The SAS System

The FREQ Procedure

Frequency
Expected
Percent
Table 1 of S by A
Controlling for D=DeptA
S A
Reject Accept Total
Male
313
293.57
33.55
512
531.43
54.88
825
 
88.42
Female
19
38.431
2.04
89
69.569
9.54
108
 
11.58
Total
332
35.58
601
64.42
933
100.00

Statistics for Table 1 of S by A
Controlling for D=DeptA

Statistic DF Value Prob
Chi-Square 1 17.2480 <.0001
Likelihood Ratio Chi-Square 1 19.0540 <.0001
Continuity Adj. Chi-Square 1 16.3718 <.0001
Mantel-Haenszel Chi-Square 1 17.2295 <.0001
Phi Coefficient   0.1360  
Contingency Coefficient   0.1347  
Cramer's V   0.1360  
Fisher's Exact Test
Cell (1,1) Frequency (F) 313
Left-sided Pr <= F 1.0000
Right-sided Pr >= F <.0001
   
Table Probability (P) <.0001
Two-sided Pr <= P <.0001
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 2.8636 1.7112 4.7921
Relative Risk (Column 1) 2.1566 1.4206 3.2737
Relative Risk (Column 2) 0.7531 0.6799 0.8341

Sample Size = 933

Frequency
Expected
Percent
Table 2 of S by A
Controlling for D=DeptB
S A
Reject Accept Total
Male
207
205.81
35.38
353
354.19
60.34
560
 
95.73
Female
8
9.188
1.37
17
15.812
2.91
25
 
4.27
Total
215
36.75
370
63.25
585
100.00

Statistics for Table 2 of S by A
Controlling for D=DeptB

Statistic DF Value Prob
Chi-Square 1 0.2537 0.6145
Likelihood Ratio Chi-Square 1 0.2586 0.6111
Continuity Adj. Chi-Square 1 0.0851 0.7705
Mantel-Haenszel Chi-Square 1 0.2533 0.6148
Phi Coefficient   0.0208  
Contingency Coefficient   0.0208  
Cramer's V   0.0208  
Fisher's Exact Test
Cell (1,1) Frequency (F) 207
Left-sided Pr <= F 0.7598
Right-sided Pr >= F 0.3918
   
Table Probability (P) 0.1516
Two-sided Pr <= P 0.6771
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 1.2461 0.5285 2.9379
Relative Risk (Column 1) 1.1551 0.6457 2.0664
Relative Risk (Column 2) 0.9270 0.7032 1.2220

Sample Size = 585

Frequency
Expected
Percent
Table 3 of S by A
Controlling for D=DeptC
S A
Reject Accept Total
Male
205
211
22.33
120
114
13.07
325
 
35.40
Female
391
385
42.59
202
208
22.00
593
 
64.60
Total
596
64.92
322
35.08
918
100.00

Statistics for Table 3 of S by A
Controlling for D=DeptC

Statistic DF Value Prob
Chi-Square 1 0.7535 0.3854
Likelihood Ratio Chi-Square 1 0.7510 0.3862
Continuity Adj. Chi-Square 1 0.6332 0.4262
Mantel-Haenszel Chi-Square 1 0.7527 0.3856
Phi Coefficient   -0.0287  
Contingency Coefficient   0.0286  
Cramer's V   -0.0287  
Fisher's Exact Test
Cell (1,1) Frequency (F) 205
Left-sided Pr <= F 0.2129
Right-sided Pr >= F 0.8265
   
Table Probability (P) 0.0394
Two-sided Pr <= P 0.3866
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 0.8826 0.6656 1.1702
Relative Risk (Column 1) 0.9566 0.8645 1.0586
Relative Risk (Column 2) 1.0839 0.9045 1.2989

Sample Size = 918

Frequency
Expected
Percent
Table 4 of S by A
Controlling for D=DeptD
S A
Reject Accept Total
Male
278
274.84
35.10
139
142.16
17.55
417
 
52.65
Female
244
247.16
30.81
131
127.84
16.54
375
 
47.35
Total
522
65.91
270
34.09
792
100.00

Statistics for Table 4 of S by A
Controlling for D=DeptD

Statistic DF Value Prob
Chi-Square 1 0.2250 0.6353
Likelihood Ratio Chi-Square 1 0.2249 0.6353
Continuity Adj. Chi-Square 1 0.1594 0.6897
Mantel-Haenszel Chi-Square 1 0.2247 0.6355
Phi Coefficient   0.0169  
Contingency Coefficient   0.0169  
Cramer's V   0.0169  
Fisher's Exact Test
Cell (1,1) Frequency (F) 278
Left-sided Pr <= F 0.7087
Right-sided Pr >= F 0.3448
   
Table Probability (P) 0.0535
Two-sided Pr <= P 0.6529
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 1.0738 0.8001 1.4410
Relative Risk (Column 1) 1.0246 0.9266 1.1329
Relative Risk (Column 2) 0.9542 0.7862 1.1581

Sample Size = 792

Frequency
Expected
Percent
Table 5 of S by A
Controlling for D=DeptE
S A
Reject Accept Total
Male
138
142.92
23.63
53
48.077
9.08
191
 
