Description

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.

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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.

/

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.

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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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Running Head: OUTPUTS AND METHODS

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

Comments

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

math grades *

gender

Percent

75

100.0%

Missing

N

Total

Percent

0

0.0%

N

Percent

75

100.0%

4

OUTPUTS AND METHODS

math grades * gender Crosstabulation

gender

male

math grades less A-B

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 (

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