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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

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