BUSI 820 Liberty Analyzing Chi Square Phi Or Cramers V and Writing Research Questions

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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

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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...


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