NORTHCENTRAL

UNIVERSITY

ASSIGNMENT

COVER SHEET

Student:

Scott Leonard Burgess

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EDR8201

Dr. Watts/Dr. Barnhart

Statistics I

Week 7 – Assignment:

Analyze a Chi-Square Test

Faculty

Use Only

Week 7—Assignment: Analyze

a Chi-Square Test (10 Points)

Download the

EDR-8201 Week 7 Worksheet found in this week’s resources and use it to complete

this assignment.

SPSS Week 7:

Chi-Square

Assume a researcher is interested in gathering information

related to the distribution of teachers used in a research sample; or, if the

surveyed teachers were evenly distributed across gender, across topic area, and

gender across topic area.

Download the SPSS data

set “teachersurvey.sav.” Not all of the variables in this SPSS file will be

used for this assignment.

In this SPSS assignment, you will expand your understanding

of inferential statistics involving a chi-square analysis.

1.

For each variable gender and topic, conduct a Chi

Square analysis to test if there is an even distribution across each level of

each variable. (Hint: For this test, use the Nonparametric Test under the

Analyze tab.)

a. Upload the SPSS output.

1=male, 2=female

Observed N

Expected N

Residual

1

18

20.0

-2.0

2

22

20.0

2.0

Total

40

1=math,2=science,3=art,4=foreign

language

Observed N

Expected N

Residual

1

10

10.0

.0

2

14

10.0

4.0

3

9

10.0

-1.0

4

7

10.0

-3.0

Total

40

Test Statistics

1=male, 2=female

1=math,2=science,3=art,4=foreign

language

Chi-Square

.400a

2.600b

df

1

3

Asymp. Sig.

.527

.457

a. 0 cells (0.0%) have expected frequencies less than 5. The minimum

expected cell frequency is 20.0.

b. 0 cells (0.0%) have expected frequencies less than 5. The

minimum expected cell frequency is 10.0.

For

Gender:

1=male, 2=female

Observed N

Expected N

Residual

1

18

20.0

-2.0

2

22

20.0

2.0

Total

40

Test Statistics

1=male, 2=female

Chi-Square

.400a

df

1

Asymp. Sig.

.527

a. 0 cells (0.0%) have expected frequencies less than 5. The

minimum expected cell frequency is 20.0.

For

Topic Area:

1=math,2=science,3=art,4=foreign

language

Observed N

Expected N

Residual

1

10

10.0

.0

2

14

10.0

4.0

3

9

10.0

-1.0

4

7

10.0

-3.0

Total

40

Test Statistics

1=math,2=science,3=art,4=foreign

language

Chi-Square

2.600a

df

3

Asymp. Sig.

.457

a. 0 cells (0.0%) have expected frequencies less than 5. The

minimum expected cell frequency is 10.0.

b. What are the null and alternative

hypotheses for each variable?

For Gender:

Ho: There is a non-significant un-even distribution

between the male and female gender of teachers.

Ha: There is a significant even distribution

between the male and female gender of teachers.

For Topic Area:

Ho: There is a non-significant un-even distribution

across the topic areas.

Ha: There is a significant even distribution

across the topic areas.

c.

Report the

results in APA format of the test for each of these hypotheses.

A chi-square test was conducted

for the purposes of the hypotheses involving genders. The results as observed

showed X2(1) = 0.400, p-value > 0.05. Therefore, a conclusion can

be established for there being not a significant difference between the genders

and an even distribution can be present between the genders. A chi-square test

was conducted for the purposes of the hypotheses on the subjects. The results

as observed showed, X2(3) = 2.600, p-value > 0.05. Therefore,

there is not a significant with the involved number of classes being taught within

each subject matter and with each subject level there is an even distribution.

2.

Once this analysis has been completed, the researcher

is interested in determining how the distribution appears across the two

variables combined. Conduct a Chi Square goodness-of-fit test for cross

tabulation of gender and topic area. (Hint: For this test, use the Descriptive

=> Crosstabs under the Analyze tab.)

a. Upload the SPSS output

Case Processing

Summary

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

1=math,2=science,3=art,4=foreign language * 1=male, 2=female

40

100.0%

0

0.0%

40

100.0%

1=math,2=science,3=art,4=foreign

language * 1=male, 2=female Crosstabulation

Count

1=male, 2=female

Total

1

2

1=math,2=science,3=art,4=foreign language

1

5

5

10

2

7

7

14

3

3

6

9

4

3

4

7

Total

18

22

40

Chi-Square Tests

Value

df

Asymptotic

Significance (2-sided)

Pearson Chi-Square

.750a

3

.861

Likelihood Ratio

.762

3

.859

Linear-by-Linear Association

.315

1

.575

N of Valid Cases

40

a. 5 cells (62.5%) have expected count less than 5. The

minimum expected count is 3.15.

