The Department of Social Events of the State of New Jersey is facing a discrimination complaint. The plaintiff is an individual who was not promoted after the last election for governor.

Facts
 

• 10 individuals where up for promotion.
• 7 were promoted and 3 were not.
• Of the seven promoted 6 contributed to the campaign of the wining candidate.
• The 3 not promoted did not contribute to the campaign of the wining candidate.

• The 10 individuals were ranked as follows.

• The promotion procedure says that only one of the first 3 ranked individuals can be promoted.
• The plaintiff was ranked number 4.

• In addition, employees who were not part of this group were asked if they felt a positive or negative change in their job conditions after he election was held, and if they made any contributions to the wining candidate.


                  +change   -change  ?change

QUESTION : Is there evidence of discrimination?
 

options ls=78;
data a;
input x y fr;
cards;
1 1 6
1 2 1
2 1 0
2 2 3
;
proc freq;
tables x*y/ chisq exact;
weight fr;

data b;
input x y fr;
cards;
1 1 4
1 2 0
1 3 2
2 1 0
2 2 7
2 3 0
3 1 1
3 2 9
3 3 2
;
proc freq;
tables x*y/ chisq exact;
weight fr;
 

run;
 

The SAS System 1
15:49 Thursday, February 2, 1995

TABLE OF X BY Y

X Y

Frequency|
 Percent |
 Row Pct |
 Col Pct | 1      | 2      | Total
---------+--------+--------+
       1 | 6      | 1      | 7
         | 60.00  | 10.00  | 70.00
         | 85.71  | 14.29  |
         | 100.00 | 25.00  |
---------+--------+--------+
       2 | 0      | 3      | 3
         | 0.00   | 30.00  | 30.00
         | 0.00   | 100.00 |
         | 0.00   | 75.00  |
---------+--------+--------+
   Total       6        4        10
           60.00    40.00    100.00
 

STATISTICS FOR TABLE OF X BY Y

Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 6.429 0.011
Likelihood Ratio Chi-Square 1 7.719 0.005
Continuity Adj. Chi-Square 1 3.353 0.067
Mantel-Haenszel Chi-Square 1 5.786 0.016
Fisher's Exact Test (Left) 1.000
(Right) 0.033
(2-Tail) 0.033
Phi Coefficient 0.802
Contingency Coefficient 0.626
Cramer's V 0.802

Sample Size = 10
WARNING: 100% of the cells have expected counts less
than 5. Chi-Square may not be a valid test.
 
 
 

The SAS System 2 15:49 Thursday, February 2, 1995

TABLE OF X BY Y

X Y

 Frequency|
  Percent |
  Row Pct |
  Col Pct |       1|       2|       3| Total
 ---------+--------+--------+--------+
        1 |      4 |      0 |      2 | 6
          |  16.00 |   0.00 |   8.00 | 24.00
          | 66.67  |   0.00 |  33.33 |
          |  80.00 |   0.00 |  50.00 |
 ---------+--------+--------+--------+
        2 |      0 |      7 |      0 | 7
          | 0.00   |  28.00 |   0.00 | 28.00
          | 0.00   | 100.00 |   0.00 |
          | 0.00   |  43.75 |   0.00 |
 ---------+--------+--------+--------+
        3 |      1 |      9 |      2 | 12
          |   4.00 |  36.00 |   8.00 | 48.00
          |   8.33 |  75.00 |  16.67 |
          |  20.00 |  56.25 |  50.00 |
 ---------+--------+--------+--------+
    Total        5       16        4    25
             20.00    64.00    16.00    100.00
 

STATISTICS FOR TABLE OF X BY Y

Statistic                     DF Value Prob
------------------------------------------------------
Chi-Square                    4 16.484 0.002
Likelihood Ratio Chi-Square   4 20.083 0.000
Mantel-Haenszel Chi-Square    1  1.698 0.193
Fisher's Exact Test (2-Tail)           7.11E-04
Phi Coefficient                  0.812
Contingency Coefficient          0.630
Cramer's V                       0.574

Sample Size = 25
WARNING: 89% of the cells have expected counts less
than 5. Chi-Square may not be a valid test.