The SAS System 23:47 Monday, February 20, 2006 1 The FREQ Procedure Table of defendant by penalty defendant penalty Frequency| Row Pct |no |yes | Total ---------+--------+--------+ black | 149 | 17 | 166 | 89.76 | 10.24 | ---------+--------+--------+ white | 141 | 19 | 160 | 88.13 | 11.88 | ---------+--------+--------+ Total 290 36 326 Statistics for Table of defendant by penalty Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.2214 0.6379 Likelihood Ratio Chi-Square 1 0.2215 0.6379 Continuity Adj. Chi-Square 1 0.0863 0.7689 Mantel-Haenszel Chi-Square 1 0.2208 0.6385 Phi Coefficient 0.0261 Contingency Coefficient 0.0261 Cramer's V 0.0261 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 149 Left-sided Pr <= F 0.7412 Right-sided Pr >= F 0.3843 Table Probability (P) 0.1255 Two-sided Pr <= P 0.7246 The SAS System 23:47 Monday, February 20, 2006 2 The FREQ Procedure Statistics for Table of defendant by penalty Statistic Value ASE ------------------------------------------------------ Gamma 0.0830 0.1757 Kendall's Tau-b 0.0261 0.0553 Stuart's Tau-c 0.0163 0.0347 Somers' D C|R 0.0163 0.0348 Somers' D R|C 0.0416 0.0882 Pearson Correlation 0.0261 0.0553 Spearman Correlation 0.0261 0.0553 Lambda Asymmetric C|R 0.0000 0.0000 Lambda Asymmetric R|C 0.0125 0.0373 Lambda Symmetric 0.0102 0.0304 Uncertainty Coefficient C|R 0.0010 0.0042 Uncertainty Coefficient R|C 0.0005 0.0021 Uncertainty Coefficient Symmetric 0.0007 0.0028 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits ----------------------------------------------------------------- Case-Control (Odds Ratio) 1.1811 0.5902 2.3634 Cohort (Col1 Risk) 1.0185 0.9434 1.0997 Cohort (Col2 Risk) 0.8624 0.4652 1.5987 Sample Size = 326 The SAS System 23:47 Monday, February 20, 2006 3 The FREQ Procedure Summary Statistics for defendant by penalty Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob --------------------------------------------------------------- 1 Nonzero Correlation 1 0.2208 0.6385 2 Row Mean Scores Differ 1 0.2208 0.6385 3 General Association 1 0.2208 0.6385 Estimates of the Common Relative Risk (Row1/Row2) Type of Study Method Value 95% Confidence Limits ------------------------------------------------------------------------- Case-Control Mantel-Haenszel 1.1811 0.5902 2.3634 (Odds Ratio) Logit 1.1811 0.5902 2.3634 Cohort Mantel-Haenszel 1.0185 0.9434 1.0997 (Col1 Risk) Logit 1.0185 0.9434 1.0997 Cohort Mantel-Haenszel 0.8624 0.4652 1.5987 (Col2 Risk) Logit 0.8624 0.4652 1.5987 Total Sample Size = 326 Table 1 of defendant by penalty Controlling for victim=black defendant penalty Frequency| Row Pct |no |yes | Total ---------+--------+--------+ black | 97 | 6 | 103 | 94.17 | 5.83 | ---------+--------+--------+ white | 9 | 0 | 9 | 100.00 | 0.00 | ---------+--------+--------+ Total 106 6 112 The SAS System 23:47 Monday, February 20, 2006 4 The FREQ Procedure Statistics for Table 1 of defendant by penalty Controlling for victim=black Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.5539 0.4567 Likelihood Ratio Chi-Square 1 1.0344 0.3091 Continuity Adj. Chi-Square 1 0.0000 1.0000 Mantel-Haenszel Chi-Square 1 0.5490 0.4587 Phi Coefficient -0.0703 Contingency Coefficient 0.0702 Cramer's V -0.0703 WARNING: 25% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 97 Left-sided Pr <= F 0.5977 Right-sided Pr >= F 1.0000 Table Probability (P) 0.5977 Two-sided Pr <= P 1.0000 Sample Size = 112 Table 2 of defendant by penalty Controlling for victim=white defendant penalty Frequency| Row Pct |no |yes | Total ---------+--------+--------+ black | 52 | 11 | 63 | 82.54 | 17.46 | ---------+--------+--------+ white | 132 | 19 | 151 | 87.42 | 12.58 | ---------+--------+--------+ Total 184 30 214 The SAS System 23:47 Monday, February 20, 2006 5 The FREQ Procedure Statistics for Table 2 of defendant by penalty Controlling for victim=white Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.8774 0.3489 Likelihood Ratio Chi-Square 1 0.8475 0.3573 Continuity Adj. Chi-Square 1 0.5194 0.4711 Mantel-Haenszel Chi-Square 1 0.8733 0.3500 Phi Coefficient -0.0640 Contingency Coefficient 0.0639 Cramer's V -0.0640 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 52 Left-sided Pr <= F 0.2325 Right-sided Pr >= F 0.8744 Table Probability (P) 0.1070 Two-sided Pr <= P 0.3893 Sample Size = 214 The SAS System 23:47 Monday, February 20, 2006 6 The FREQ Procedure Summary Statistics for defendant by penalty Controlling for victim Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob --------------------------------------------------------------- 1 Nonzero Correlation 1 1.2097 0.2714 2 Row Mean Scores Differ 1 1.2097 0.2714 3 General Association 1 1.2097 0.2714 Estimates of the Common Relative Risk (Row1/Row2) Type of Study Method Value 95% Confidence Limits ------------------------------------------------------------------------- Case-Control Mantel-Haenszel 0.6353 0.2864 1.4092 (Odds Ratio) Logit ** 0.6875 0.3151 1.5001 Cohort Mantel-Haenszel 0.9438 0.8485 1.0498 (Col1 Risk) Logit 0.9420 0.9006 0.9854 Cohort Mantel-Haenszel 1.4738 0.7400 2.9355 (Col2 Risk) Logit ** 1.3796 0.7112 2.6760 ** These logit estimators use a correction of 0.5 in every cell of those tables that contain a zero. Breslow-Day Test for Homogeneity of the Odds Ratios ------------------------------ Chi-Square 0.3806 DF 1 Pr > ChiSq 0.5373 Total Sample Size = 326 The SAS System 23:47 Monday, February 20, 2006 7 The FREQ Procedure Table 1 of defendant by penalty Controlling for victim=black defendant penalty Frequency| Row Pct |no |yes | Total ---------+--------+--------+ black | 97 | 6 | 103 | 94.17 | 5.83 | ---------+--------+--------+ white | 9 | 0 | 9 | 100.00 | 0.00 | ---------+--------+--------+ Total 106 6 112 Statistics for Table 1 of defendant by penalty Controlling for victim=black Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.5539 0.4567 Likelihood Ratio Chi-Square 1 1.0344 0.3091 Continuity Adj. Chi-Square 1 0.0000 1.0000 Mantel-Haenszel Chi-Square 1 0.5490 0.4587 Phi Coefficient -0.0703 Contingency Coefficient 0.0702 Cramer's V -0.0703 WARNING: 25% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 97 Left-sided Pr <= F 0.5977 Right-sided Pr >= F 1.0000 Table Probability (P) 0.5977 Two-sided Pr <= P 1.0000 Sample Size = 112 The SAS System 23:47 Monday, February 20, 2006 8 The FREQ Procedure Table 2 of defendant by penalty Controlling for victim=white defendant penalty Frequency| Row Pct |no |yes | Total ---------+--------+--------+ black | 52 | 11 | 63 | 82.54 | 17.46 | ---------+--------+--------+ white | 132 | 19 | 151 | 87.42 | 12.58 | ---------+--------+--------+ Total 184 30 214 Statistics for Table 2 of defendant by penalty Controlling for victim=white Statistic DF Value Prob ------------------------------------------------------ Chi-Square 1 0.8774 0.3489 Likelihood Ratio Chi-Square 1 0.8475 0.3573 Continuity Adj. Chi-Square 1 0.5194 0.4711 Mantel-Haenszel Chi-Square 1 0.8733 0.3500 Phi Coefficient -0.0640 Contingency Coefficient 0.0639 Cramer's V -0.0640 Fisher's Exact Test ---------------------------------- Cell (1,1) Frequency (F) 52 Left-sided Pr <= F 0.2325 Right-sided Pr >= F 0.8744 Table Probability (P) 0.1070 Two-sided Pr <= P 0.3893 Sample Size = 214