Description
IBM SPSS for Introductory Statistics:
Chapter 8, Cross-Tabulation, Chi-Square, and Nonparametric Measures of Association
- Chapter Outlines: IBM SPSS for Introductory Statistics
Review chapters 8 available in Course Guide and Assignment Instructions
- Use the outlines to guide your study
Explanation & Answer
Attached. Please let me know if you have any questions or need revisions.
1
Analyzing Chi-Square, Phi (Or Cramer’s V) and Writing Research Questions
Student’s Name
Institution Affiliation
Date
2
5.1: Chapter 8, Problem 8.1, Chi‐Square and Phi (Or Cramer’s V)
The cross-tabulation is a descriptive statistics measure that harbors intensive analytics on
the data, explaining the possibility of significant relationships between the variables. The chisquare tests are applicable in estimating the relationship between gender and Mathematics course
performance. Some of the assumptions made before this analysis are the independence of
variables and the assumption that the variables are nominal, even if they are not ordered (Morgan
et al., 2013). The analysis's main objective is to investigate whether there exist any significant
differences in the Maths performance between males and females in the class. The following are
the results indicating the case processing summary of the variables, cross-tabulation, chi-square
tests, and symmetric measures;
Case Processing Summary
Valid
N
Percent
math grades *
gender
75
Cases
Missing
N
Percent
100.0%
0
.0%
Total
N
Percent
75
100.0%
The Case processing summary indicates that the total number of participants in this study is 75
which implies that all of them have no missing information.
Math Grades * Gender Cross-Tabulation
Gender
Male
math grades
less A-B
Count
Expected Count
% within gender
most A-B
Count
Expected Count
% within gender
Female
Total
24
20
44
19.9
24.1
44.0
70.6%
48.8%
58.7%
10
21
31
14.1
16.9
31.0
29.4%
51.2%
41.3%
3
Total
Count
34
41
75
34.0
41.0
75.0
100.0%
100.0%
100.0%
Expected Count
% within gender
Chi-Square Tests
Value
Asymp. Sig. (2- Exact Sig. (2sided)
sided)
Df
Pearson Chi-Square
Continuity Correctionb
3.645a
2.801
1
1
.056
.094
Likelihood Ratio
3.699
1
.054
Fisher's Exact Test
Linear-by-Linear
Association
Exact Sig. (1sided)
.064
3.597
N of Valid Casesb
1
.046
.058
75
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 14.05.
b. Computed only for a 2x2 table
The cross-tabulation indicates that most male students represented by 24 (70.6%) scored less A-B
than females represented by 20 (48.8%). Twenty-one females scored most A-B, represented by
51.2%, while ten males achieved Most A-B, representing 29.4% of the total. These results indicate
that the female students’ performance was exemplary better than the one for males. The significant
differences in the performances based on individual gender will be further be identified using the
chi-squares and Fisher exact tests.
The Chi-square test indicates that the p-value is 0.056, which is greater than the statistical
significance level of 0.05, which implies that we cannot ascertain whether there are significant
relationships between gender and Mathematics performance.
Symmetric Measures
Value
Nominal by Nominal
N of Valid Cases
Approx. Sig.
Phi
.220
.056
Cramer's V
.220
75
.056
4
The Phi symmetric measure is 0.220, which is close to zero, but this association and strength of
the association is not significant because the corresponding p-value is greater than 0.05.
A5.2: Chapter 8, Problem 8.2, Risk Ratios and Odds Ratios
The risk estimates of the students' math scores taking algebra are done using the cross-tabulation
descriptive measure in SPSS. The statistics selected is the Risk estimate which indicates the odds
of performing poorly in Maths, given that the student takes the algebra course. The following
are the analysis results from SPSS;
Case Processing Summary
Valid
N
Percent
algebra 1 in h.s. * math
grades
75
Cases
Missing
N
Percent
100.0%
0
.0%
Total
N
Percent
75
100.0%
Algebra 1 in h.s. * Math Grades Cross-Tabulation
Math grades
less A-B
Algebra 1 in h.s.
not taken
Count
% within math grades
taken
Count
% within math grades
Total
Count
% within math grades
most A-B
Total
11
5
16
25.0%
16.1%
21.3%
33
26
59
75.0%
83.9%
78.7%
44
31
75
100.0%
100.0%
100.0%
Risk Estimate
95% Confidence Interval
Value
Odds Ratio for algebra 1 in h.s. (not taken /
taken)
For cohort math grades = less A-B
For cohort math grades = most A-B
Lower
Upper
1.733
.535
5.615
1.229
.823
1.835
.709
.325
1.549
5
N of Valid Cases
75
The case processing summary indicates that all the variables were included for the
participants, which means no missing values. For the students who took algebra, 33 (75.0)
students scored less A-B, while 26 (83.9%)students scored most A-B. The majority of the
students who did mathematics courses also selected the algebra course. The students who did not
take mathematics had significantly low scored in Mathematics. This risk ratio can be interpreted
to mean that students who didn’t take algebra 2 are 1.53 times more likely to have low math
grades than students who did take algebra 2. This risk ratio implies that the students who didn’t
take algebra 2 are only about half as likely to have high math grades as those who took algebra 2.
A5.3: Chapter 8, Problem 8.3, Other Nonparametric Associational Statistics
The non-parametric measures of association are utilized in analysis to describe relationships
between variables that do not follow any distribution such as the normal distribution. The
Cramer’s V and the Phi are used to showcase the nature of associations between two categorical
variables.
Case Processing Summary
Valid
N
Percent
Mothers educ revised *
father's educ revised
73
97.3%
Cases
Missing
N
Percent
2
Total
N
Percent
2.7%
75
100.0%
Mothers educ revised * Father's educ Revised Cross-Tabulation
Father's Educ Revised
HS Grad or
Less
Some College BS or More
Mothers educ
revised
HS Grad or Less Count
Expected Count
Total
33
9
4
46
23.9
10.1
12.0
46.0
6
Some College
Count
Expected Count
BS or More
7
7
19
9.9
4.2
4.9
19.0
0
0
8
8
4.2
38
1.8
16
2.1
19
8.0
73
38.0
16.0
19.0
73.0
Count
Expected Count
Total
5
Count
Expected Count
Symmetric Measures
Asymp. Std.
Errora
Value
Nominal by Nominal
Ordinal by Ordinal
N of Valid Cases
Approx. Tb
Approx. Sig.
Phi
.710
.000
Cramer's V
.502
.000
Kendall's tau-b
.572
.084
5.835
73
a. Not assuming the null hypothesis.
b. Using...