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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  

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