1=male, 2=female * 1=math,2=science,3=art,4=foreign

language Crosstabulation

1=math,2=science,3=art,4=foreign

language

Total

1

2

3

4

1=male, 2=female

1

Count

5

7

3

3

18

Expected Count

4.5

6.3

4.1

3.2

18.0

O-E

0.5

0.7

-1.1

0.2

(O-E)2/E

0.06

0.08

0.30

0.1

0.54

2

Count

5

7

6

4

22

Expected Count

5.5

7.7

5.0

3.9

22.0

O-E

-0.5

-0.7

1.0

0.1

(O-E)2/E

0.045

0.064

0.2

0.003

0.312

Total

Count

10

14

9

7

40

Expected Count

10.0

14.0

9.0

7.0

40.0

b. What are the null and alternative

hypotheses for this test?

For Gender and Topic

Area:

Ho: There is a non-significant un-even

distribution in association between the gender and the topic area.

Ha: There is a significant even distribution in

association between the gender and topic area.

c. Report the results in APA format of the

test for each of these hypotheses.

A chi-square test was conducted

for the reasoning for whether there is data support within the null hypothesis.

There is not an association between the gender and the topic areas. The results

indicate there is no relationship which exists, as with the results observed X2

(3, n=40) = 0.861, p < .05. Therefore, the tested p-value is (0.861)
exceeds the level of significance and one will fail to reject the null
hypothesis since the variables of gender and topic are observed to have no
significant difference within the sample.
3. Based
on your personal experiences and interests, briefly discuss two variables to be
used in a chi-square analysis.
As can be observed with a chi-square analysis there is an
analysis which is occurring between the association or the relationship of two
variables. Therefore, within my personal experiences of being a teacher and my
interests of being an online teacher I would chose variables within those
categories. For the independent variable there would be a chi-square analysis
for how there is not a relationship between the gender and whether an
individual has completed a course online or has not. For the dependent variable
there would be a chi-square analysis for the relationship between the gender
and whether the individual has completed a course online. The chi-square
analysis would then allow the observation for the significant association
between gender and courses online.
References
Chuang, J., Savalei, V., & Falk, C. F. (2015).
Investigation of type I error rates of three versions of robust chi-square
difference tests. Structural Equation Modeling, 22(4),
517-530. doi:10.1080/10705511.2014.938713
Cramer, D. &
Howett, D. (2004) Chi-square or chi-squared (x2). In N.J. Salkind (Ed.), The
SAGE dictionary of statistics (pp. 22-24). Thousand Oaks, CA: SAGE Public
Gao, X. (2012). Nonparametric
statistics. In N. J. Salkind (Ed.), Encyclopedia of research design
(pp. 915-920). Thousand Oaks, CA: SAGE Publications
Hansen, A. M., Jeske, D., & Kirsch, W. (2015). A
chi-square goodness-of-fit test for autoregressive logistic regression models
with applications to patient screening. Journal of Biopharmaceutical
Statistics, 25(1), 89-108. doi:10.1080/10543406.2014.919938
Knapp, H.
(Academic). (2017). An introduction to the chi-square test Video file.
London: SAGE Publications Ltd.
Shih, J. H., & Fay, M. P. (2017). Pearson's chi-square
test and rank correlation inferences for clustered data. Biometrics, 73(3),
822-834. doi:10.1111/biom.12653
Thatcher Kantor, P., & Kershaw, S. (2012). Parametric statistics. In N.
J. Salkind (Ed.),
Encyclopedia
of research design (pp. 1000-1003). Thousand Oaks, CA: SAGE Publications
Wall
Emerson, R. (2017). The ?² (chi-square) statistic. Journal of Visual
Impairment & Blindness, 111(4), 396-396. Retrieved from http://proxy1.ncu.edu/login?url=http://search.ebscohost.com.proxy1.ncu.edu/login.aspx?direct=true&db=ccm&AN=124402388&site=eds-live