Results_ Phillip Nguyen HW2.sas - Copy

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 1/14 part 1(a) The FREQ Procedure Frequency Percent Table of Greater100 by South Greater100 South no yes Total no 20 42.55 13 27.66 33 70.21 yes 11 23.40 3 6.38 14 29.79 Total 31 65.96 16 34.04 47 100.00 part 1(b) The FREQ Procedure Frequency Expected Percent Row Pct Col Pct Table of Greater100 by South Greater100 South no yes Total no 20 21.766 42.55 60.61 64.52 13 11.234 27.66 39.39 81.25 33 70.21 yes 11 9.234 23.40 78.57 35.48 3 4.766 6.38 21.43 18.75 14 29.79 Total 31 65.96 16 34.04 47 100.00 Statistics for Table of Greater100 by South Statistic DF Value Prob Chi-Square 1 1.4130 0.2346 Likelihood Ratio Chi-Square 1 1.4841 0.2231 Continuity Adj. Chi-Square 1 0.7261 0.3941 Mantel-Haenszel Chi-Square 1 1.3829 0.2396 Phi Coefficient -0.1734 Contingency Coefficient 0.1708 Cramer's V -0.1734 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) 20 Left-sided Pr <= F 0.1988 Right-sided Pr >= F 0.9400 Table Probability (P) 0.1388

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 2/14 Fisher's Exact Test Two-sided Pr <= P 0.3211 Sample Size = 47 the p-value (0.2346) is greater than the typical significance level of 0.05, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that there is an association between crime rates greater than 100 crimes per million population and whether or not the state is in the South at the 0.05 significance level. part 1(c) The FREQ Procedure Frequency Percent Row Pct Col Pct Table of South by Greater100 South Greater100 no yes Total no 20 42.55 64.52 60.61 11 23.40 35.48 78.57 31 65.96 yes 13 27.66 81.25 39.39 3 6.38 18.75 21.43 16 34.04 Total 33 70.21 14 29.79 47 100.00 Statistics for Table of South by Greater100 Column 1 Risk Estimates Risk ASE 95% Confidence Limits Exact 95% Confidence Limits Row 1 0.6452 0.0859 0.4767 0.8136 0.4537 0.8077 Row 2 0.8125 0.0976 0.6213 1.0000 0.5435 0.9595 Total 0.7021 0.0667 0.5714 0.8329 0.5511 0.8266 Difference -0.1673 0.1300 -0.4222 0.0875 Difference is (Row 1 - Row 2) Column 2 Risk Estimates Risk ASE 95% Confidence Limits Exact 95% Confidence Limits Row 1 0.3548 0.0859 0.1864 0.5233 0.1923 0.5463 Row 2 0.1875 0.0976 0.0000 0.3787 0.0405 0.4565 Total 0.2979 0.0667 0.1671 0.4286 0.1734 0.4489 Difference 0.1673 0.1300 -0.0875 0.4222 Difference is (Row 1 - Row 2) Sample Size = 47 There is a difference in the probability of crime rates greater than 100 crimes per million population between Southern and non-Southern states, but this difference is not statistically significant based on the confidence intervals provided. part 2(a) The FREQ Procedure Frequency

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 4/14 Frequency Expected Percent Row Pct Col Pct Table of eyecolor by haircolor eyecolor haircolor fair medium Total dark 1 1 16.67 50.00 33.33 1 1 16.67 50.00 33.33 2 33.33 light 1 1 16.67 50.00 33.33 1 1 16.67 50.00 33.33 2 33.33 medium 1 1 16.67 50.00 33.33 1 1 16.67 50.00 33.33 2 33.33 Total 3 50.00 3 50.00 6 100.00 Statistics for Table of eyecolor by haircolor Statistic DF Value Prob Chi-Square 2 0.0000 1.0000 Likelihood Ratio Chi-Square 2 0.0000 1.0000 Mantel-Haenszel Chi-Square 1 0.0000 1.0000 Phi Coefficient 0.0000 Contingency Coefficient 0.0000 Cramer's V 0.0000 WARNING: 100% of the cells have expected counts less than 5. Chi-Square may not be a valid test. Sample Size = 6 The chi-squared test does not show a significant association between eyecolor and haircolor. This suggests that there is no evidence of an association between these variables in the subset of the data analyzed. part 2(c) The FREQ Procedure

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 5/14 Frequency Percent Row Pct Col Pct Table of eyecolor by haircolor eyecolor haircolor fair medium Total dark 1 16.67 50.00 33.33 1 16.67 50.00 33.33 2 33.33 light 1 16.67 50.00 33.33 1 16.67 50.00 33.33 2 33.33 medium 1 16.67 50.00 33.33 1 16.67 50.00 33.33 2 33.33 Total 3 50.00 3 50.00 6 100.00 Based on the provided frequency table, there doesn't seem to be a significant difference in the frequency of fair hair between different eyecolor categories. Therefore, there's no evidence to suggest that individuals with light eyecolor are significantly more likely to have fair hair compared to those with medium eyecolor in this dataset. part 3(a) The GLM Procedure Class Level Information Class Levels Values BP_Status 3 High Normal Optimal Number of Observations Read 541 Number of Observations Used 541 part 3(a) The GLM Procedure Dependent Variable: Cholesterol Source DF Sum of Squares Mean Square F Value Pr > F Model 2 25210.845 12605.422 6.67 0.0014 Error 538 1016631.488 1889.650 Corrected Total 540 1041842.333 R-Square Coeff Var Root MSE Cholesterol Mean 0.024198 18.65388 43.47010 233.0351 Source DF Type I SS Mean Square F Value Pr > F BP_Status 2 25210.84472 12605.42236 6.67 0.0014 Source DF Type III SS Mean Square F Value Pr > F BP_Status 2 25210.84472 12605.42236 6.67 0.0014

