The SAS System 10 The FREQ Procedure Cumulative Cumulative SES Frequency Percent Frequency Percent ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ high 265 33.13 265 33.13 low 265 33.13 530 66.25 med 270 33.75 800 100.00 Cumulative Cumulative scout Frequency Percent Frequency Percent ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ no 424 53.00 424 53.00 yes 376 47.00 800 100.00 Cumulative Cumulative delinquent Frequency Percent Frequency Percent ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ no 703 87.88 703 87.88 yes 97 12.13 800 100.00 Table of SES by scout SES scout Frequency‚ Row Pct ‚no ‚yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ high ‚ 61 ‚ 204 ‚ 265 ‚ 23.02 ‚ 76.98 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ low ‚ 211 ‚ 54 ‚ 265 ‚ 79.62 ‚ 20.38 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ med ‚ 152 ‚ 118 ‚ 270 ‚ 56.30 ‚ 43.70 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 424 376 800 The SAS System 11 The FREQ Procedure Statistics for Table of SES by scout Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 2 172.2025 <.0001 Likelihood Ratio Chi-Square 2 182.2475 <.0001 Mantel-Haenszel Chi-Square 1 58.5016 <.0001 Phi Coefficient 0.4640 Contingency Coefficient 0.4209 Cramer's V 0.4640 Statistic Value ASE ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Gamma -0.3984 0.0498 Kendall's Tau-b -0.2542 0.0336 Stuart's Tau-c -0.2929 0.0388 Somers' D C|R -0.2197 0.0291 Somers' D R|C -0.2940 0.0389 Pearson Correlation -0.2706 0.0341 Spearman Correlation -0.2696 0.0357 Lambda Asymmetric C|R 0.3803 0.0341 Lambda Asymmetric R|C 0.2736 0.0421 Lambda Symmetric 0.3179 0.0342 Uncertainty Coefficient C|R 0.1648 0.0225 Uncertainty Coefficient R|C 0.1037 0.0142 Uncertainty Coefficient Symmetric 0.1273 0.0174 Sample Size = 800 The SAS System 12 The FREQ Procedure Summary Statistics for SES by scout Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Nonzero Correlation 1 58.5016 <.0001 2 Row Mean Scores Differ 2 171.9873 <.0001 3 General Association 2 171.9873 <.0001 Total Sample Size = 800 Table of SES by delinquent SES delinquent Frequency‚ Row Pct ‚no ‚yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ high ‚ 255 ‚ 10 ‚ 265 ‚ 96.23 ‚ 3.77 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ low ‚ 212 ‚ 53 ‚ 265 ‚ 80.00 ‚ 20.00 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ med ‚ 236 ‚ 34 ‚ 270 ‚ 87.41 ‚ 12.59 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 703 97 800 Statistics for Table of SES by delinquent Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 2 32.8263 <.0001 Likelihood Ratio Chi-Square 2 36.2523 <.0001 Mantel-Haenszel Chi-Square 1 9.5892 0.0020 Phi Coefficient 0.2026 Contingency Coefficient 0.1985 Cramer's V 0.2026 The SAS System 13 The FREQ Procedure Statistics for Table of SES by delinquent Statistic Value ASE ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Gamma 0.2675 0.0697 Kendall's Tau-b 0.1029 0.0274 Stuart's Tau-c 0.0775 0.0213 Somers' D C|R 0.0582 0.0160 Somers' D R|C 0.1819 0.0478 Pearson Correlation 0.1096 0.0285 Spearman Correlation 0.1091 0.0290 Lambda Asymmetric C|R 0.0000 0.0000 Lambda Asymmetric R|C 0.0717 0.0437 Lambda Symmetric 0.0606 0.0371 Uncertainty Coefficient C|R 0.0613 0.0180 Uncertainty Coefficient R|C 0.0206 