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Lab 5

Lab 5. Post-hoc Tests & Planned Comparisons. Hand Calculations . Hays, page 398, has step by step instructions for computing a one-way ANOVA by hand. Very helpful. Post-hoc Tests with GLM. PROC GLM; CLASS categorical_variable; MODEL dv=iv;

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Lab 5

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  1. Lab 5 Post-hoc Tests & Planned Comparisons

  2. Hand Calculations • Hays, page 398, has step by step instructions for computing a one-way ANOVA by hand. Very helpful.

  3. Post-hoc Tests with GLM PROC GLM; CLASS categorical_variable; MODEL dv=iv; MEANS categorical_variable /TUKEY SCHEFFE BON;

  4. 1 2 3 6 11 14 9 1517 8 12 18 10 11 20 5 13 15 Math test scores for three different grades, 1st, 2nd, and 3rd. Post Hoc Example – test scores

  5. Data d1; Input grade 1 test 3-4; Cards; 1 6 1 9 1 8 1 10 1 5 2 11 2 15 2 12 2 11 2 13 3 14 3 17 3 18 3 20 3 15 ; Proc print; PROC GLM; CLASS grade; MODEL test = grade; MEANS grade /TUKEY SCHEFFE BON; MEANS grade; Run; Program Editor

  6. Output Class Level Information Class Levels Values grade 3 1 2 3 Number of observations 15

  7. Output (Cont.) Dependent Variable: test Sum of Source DF Squares Mean Square F Value Pr > F Model 2 211.733 105.86667 24.81 <.0001 Error 12 51.200 4.26667 Corrected Total 14 262.9333 R-Square Coeff Var Root MSE Mean 0.805274 16.83906 2.065591 12.26667

  8. Source Table Notes • Total Sum of Squares (“Corrected Total”) = Within SS (“Error”) + Between SS (“Model”); 211.733 + 51.2 = 262.93 • Mean Square = SSb/dfb, 211.733/2 = 105.87 • F-value = MSb/MSw = 105.87/4.27 = 24.81

  9. Source Table notes (cont.) • R-square = SSbetween/SStotal = 211.73/262.93 = .805 • Power, Hays, Table XII, Appendix F

  10. Planned comparisons • Want to know if students’ math scores improved in grade 3 from the previous two years. (.25 .25 -.5)

  11. Planned Comparison (cont.)

  12. Planned Comparisons (cont)

  13. Tukey Results Tukey's Studentized Range (HSD) Test NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 12 Error Mean Square 4.266667 Critical Value of Studentized Range 3.77278 Minimum Significant Difference 3.4851 Means with the same letter are not significantly different. Dependent Variable: Grouping Mean N dv A 16.800 5 3 B 12.400 5 2 C 7.600 5 1

  14. Scheffe Results Scheffe's Test for test NOTE: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 12 Error Mean Square 4.266667 Critical Value of F 3.88529 Minimum Significant Difference 3.6417 Means with the same letter are not significantly different. Dependent Variable: Grouping Mean N dv A 16.800 5 3 B 12.400 5 2 C 7.600 5 1

  15. Bonferroni Test Bonferroni (Dunn) t Tests for test NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 12 Error Mean Square 4.266667 Critical Value of t 2.77947 Minimum Significant Difference 3.6311 Means with the same letter are not significantly different. Bon Grouping Mean N grade A 16.800 5 3 B 12.400 5 2 C 7.600 5 1

  16. Proc Means results The GLM Procedure Level of Dependent Variable: dv N Mean Std Dev 1 5 7.6000 2.07364 2 5 12.4000 1.67332 3 5 16.8000 2.38747

  17. Second Tukey Example Tukey's Studentized Range (HSD) Test for dv NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 12 Error Mean Square 5.833333 Critical Value of Studentized Range 3.77278 Minimum Significant Difference 4.0751 Means with the same letter are not significantly different. Tukey Grouping Mean N group A 13.000 5 3 B 6.600 5 2 B B 5.800 5 1

  18. Second Scheffe example Scheffe's Test for dv NOTE: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 12 Error Mean Square 5.833333 Critical Value of F 3.88529 Minimum Significant Difference 4.2581 Means with the same letter are not significantly different. Scheffe Grouping Mean N group A 13.000 5 3 B 6.600 5 2 B B 5.800 5 1

  19. In-Class Example • Download “lab 5 data.sas” from Regression Web site. • Column 1 “rewgrp” • 1 = low-reward condition • 2 = mixed-reward condition • 3 = high-reward condition • Column 3-4 “commit” scale that measures employee commitment (Range 0 to 36)

  20. In class example (cont.) • Compute Scheffe, Tukey and Bonferroni post hoc tests. What do the results tell you about the affect of reward on organizational commitment?

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