32.71
Female
299
294.08
51.20
94
98.923
16.10
393
 
67.29
Total
437
74.83
147
25.17
584
100.00

Statistics for Table 5 of S by A
Controlling for D=DeptE

Statistic DF Value Prob
Chi-Square 1 1.0011 0.3171
Likelihood Ratio Chi-Square 1 0.9904 0.3196
Continuity Adj. Chi-Square 1 0.8080 0.3687
Mantel-Haenszel Chi-Square 1 0.9994 0.3175
Phi Coefficient   -0.0414  
Contingency Coefficient   0.0414  
Cramer's V   -0.0414  
Fisher's Exact Test
Cell (1,1) Frequency (F) 138
Left-sided Pr <= F 0.1841
Right-sided Pr >= F 0.8646
   
Table Probability (P) 0.0486
Two-sided Pr <= P 0.3604
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 0.8186 0.5529 1.2120
Relative Risk (Column 1) 0.9497 0.8559 1.0536
Relative Risk (Column 2) 1.1601 0.8690 1.5487

Sample Size = 584

Frequency
Expected
Percent
Table 6 of S by A
Controlling for D=DeptF
S A
Reject Accept Total
Male
351
348.97
49.16
22
24.031
3.08
373
 
52.24
Female
317
319.03
44.40
24
21.969
3.36
341
 
47.76
Total
668
93.56
46
6.44
714
100.00

Statistics for Table 6 of S by A
Controlling for D=DeptF

Statistic DF Value Prob
Chi-Square 1 0.3841 0.5354
Likelihood Ratio Chi-Square 1 0.3836 0.5357
Continuity Adj. Chi-Square 1 0.2182 0.6404
Mantel-Haenszel Chi-Square 1 0.3836 0.5357
Phi Coefficient   0.0232  
Contingency Coefficient   0.0232  
Cramer's V   0.0232  
Fisher's Exact Test
Cell (1,1) Frequency (F) 351
Left-sided Pr <= F 0.7801
Right-sided Pr >= F 0.3198
   
Table Probability (P) 0.1000
Two-sided Pr <= P 0.5458
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 1.2079 0.6642 2.1968
Relative Risk (Column 1) 1.0123 0.9738 1.0522
Relative Risk (Column 2) 0.8380 0.4789 1.4665

Sample Size = 714

The SAS System

The FREQ Procedure

Summary Statistics for S by A
Controlling for D

Cochran-Mantel-Haenszel Statistics (Based on Table Scores)
Statistic Alternative Hypothesis DF Value Prob
1 Nonzero Correlation 1 1.4313 0.2316
2 Row Mean Scores Differ 1 1.4313 0.2316
3 General Association 1 1.4313 0.2316
Common Odds Ratio and Relative Risks
Statistic Method Value 95% Confidence Limits
Odds Ratio Mantel-Haenszel 1.1019 0.9402 1.2914
  Logit 1.0739 0.9142 1.2616
Relative Risk (Column 1) Mantel-Haenszel 1.0268 0.9821 1.0736
  Logit 1.0065 0.9746 1.0394
Relative Risk (Column 2) Mantel-Haenszel 0.9466 0.8681 1.0323
  Logit 0.8677 0.8056 0.9346
Breslow-Day Test for
Homogeneity of Odds Ratios
Chi-Square 18.8330
DF 5
Pr > ChiSq 0.0021

Total Sample Size = 4526

The SAS System; Plot of Odds Ratios with 95% Wald Confidence Limits S by A Odds Ratios with 95% Wald Confidence Limits Common DeptF DeptE DeptD DeptC DeptB DeptA Controlling for D 1 2 3 4 5 Odds Ratio
The SAS System; Plot of Relative Risks with 95% Wald Confidence Limits Risks computed for column 1 (A = Reject) S by A Relative Risks with 95% Wald Confidence Limits Common DeptF DeptE DeptD DeptC DeptB DeptA Controlling for D 0.5 1.0 1.5 2.0 2.5 3.0 Relative Risk
Frequency
Percent
Row Pct
Col Pct
Table of S by A
S A
Reject Accept Total
Male
1492
32.97
55.44
53.86
1199
26.49
44.56
68.28
2691
59.46
 
 
Female
1278
28.24
69.65
46.14
557
12.31
30.35
31.72
1835
40.54
 
 
Total
2770
61.20
1756
38.80
4526
100.00

Statistics for Table of S by A

Statistic DF Value Prob
Chi-Square 1 92.6704 <.0001
Likelihood Ratio Chi-Square 1 93.9232 <.0001
Continuity Adj. Chi-Square 1 92.0733 <.0001
Mantel-Haenszel Chi-Square 1 92.6499 <.0001
Phi Coefficient   -0.1431  
Contingency Coefficient   0.1416  
Cramer's V   -0.1431  
Fisher's Exact Test
Cell (1,1) Frequency (F) 1492
Left-sided Pr <= F <.0001
Right-sided Pr >= F 1.0000
   
Table Probability (P) <.0001
Two-sided Pr <= P <.0001
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 0.5423 0.4785 0.6147
Relative Risk (Column 1) 0.7961 0.7608 0.8330
Relative Risk (Column 2) 1.4679 1.3535 1.5919

Sample Size = 4526