0.0063 Uncertainty Coefficient Symmetric 0.0309 0.0093 Sample Size = 800 Summary Statistics for SES by delinquent Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Nonzero Correlation 1 9.5892 0.0020 2 Row Mean Scores Differ 2 32.7853 <.0001 3 General Association 2 32.7853 <.0001 Total Sample Size = 800 The SAS System 14 The FREQ Procedure Table of scout by delinquent scout delinquent Frequency‚ Row Pct ‚no ‚yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ no ‚ 360 ‚ 64 ‚ 424 ‚ 84.91 ‚ 15.09 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ yes ‚ 343 ‚ 33 ‚ 376 ‚ 91.22 ‚ 8.78 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 703 97 800 Statistics for Table of scout by delinquent Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 1 7.4652 0.0063 Likelihood Ratio Chi-Square 1 7.6126 0.0058 Continuity Adj. Chi-Square 1 6.8840 0.0087 Mantel-Haenszel Chi-Square 1 7.4559 0.0063 Phi Coefficient -0.0966 Contingency Coefficient 0.0962 Cramer's V -0.0966 Fisher's Exact Test ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Cell (1,1) Frequency (F) 360 Left-sided Pr <= F 0.0041 Right-sided Pr >= F 0.9979 Table Probability (P) 0.0020 Two-sided Pr <= P 0.0066 The SAS System 15 The FREQ Procedure Statistics for Table of scout by delinquent Statistic Value ASE ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Gamma -0.2977 0.1035 Kendall's Tau-b -0.0966 0.0340 Stuart's Tau-c -0.0630 0.0226 Somers' D C|R -0.0632 0.0227 Somers' D R|C -0.1477 0.0517 Pearson Correlation -0.0966 0.0340 Spearman Correlation -0.0966 0.0340 Lambda Asymmetric C|R 0.0000 0.0000 Lambda Asymmetric R|C 0.0000 0.0000 Lambda Symmetric 0.0000 0.0000 Uncertainty Coefficient C|R 0.0129 0.0092 Uncertainty Coefficient R|C 0.0069 0.0049 Uncertainty Coefficient Symmetric 0.0090 0.0064 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Case-Control (Odds Ratio) 0.5412 0.3467 0.8448 Cohort (Col1 Risk) 0.9307 0.8845 0.9794 Cohort (Col2 Risk) 1.7198 1.1570 2.5565 Sample Size = 800 The SAS System 16 The FREQ Procedure Summary Statistics for scout by delinquent Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Nonzero Correlation 1 7.4559 0.0063 2 Row Mean Scores Differ 1 7.4559 0.0063 3 General Association 1 7.4559 0.0063 Estimates of the Common Relative Risk (Row1/Row2) Type of Study Method Value 95% Confidence Limits ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Case-Control Mantel-Haenszel 0.5412 0.3467 0.8448 (Odds Ratio) Logit 0.5412 0.3467 0.8448 Cohort Mantel-Haenszel 0.9307 0.8845 0.9794 (Col1 Risk) Logit 0.9307 0.8845 0.9794 Cohort Mantel-Haenszel 1.7198 1.1570 2.5565 (Col2 Risk) Logit 1.7198 1.1570 2.5565 Total Sample Size = 800 Table 1 of scout by delinquent Controlling for SES=high scout delinquent Frequency‚ Expected ‚ Row Pct ‚no ‚yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ no ‚ 59 ‚ 2 ‚ 61 ‚ 58.698 ‚ 2.3019 ‚ ‚ 96.72 ‚ 3.28 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ yes ‚ 196 ‚ 8 ‚ 204 ‚ 196.3 ‚ 7.6981 ‚ ‚ 96.08 ‚ 3.92 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 255 10 265 The SAS System 17 The FREQ Procedure Statistics for Table 1 of scout by delinquent Controlling for SES=high Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 1 0.0534 0.8172 Likelihood Ratio Chi-Square 1 0.0551 0.8143 Continuity