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Assignment: Analyzing Chi-Square, Phi (Or CramerÃ¢â‚¬â„¢s V) and Writing Research Questions

A5.1: Chapter 8, Problem 8.1, Chi?Square and Phi (Or CramerÃ¢â‚¬â„¢s V). Write a short narrative of your process, an interpretation of your findings, and write your results to include tables. Cut and paste the Case Processing Summary, Crosstabulation, Chi?Square Tests, and Symetric Measures tables directly into your document and refer to them in your interpretation.

A5.2: Chapter 8, Problem 8.2, Risk Ratios and Odds Ratios. Write a short narrative of your process, an interpretation of your findings, and write your results. Cut and paste the Case Processing Summary, Crosstabulation, and Risk Estimate tables directly into your document and refer to them in your interpretation.

A5.3: Chapter 8, Problem 8.3, Other Nonparametric Associational Statistics. Write a short narrative of your process, an interpretation of your findings, and write your results. Cut and paste the Case Processing Summary, Crosstabulation, and Symetric Measures tables directly into your document and refer to them in your interpretation.

A5.4: Chapter 8, Problem 8.4, Cross?Tabulation and Eta. Write a short narrative of your process, an interpretation of your findings, and write your results to include tables. Cut and paste the Case Processing Summary, Crosstabulation, and Directional Measures tables directly into your document and refer to them in your interpretation.

A5.5, Application Problem ? Crosstabulation and Chi?Square. Using the Ã¢â‚¬Å“college student data.savÃ¢â‚¬Â and Ã¢â‚¬Å“hsbdata.savÃ¢â‚¬Â files, do the following problems. Write a short narrative of your process, an interpretation of your findings, and write your results. Cut and paste your outputs directly into your document and refer to them in your interpretation.

A5.5a. Write two research questions and two null hypotheses relating to the following pairs of data, run crosstabs and interpret the results of chi?square and phi (or CramerÃ¢â‚¬â„¢s V), as discussed in Chapter 6 and in the interpretation of Output 8.1 for the following data pairs: 1) Ã¢â‚¬Å“genderÃ¢â‚¬Â and Ã¢â‚¬Å“marital statusÃ¢â‚¬Â and 2) Ã¢â‚¬Å“age groupÃ¢â‚¬Â and Ã¢â‚¬Å“marital statusÃ¢â‚¬Â. Before beginning the test, recode marital status to BinaryMarital where Single and Divorced (1 & 3) are listed as Single (1) and Married (2) is listed as Married (2).

Include Case Processing Summary, Crosstabulation, Chi?Square Tests, and Symetric Measures tables and refer to them in your interpretation. Include a discussion of relevant differences or similarities. Prior to running the analysis, discuss how the data meets the assumptions and conditions for the tests you are going to conduct. Support your assertion with the appropriate descriptive statistics.

A5.5b. Write two research questions and two null hypotheses relating to the following pairs of data, run crosstabs and interpret the results of chi?square and phi (or CramerÃ¢â‚¬â„¢s V), as discussed in Chapter 6 and in the interpretation of Output 8.1 for the following data pairs: 1) Ã¢â‚¬Å“mathachÃ¢â‚¬Â and Ã¢â‚¬Å“calcÃ¢â‚¬Â and 2) Ã¢â‚¬Å“mathachÃ¢â‚¬Â and Ã¢â‚¬Å“trigÃ¢â‚¬Â. Before beginning the test, recode math achievement into two groups HighAch and LowAch using the median score as the dividing point.

Include Case Processing Summary, Crosstabulation, Chi?Square Tests, and Symetric Measures tables and refer to them in your interpretation. Include a discussion of relevant differences or similarities. Prior to running the analysis, discuss how the data meets the assumptions and conditions for the tests you are going to conduct. Support your assertion with the appropriate descriptive statistics.

Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
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Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
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Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
/
Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
/
Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
/
Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
/
Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
/
Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
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Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
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Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
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Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
/
Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
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Printed by: jjeanbaptiste1@liberty.edu. Printing is for personal, private use only. No part of this book may be
reproduced or transmitted without publisher’s prior permission. Violators will be prosecuted.
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1
Outputs and methods
8.1
Output
Fisher’s exact test is well known for making one likely to make different interpretations
depending on the number of columns that one may want. For the one-tailed column, it is only
used when one had made a prior prediction regarding the events that would occur. In an instance
where one may want to learn about the difference in the results that males and females may
experience in relation to their grades, the use of chi-square statistic may be necessary. In the
presented case, the assessment of all the made assumptions made it easy for determining the
effectiveness of the results. From the results, males are not expected to have high or low grades
in math as compared to females.
Method
From the presented data, it is worth noting that the participants had all the data included.
The cross-tabulation table has the expected counts as well as counts. It is worth noting that about
20 out of the 41 females who took part had low math grades, which represents 49% of the
females. This case is different from the 24 males who had low math grades. From the assessment
2
OUTPUTS AND METHODS
of the chi-square test, one can gain more confidence that the appearance did not occur by chance.
To learn about the statistical relationship that may exist between two nominal variables, the use
of the chi-test is the most appropriate tool that can be considered. Through this, one can use
Fisher’s exact test in order to interpret the results of the test.
Crosstabs
Notes
Output Created
16-SEP-2020 21:13:48
Input
Data
C:UsersukacaAppDat
aLocalTempTemp1_2
0200915160222data_s
et_for_all_problems.zip
Data set for all
problemshsbdata.sav
Active Dataset
DataSet3
Filter
Weight
Split File
N of Rows in Working
Data File
Missing Value
Handling
Definition of Missing
75
User-defined missing
values are treated as
missing.
3
OUTPUTS AND METHODS
Cases Used
Statistics for each table
are based on all the
cases with valid data in
the specified range(s)
for all variables in each
table.
Syntax
CROSSTABS
/TABLES=mathgr BY
gender
/FORMAT=AVALUE
TABLES
/STATISTICS=CHISQ
PHI KAPPA
/CELLS=COUNT
EXPECTED COLUMN
/COUNT ROUND
CELL.
Resources
Processor Time
00:00:00.02
Elapsed Time
00:00:00.17
Dimensions Requested
2
Cells Available
524245
Case Processing Summary
Cases
Valid
N
gender
Percent
75
100.0%
Missing
N
Total
Percent
0
0.0%
N
Percent
75
100.0%
4
OUTPUTS AND METHODS
gender
male
Count
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%
34
41
75
34.0
41.0
75.0
100.0%
100.0%
100.0%
most A-B Count
Expected
Count
% within
gender
Total
Count
Expected
Count
% within
gender
Total
24
Expected
Count
% within
gender
female
Chi-Square Tests
Value
Asymptotic
Significance Exact Sig. (2- Exact Sig. (1(2-sided)
sided)
sided)
df
3.645a
1
.056
Continuity Correctionb
2.801
1
.094
Likelihood Ratio
3.699
1
.054
Pearson Chi-Square
5
OUTPUTS AND METHODS
Fisher’s Exact Test
.064
Linear-by-Linear
Association
3.597
N of Valid Cases
75
1
.046
.058
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 14.05.
b. Computed only for a 2×2 table
Symmetric Measures
Value
Nominal by Nominal Phi
Measure of
Agreement
Asymptotic
Standard
Errora
Approximate
Tb
.220
.056
Cramer’s V
.220
.056
Kappa
.213
N of Valid Cases
.108
75
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.
CROSSTABS
/TABLES=gender BY mathach
8.2
Output
Approximate
Significance
1.909
.056
6
OUTPUTS AND METHODS
From this study, since binary variables are used in this, the assessment of the odds ratio
was necessary. This was made possible by the fact that taking or not taking algebra two and
whether the recorded grades were high or low were binary variables. The obtained odds ratio was
2.77, and as a result of the results of this, it is worth noting that students who may not take
algebra 2 have a 2.77 higher percentage of getting lower grades in math as compared to the
learners who took the course. Additional, from this study, there was a 1.07-7.15 confidence in
relation to the expected results.
Method
Evaluating the first two tables, one can notice that there is a notable similarity between
them and the output realized in 8.1 apart for the fact that the variables are different in various
ways. 44 of the students had low recordings in their math grades. Since there are students who
did not take algebra 2, the results show that the students who did not complete Algebra 2 are
more likely to have low math grades as compared to the students who completed this course. The
above is contributed significantly by the fact that both the lower and upper bounds can either be
greater than 1 or less than 1, which means that the application of the risk ration is a practical
approach that has high significance in facilitating the needed results.
8.3
Output
For one to look at the relationship that exists between the education between the mother
and that of the father, the use of Kendall’s tau-b. There was a statistically positive association
between the knowledge of both the father and the mother. From this study, it is worth noting that
there was a tendency in which the highly educated fathers were married to more highly educated
7
OUTPUTS AND METHODS
mothers. In addition to this, the less educated fathers were married to less educated mothers. The
use of this tau is directly associated with the large effect size.
Method
There are several forms that can be used in the assessment of the results associated with a
given correlation. The use of the right non-parametric measure may make it easy for the
collection of the correct data that may be needed in a study. From the various nonparametric
measures, they are necessary for the measurement of the strength of the association that may
exist between variables. In an instance where one may experience a weak association between
the variables, the value of the statistics tends to move close to 0, and then the level of
significance is likely to be more than 0.5. On the other hand, where the association is significant
statistically, the results obtained are a small p (