Results: berkeley.sas

Berkeley Graduate Admissions Data:

The FREQ Procedure

The Freq Procedure

Table sex * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table of sex by admit
sex admit
No Yes Total
Male
1493
55.48
1198
44.52
2691
 
Female
1278
69.65
557
30.35
1835
 
Total
2771
1755
4526

Statistics for Table of sex by admit

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 1 92.2053 <.0001
Likelihood Ratio Chi-Square 1 93.4494 <.0001
Continuity Adj. Chi-Square 1 91.6096 <.0001
Mantel-Haenszel Chi-Square 1 92.1849 <.0001
Phi Coefficient   -0.1427  
Contingency Coefficient   0.1413  
Cramer's V   -0.1427  

Fisher's Exact Test

Fisher's Exact Test
Cell (1,1) Frequency (F) 1493
Left-sided Pr <= F <.0001
Right-sided Pr >= F 1.0000
   
Table Probability (P) <.0001
Two-sided Pr <= P <.0001

Sample Size = 4526

Table 1 of sex * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table 1 of sex by admit
Controlling for dept=A
sex admit
No Yes Total
Male
313
37.94
512
62.06
825
 
Female
19
17.59
89
82.41
108
 
Total
332
601
933

Statistics for Table 1 of sex by admit
Controlling for dept=A

Chi-Square Tests

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

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

Sample Size = 933

Table 2 of sex * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table 2 of sex by admit
Controlling for dept=B
sex admit
No Yes Total
Male
207
36.96
353
63.04
560
 
Female
8
32.00
17
68.00
25
 
Total
215
370
585

Statistics for Table 2 of sex by admit
Controlling for dept=B

Chi-Square Tests

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

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

Sample Size = 585

Table 3 of sex * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table 3 of sex by admit
Controlling for dept=C
sex admit
No Yes Total
Male
205
63.08
120
36.92
325
 
Female
391
65.94
202
34.06
593
 
Total
596
322
918

Statistics for Table 3 of sex by admit
Controlling for dept=C

Chi-Square Tests

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

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

Sample Size = 918

Table 4 of sex * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table 4 of sex by admit
Controlling for dept=D
sex admit
No Yes Total
Male
279
66.91
138
33.09
417
 
Female
244
65.07
131
34.93
375
 
Total
523
269
792

Statistics for Table 4 of sex by admit
Controlling for dept=D

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 1 0.2980 0.5852
Likelihood Ratio Chi-Square 1 0.2979 0.5852
Continuity Adj. Chi-Square 1 0.2216 0.6378
Mantel-Haenszel Chi-Square 1 0.2976 0.5854
Phi Coefficient   0.0194  
Contingency Coefficient   0.0194  
Cramer's V   0.0194  

Fisher's Exact Test

Fisher's Exact Test
Cell (1,1) Frequency (F) 279
Left-sided Pr <= F 0.7328
Right-sided Pr >= F 0.3188
   
Table Probability (P) 0.0516
Two-sided Pr <= P 0.5995

Sample Size = 792

Table 5 of sex * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table 5 of sex by admit
Controlling for dept=E
sex admit
No Yes Total
Male
138
72.25
53
27.75
191
 
Female
299
76.08
94
23.92
393
 
Total
437
147
584

Statistics for Table 5 of sex by admit
Controlling for dept=E

Chi-Square Tests

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

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

Sample Size = 584

Table 6 of sex * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table 6 of sex by admit
Controlling for dept=F
sex admit
No Yes Total
Male
351
94.10
22
5.90
373
 
Female
317
92.96
24
7.04
341
 
Total
668
46
714

Statistics for Table 6 of sex by admit
Controlling for dept=F

Chi-Square Tests

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

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

Sample Size = 714

Table dept * sex

Cross-Tabular Freq Table

Frequency
Row Pct
Table of dept by sex
dept sex
Male Female Total
A
825
88.42
108
11.58
933
 
B
560
95.73
25
4.27
585
 
C
325
35.40
593
64.60
918
 
D
417
52.65
375
47.35
792
 
E
191
32.71
393
67.29
584
 
F
373
52.24
341
47.76
714
 
Total
2691
1835
4526

Statistics for Table of dept by sex

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 5 1068.3717 <.0001
Likelihood Ratio Chi-Square 5 1220.6148 <.0001
Mantel-Haenszel Chi-Square 1 507.0346 <.0001
Phi Coefficient   0.4859  
Contingency Coefficient   0.4370  
Cramer's V   0.4859  

Sample Size = 4526

Table dept * admit

Cross-Tabular Freq Table

Frequency
Row Pct
Table of dept by admit
dept admit
No Yes Total
A
332
35.58
601
64.42
933
 
B
215
36.75
370
63.25
585
 
C
596
64.92
322
35.08
918
 
D
523
66.04
269
33.96
792
 
E
437
74.83
147
25.17
584
 
F
668
93.56
46
6.44
714
 
Total
2771
1755
4526

Statistics for Table of dept by admit

Chi-Square Tests

Statistic DF Value Prob
Chi-Square 5 778.9065 <.0001
Likelihood Ratio Chi-Square 5 855.3209 <.0001
Mantel-Haenszel Chi-Square 1 724.8170 <.0001
Phi Coefficient   0.4148  
Contingency Coefficient   0.3832  
Cramer's V   0.4148  

Sample Size = 4526

Berkeley Graduate Admissions Data:

The IML Procedure

x_pval

  x   pval
Pooled chisquare = 19.9384 df=6, p = 0.0028402

Bonferroni

  Bonferroni
Reject with Bonferroni correction if p < 0.0083333