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

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