted Chi-Square
Likelihood Ratio Chi-Square
Value
0.327
0.167
0.341
df
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.015
0.015
0.015
-0.099
0.172
-0.015
0.025
-0.005
0.008
-0.024
0.039
-0.010
0.016
1
1
1
p-value
0.567
0.683
0.559
p-value
0.566
0.542
0.543
0.542
0.543
Should Federal Spending on Child Care Be Increased?
Test Statistics
Value
df
Pearson Chi-Square
26.064
1
Continuity Adjusted Chi-Square
24.895
1
Likelihood Ratio Chi-Square
36.186
1
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.154
0.152
0.154
-0.798
0.093
-0.154
0.016
-0.080
0.010
-0.162
0.018
-0.146
0.016
Should Federal Spending on Welfare Be Increased?
Test Statistics
Value
df
Pearson Chi-Square
37.220
2
Continuity Adjusted Chi-Square
35.672
2
Likelihood Ratio Chi-Square
31.351
2
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Value
Std. Error
0.182
0.179
0.182
-0.468
0.074
-0.162
0.035
-0.084
0.019
-0.134
0.030
-0.195
0.043
Should Federal Spending on Social Security Be Increased?
Test Statistics
Value
df
p-value
Pearson Chi-Square
3.455
1
0.063
Continuity Adjusted Chi-Square
2.926
1
0.087
Likelihood Ratio Chi-Square
3.884
1
0.049
Should Federal Spending on Defense Be Increased?
Test Statistics
Value
df
Pearson Chi-Square
104.711
2
Continuity Adjusted Chi-Square
99.522
2
Likelihood Ratio Chi-Square
93.210
2
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
Measures of Association
Phi
Contigency
Cramer's V
Goodman-Kruskal Gamma
Kendalls tau-b
Stuart's tau-c
Somer's D (C|R)
Somer's D (R|C)
b.
Value
Std. Error
0.060
0.060
0.060
-0.320
0.163
-0.060
0.026
-0.026
0.012
-0.084
0.037
-0.043
0.019
p-value
0.049
0.024
0.027
0.024
0.026
Value
Std. Error
0.457
0.415
0.457
0.788
0.043
0.445
0.046
0.328
0.040
0.473
0.050
0.420
0.045
p-value
0.000
0.000
0.000
p-value
0.000
0.000
0.000
0.000
0.000
p-value
0.000
0.000
0.000
p-value
0.000
0.000
0.000
0.000
0.000
p-value
0.000
0.000
0.000
p-value
0.000
0.000
0.000
0.000
0.000
Should Federal Spending on Child Care be Increased?
Should Federal Spending on Defnese be Increased?
Should Federal Spending on Welfare be Increased?
Should Federal Spending on Social Security be Increased?
c.
A higher than expected number of respondents from the Black and Other race category believe that
spending should be increased in child care and welfare. Also a higher than expected number of
blacks believe that social security spending should be increased. A higher than expected number of
whites believe that defense spending should be increased. In each case the differences were
statistically significant at the 5% level., leading to the conclusion that the race of the respondent for
these questions is associated with the response.
12
Chapter 7: Tables
12.
a.
The hypotheses are:
H0: The number of cylinders put in each car is independent of the country of origin.
Ha: The number of cylinders is related to the country.
b.
The pivot table appears as:
Count of Origin
Cylinders
Origin
3
4
5
6
8
American
0
69
0
73
103
245
European
0
61
3
4
0
68
Japanese
4
69
0
6
0
79
Grand Total
4
199
3
83
103
392
c.
Grand Total
The table statistics are:
Test Statistics
Value
Pearson Chi-Square
194.322
df
8
0.000
Continuity Adjusted Chi-Square
176.234
8
0.000
Likelihood Ratio Chi-Square
260.851
8
0.000
Measures of Association
Value
Std. Error
Phi
0.682
Contigency
0.563
Cramer's V
p-value
p-value
0.482
Goodman-Kruskal Gamma
-0.907
0.027
0.000
Kendalls tau-b
-0.451
0.028
0.000
Stuart's tau-c
-0.427
0.026
0.000
Somer's D (C|R)
-0.479
0.024
0.000
Somer's D (R|C)
-0.423
0.024
0.000
Warning: More than 1/5 of Fitted Cells are Sparse
d.
Since there is a problem with sparse cells, we'll group the cars with 3-5 cylinders and we'll also
group the non-American cars. The pivot table appears as:
Count of Origin
Cylinders2
Origin2
3-5
American
6
8
Grand Total
69
73
103
245
Non-American
137
10
0
147
Grand Total
206
83
103
392
13
Chapter 7: Tables
The table statistics are:
Test Statistics
Value
Pearson Chi-Square
164.834
2
0.000
Continuity Adjusted Chi-Square
160.799
2
0.000
Likelihood Ratio Chi-Square
222.405
2
0.000
Measures of Association
Value
Phi
0.637
Contigency
0.537
Cramer's V
df
p-value
Std. Error
p-value
0.637
Goodman-Kruskal Gamma
-0.947
0.018
0.000
Kendalls tau-b
-0.523
0.030
0.000
Stuart's tau-c
-0.593
0.034
0.000
Somer's D (C|R)
-0.588
0.028
0.000
Somer's D (R|C)
-0.466
0.026
0.000
e.
Based on the results of the table statistics, we reject the null hypothesis with a p-value of < 0.0001
and conclude that there is a relationship between origin and the number of cylinders placed in the
car. Generally, American cars have more cylinders than non-American cars.
a.
The pivot table is:
13.
Count of Offer Pending
NE Sector
Offer Pending
No
No
Yes
Grand Total
Yes
Grand Total
30
65
95
9
13
22
39
78
117
The table statistics are:
Test Statistics
Value
df
p-value
Pearson Chi-Square
0.700
1
0.403
Continuity Adjusted Chi-Square
0.343
1
0.558
Likelihood Ratio Chi-Square
0.683
1
0.409
Measures of Association
Value
Phi
0.077
Contigency
0.077
Cramer's V
0.077
Std. Error
p-value
Goodman-Kruskal Gamma
-0.200
0.234
0.392
Kendalls tau-b
-0.077
0.096
0.418
Stuart's tau-c
-0.057
0.071
0.421
Somer's D (C|R)
-0.093
0.115
0.418
Somer's D (R|C)
-0.064
0.080
0.420
There is no evidence of a relationship between Offer Pending and the sector in which the house is
located.
14
15