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 7/14 part 3(a) The GLM Procedure Tukey's Studentized Range (HSD) Test for Cholesterol Note: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 538 Error Mean Square 1889.65 Critical Value of Studentized Range 3.32371 Comparisons significant at the 0.05 level are indicated by ***. BP_Status Comparison Difference Between Means Simultaneous 95% Confidence Limits High - Normal 11.543 2.153 20.934 *** High - Optimal 18.647 4.456 32.837 *** Normal - High -11.543 -20.934 -2.153 *** Normal - Optimal 7.103 -6.982 21.188 Optimal - High -18.647 -32.837 -4.456 *** Optimal - Normal -7.103 -21.188 6.982

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 8/14 part 3(b) The GLM Procedure Class Level Information Class Levels Values BP_Status 3 High Normal Optimal Number of Observations Read 541 Number of Observations Used 541 part 3(b) The GLM Procedure Dependent Variable: Cholesterol Source DF Sum of Squares Mean Square F Value Pr > F Model 2 25210.845 12605.422 6.67 0.0014 Error 538 1016631.488 1889.650 Corrected Total 540 1041842.333 R-Square Coeff Var Root MSE Cholesterol Mean 0.024198 18.65388 43.47010 233.0351 Source DF Type I SS Mean Square F Value Pr > F BP_Status 2 25210.84472 12605.42236 6.67 0.0014 Source DF Type III SS Mean Square F Value Pr > F BP_Status 2 25210.84472 12605.42236 6.67 0.0014

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 10/14 part 3(b) The GLM Procedure Tukey's Studentized Range (HSD) Test for Cholesterol Note: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 538 Error Mean Square 1889.65 Critical Value of Studentized Range 3.32371 Comparisons significant at the 0.05 level are indicated by ***. BP_Status Comparison Difference Between Means Simultaneous 95% Confidence Limits High - Normal 11.543 2.153 20.934 *** High - Optimal 18.647 4.456 32.837 *** Normal - High -11.543 -20.934 -2.153 *** Normal - Optimal 7.103 -6.982 21.188 Optimal - High -18.647 -32.837 -4.456 *** Optimal - Normal -7.103 -21.188 6.982 the ANOVA results indicate that blood pressure status (BP_Status) significantly affects cholesterol levels (p-value = 0.0014). However, the model explains only a small proportion (2.42) of the total variance in cholesterol levels.So, other factors not included in the model may affect the variability in cholesterol levels.The

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 11/14 Tukey's HSD test reveals significant differences in mean cholesterol levels: High BP vs. Normal BP (11.543, p < 0.05), High BP vs. Optimal BP (18.647, p < 0.05). No significant difference exists between Normal BP and Optimal BP. This suggest a correlation between blood pressure status and cholesterol levels, with high blood pressure associated with higher cholesterol levels. part 3(c) The GLM Procedure Class Level Information Class Levels Values BP_Status 3 High Normal Optimal Number of Observations Read 541 Number of Observations Used 541 part 3(c) The GLM Procedure Dependent Variable: Cholesterol Source DF Sum of Squares Mean Square F Value Pr > F Model 2 25210.845 12605.422 6.67 0.0014 Error 538 1016631.488 1889.650 Corrected Total 540 1041842.333 R-Square Coeff Var Root MSE Cholesterol Mean 0.024198 18.65388 43.47010 233.0351 Source DF Type I SS Mean Square F Value Pr > F BP_Status 2 25210.84472 12605.42236 6.67 0.0014 Source DF Type III SS Mean Square F Value Pr > F BP_Status 2 25210.84472 12605.42236 6.67 0.0014

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 13/14 part 3(c) The GLM Procedure Tukey's Studentized Range (HSD) Test for Cholesterol Note: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 538 Error Mean Square 1889.65 Critical Value of Studentized Range 3.32371 Comparisons significant at the 0.05 level are indicated by ***. BP_Status Comparison Difference Between Means Simultaneous 95% Confidence Limits High - Normal 11.543 2.153 20.934 *** High - Optimal 18.647 4.456 32.837 *** Normal - High -11.543 -20.934 -2.153 *** Normal - Optimal 7.103 -6.982 21.188 Optimal - High -18.647 -32.837 -4.456 *** Optimal - Normal -7.103 -21.188 6.982 The GLM analysis indicates a significant difference in mean cholesterol levels among blood pressure status groups (p < 0.0014). Tukey's HSD test confirms significant differences: High BP vs. Normal BP (11.543), High BP vs. Optimal BP (18.647). No significant difference exists between Normal BP and Optimal BP,

2/16/24, 8:56 PM Results: Phillip Nguyen HW2.sas https://odamid-usw2-2.oda.sas.com/SASStudio/sasexec/submissions/32244597-fb11-4ab3-b5d0-72c906a05227/results 14/14 suggesting blood pressure status influences cholesterol levels, notably higher in hypertension.