The SAS System

The FREQ Procedure

Frequency
Expected
Percent
Row Pct
Col Pct
Table of treatment by response
treatment response
cold nocold Total
ascorbic
17
23.914
6.09
12.23
35.42
122
115.09
43.73
87.77
52.81
139
 
49.82
 
 
placebo
31
24.086
11.11
22.14
64.58
109
115.91
39.07
77.86
47.19
140
 
50.18
 
 
Total
48
17.20
231
82.80
279
100.00

Statistics for Table of treatment by response

Statistic DF Value Prob
Chi-Square 1 4.8114 0.0283
Likelihood Ratio Chi-Square 1 4.8717 0.0273
Continuity Adj. Chi-Square 1 4.1407 0.0419
Mantel-Haenszel Chi-Square 1 4.7942 0.0286
Phi Coefficient   -0.1313  
Contingency Coefficient   0.1302  
Cramer's V   -0.1313  
Fisher's Exact Test
Cell (1,1) Frequency (F) 17
Left-sided Pr <= F 0.0205
Right-sided Pr >= F 0.9910
   
Table Probability (P) 0.0115
Two-sided Pr <= P 0.0385
Column 1 Risk Estimates
  Risk ASE 95%
Confidence Limits		 Exact 95%
Confidence Limits
Difference is (Row 1 - Row 2)
Row 1 0.1223 0.0278 0.0678 0.1768 0.0729 0.1886
Row 2 0.2214 0.0351 0.1527 0.2902 0.1557 0.2993
Total 0.1720 0.0226 0.1278 0.2163 0.1297 0.2215
Difference -0.0991 0.0448 -0.1869 -0.0114    
Column 2 Risk Estimates
  Risk ASE 95%
Confidence Limits		 Exact 95%
Confidence Limits
Difference is (Row 1 - Row 2)
Row 1 0.8777 0.0278 0.8232 0.9322 0.8114 0.9271
Row 2 0.7786 0.0351 0.7098 0.8473 0.7007 0.8443
Total 0.8280 0.0226 0.7837 0.8722 0.7785 0.8703
Difference 0.0991 0.0448 0.0114 0.1869    
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 0.4900 0.2569 0.9343
Relative Risk (Column 1) 0.5523 0.3209 0.9506
Relative Risk (Column 2) 1.1273 1.0120 1.2558
Odds Ratio
Odds Ratio 0.4900
   
Asymptotic Conf Limits  
95% Lower Conf Limit 0.2569
95% Upper Conf Limit 0.9343
   
Exact Conf Limits  
95% Lower Conf Limit 0.2407
95% Upper Conf Limit 0.9740

Sample Size = 279

The SAS System

The FREQ Procedure

Frequency
Percent
Row Pct
Col Pct
Table of treatment by response
treatment response
cold nocold Total
absorbic
170
6.09
12.23
35.42
1220
43.73
87.77
52.81
1390
49.82
 
 
placebo
310
11.11
22.14
64.58
1090
39.07
77.86
47.19
1400
50.18
 
 
Total
480
17.20
2310
82.80
2790
100.00

Statistics for Table of treatment by response

Statistic DF Value Prob
Chi-Square 1 48.1141 <.0001
Likelihood Ratio Chi-Square 1 48.7170 <.0001
Continuity Adj. Chi-Square 1 47.4207 <.0001
Mantel-Haenszel Chi-Square 1 48.0969 <.0001
Phi Coefficient   -0.1313  
Contingency Coefficient   0.1302  
Cramer's V   -0.1313  
Fisher's Exact Test
Cell (1,1) Frequency (F) 170
Left-sided Pr <= F <.0001
Right-sided Pr >= F 1.0000
   
Table Probability (P) <.0001
Two-sided Pr <= P <.0001

Sample Size = 2790

The SAS System

The FREQ Procedure

Frequency
Percent
Row Pct
Col Pct
Table of treatment by response
treatment response
cold nocold Total
absorbic
2
7.14
14.29
40.00
12
42.86
85.71
52.17
14
50.00
 
 
placebo
3
10.71
21.43
60.00
11
39.29
78.57
47.83
14
50.00
 
 
Total
5
17.86
23
82.14
28
100.00

Statistics for Table of treatment by response

Statistic DF Value Prob
WARNING: 50% of the cells have expected counts less
than 5. Chi-Square may not be a valid test.
Chi-Square 1 0.2435 0.6217
Likelihood Ratio Chi-Square 1 0.2448 0.6207
Continuity Adj. Chi-Square 1 0.0000 1.0000
Mantel-Haenszel Chi-Square 1 0.2348 0.6280
Phi Coefficient   -0.0933  
Contingency Coefficient   0.0928  
Cramer's V   -0.0933  
Fisher's Exact Test
Cell (1,1) Frequency (F) 2
Left-sided Pr <= F 0.5000
Right-sided Pr >= F 0.8370
   
Table Probability (P) 0.3370
Two-sided Pr <= P 1.0000
Odds Ratio and Relative Risks
Statistic Value 95% Confidence Limits
Odds Ratio 0.6111 0.0854 4.3706
Relative Risk (Column 1) 0.6667 0.1308 3.3979
Relative Risk (Column 2) 1.0909 0.7709 1.5438
Odds Ratio
Odds Ratio 0.6111
   
Asymptotic Conf Limits  
95% Lower Conf Limit 0.0854
95% Upper Conf Limit 4.3706
   
Exact Conf Limits  
95% Lower Conf Limit 0.0441
95% Upper Conf Limit 6.5424

Sample Size = 28