Homework Six. See if you can reproduce these tables in Excel and if the comments below make any sense.

 

a.             Use the Sort command on the Excel menu bar.

b.             The pivot table appears as:

Rank Hired

F

M

Grand Total

instructor

20

17

37

asst prof

17

15

32

assoc prof

0

9

9

full prof

0

3

3

Grand Total

37

44

81


c.              The table statistics are:

Expected Counts

F

M

 

instructor

16.90

20.10

 

asst prof

14.62

17.38

 

assoc prof

4.11

4.89

 

full prof

1.37

1.63

 

 

 

 

 

Std. Residuals

F

M

 

instructor

0.75

-0.69

 

asst prof

0.62

-0.57

 

assoc prof

-2.03

1.86

 

full prof

-1.17

1.07

 

 

 

 

 

Test Statistics

Value

df

p-value

Pearson Chi-Square

11.852

3

0.008

Continuity Adjusted Chi-Square

8.039

3

0.045

Likelihood Ratio Chi-Square

16.398

3

0.001

 

 

 

 

Measures of Association

Value

Std. Error

p-value

Phi

0.383

 

 

Contigency

0.357

 

 

Cramer's V

0.383

 

 

Goodman-Kruskal Gamma

0.440

0.160

0.006

Kendalls tau-b

0.250

0.095

0.009

Stuart's tau-c

0.277

0.109

0.011

Somer's D (C|R)

0.223

0.083

0.007

Somer's D (R|C)

0.279

0.110

0.011

Warning: More than 1/5 of Fitted Cells are Sparse

Because the rank hired data is ordinal, we should use one of the ordinal statistics. However some of the table cells are sparse, leaving some question as to the validity of the statistical results. We should either remove some of the sparse cells or combine them.


d.             The revised table appears as:

Observed Counts

F

M

Instructors

20

17

asst prof

17

15

Full and Assoc

0

12

The table statistics are:

Expected Counts

F

M

 

Instructors

16.90

20.10

 

asst prof

14.62

17.38

 

Full and Assoc

5.48

6.52

 

 

 

 

 

Std. Residuals

F

M

 

Instructors

0.75

-0.69

 

asst prof

0.62

-0.57

 

Full and Assoc

-2.34

2.15

 

 

 

 

 

Test Statistics

Value

df

p-value

Pearson Chi-Square

11.852

2

0.003

Continuity Adjusted Chi-Square

9.516

2

0.009

Likelihood Ratio Chi-Square

16.398

2

0.000

 

 

 

 

Measures of Association

Value

Std. Error

p-value

Phi

0.383

 

 

Contigency

0.357

 

 

Cramer's V

0.383

 

 

Goodman-Kruskal Gamma

0.440

0.160

0.006

Kendalls tau-b

0.251

0.097

0.009

Stuart's tau-c

0.277

0.109

0.011

Somer's D (C|R)

0.226

0.085

0.008

Somer's D (R|C)

0.279

0.110

0.011

Once again, the table statistics indicate a relationship between rank hired and gender. This time there is no problem with sparse cells.


e.             Grouping the data into professors and non-professors yields: