Descriptive Statistics: Scope and Methods in Political Science (Statistics Project Sample)

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Political Science 2101PRIVATE
Scope and Methods in Political Science
Second Problem Set
QUESTIOIN 1
Below is a cross tabulation of two variables from a survey of students in PSC 2101 from the fall of 2012: (1) student political ideology and (2) student predictions regarding whether President Obama will be reelected. Calculate an appropriate measure of association for this cross tabulation, and interpret this statistic regarding the direction and strength of the association between the two variables.
SOLUTION:
The data from the above image has been summarized as shown below
 

 

Do you think president Obama will be re-elected in 2012

 

 


liberal

Slightly liberal

moderate

Slightly conservative

conservative

total

Respondent ID

No

0

1

0

1

3

5


Maybe

4

1

1

1

2

9


Yes

17

13

7

5

1

41

 

Total answered

21

13

8

7

6

55

From the table above the variables under ‘do you think president Obama will be re-elected in 2012’ are the dependent variables while the variables across respondent ID (no, yes and maybe) are the independent variables. They have been summarized in their orderly form.
To calculate the Gamma, the following formula is used
Gamma = Number of concordant pairs – number of discordant pairs
Number of concordant pairs + number of discordant pairs
= nc - nd
nc + nd
Concordant pairs are the numbers in a pair of observations where the elements of one pair have the properties such that they are greater than, equal to or less than another pair in relation to the elements in the other pair. They are indicated as shown below;
nc1 =

170

nc2 =

40

nc3 =

52

nc4 =

0

total nc

262

Discordant pairs are the numbers in a pair of observable variables whereby if one pair has a larger value of the X value then automatically the other pair has a larger value of the Y value. They are indicated as shown below;
nd1 =

0

nd2 =

104

nd3 =

0

nd4 =

13

total nd

117

Gamma = 0.382585752
This test statistic assumes that there is a weak significant relationship between the respondents and their views on whether president Obama will be re-elected in 2012
QUESTION 2
Below is a cross tabulation of two variables: (1) student gender and (2) student attitudes toward professors banning laptops during class. Calculate the chi square for this cross tabulation, and interpret this statistic regarding the statistical significance of the association between the two variables.
SOLUTION:
The observed summary is as shown below
Observed frequencies




 

 

gender

 

 


male

female

Total

ban laptops

no

17

23

40


maybe

5

7

12


yes

4

5

9

 

total

26

35

61

Before calculating the Chi-Square, we need do derive the null and alternative hypothesis required for this test.
Null hypothesis:
Ho: the two variables Ban laptops and Gender are independent
Alternative hypothesis:
H1: the two variables Ban laptops and Gender are not independent.
Test statistic: Chi square = ‑ [(oi – ei)2 / ei]
Where, [oi] = observed frequencies
And [ei] are the expected frequencies
Observed frequencies




 

 

gender

 

 


male

female

Total

ban laptops

no

17

23

40

...