Adj. Chi-Square 1 0.0000 1.0000 Mantel-Haenszel Chi-Square 1 0.0532 0.8175 Phi Coefficient 0.0142 Contingency Coefficient 0.0142 Cramer's V 0.0142 WARNING: 25% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Fisher's Exact Test ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Cell (1,1) Frequency (F) 59 Left-sided Pr <= F 0.7136 Right-sided Pr >= F 0.5853 Table Probability (P) 0.2989 Two-sided Pr <= P 1.0000 Sample Size = 265 Table 2 of scout by delinquent Controlling for SES=low scout delinquent Frequency‚ Expected ‚ Row Pct ‚no ‚yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ no ‚ 169 ‚ 42 ‚ 211 ‚ 168.8 ‚ 42.2 ‚ ‚ 80.09 ‚ 19.91 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ yes ‚ 43 ‚ 11 ‚ 54 ‚ 43.2 ‚ 10.8 ‚ ‚ 79.63 ‚ 20.37 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 212 53 265 The SAS System 18 The FREQ Procedure Statistics for Table 2 of scout by delinquent Controlling for SES=low Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 1 0.0058 0.9392 Likelihood Ratio Chi-Square 1 0.0058 0.9393 Continuity Adj. Chi-Square 1 0.0000 1.0000 Mantel-Haenszel Chi-Square 1 0.0058 0.9393 Phi Coefficient 0.0047 Contingency Coefficient 0.0047 Cramer's V 0.0047 Fisher's Exact Test ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Cell (1,1) Frequency (F) 169 Left-sided Pr <= F 0.6132 Right-sided Pr >= F 0.5364 Table Probability (P) 0.1496 Two-sided Pr <= P 1.0000 Sample Size = 265 Table 3 of scout by delinquent Controlling for SES=med scout delinquent Frequency‚ Expected ‚ Row Pct ‚no ‚yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ no ‚ 132 ‚ 20 ‚ 152 ‚ 132.86 ‚ 19.141 ‚ ‚ 86.84 ‚ 13.16 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ yes ‚ 104 ‚ 14 ‚ 118 ‚ 103.14 ‚ 14.859 ‚ ‚ 88.14 ‚ 11.86 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 236 34 270 The SAS System 19 The FREQ Procedure Statistics for Table 3 of scout by delinquent Controlling for SES=med Statistic DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 1 0.1010 0.7507 Likelihood Ratio Chi-Square 1 0.1014 0.7502 Continuity Adj. Chi-Square 1 0.0177 0.8943 Mantel-Haenszel Chi-Square 1 0.1006 0.7511 Phi Coefficient -0.0193 Contingency Coefficient 0.0193 Cramer's V -0.0193 Fisher's Exact Test ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Cell (1,1) Frequency (F) 132 Left-sided Pr <= F 0.4495 Right-sided Pr >= F 0.6906 Table Probability (P) 0.1401 Two-sided Pr <= P 0.8539 Sample Size = 270 The SAS System 20 The FREQ Procedure Summary Statistics for scout by delinquent Controlling for SES Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 Nonzero Correlation 1 0.0080 0.9287 2 Row Mean Scores Differ 1 0.0080 0.9287 3 General Association 1 0.0080 0.9287 Estimates of the Common Relative Risk (Row1/Row2) Type of Study Method Value 95% Confidence Limits ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Case-Control Mantel-Haenszel 0.9777 0.5970 1.6010 (Odds Ratio) Logit 0.9770 0.5959 1.6020 Cohort Mantel-Haenszel 0.9974 0.9426 1.0553 (Col1 Risk) Logit 1.0015 0.9581 1.0468 Cohort Mantel-Haenszel 1.0193 0.6706 1.5495 (Col2 Risk) Logit 1.0195 0.6712 1.5484 Breslow-Day Test for Homogeneity of the Odds Ratios ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Chi-Square 0.1518 DF 2 Pr > ChiSq 0.9269 Total Sample Size = 800