CLG Topic 10

CLG Topic 10 - Topic 10 Handout: ANCOVA & RCBD Designs...

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Topic 10 Handout: Learning Goals for this Activity: (1) Experience in the use of ANCOVA and RCBD Models; (2) An understanding of why such models are worthwhile. 10.1 Output for Example II (from notes) is given below on pages 1-2. Complete the analysis of this example (using the analysis of Example I completed in class as a guide). Make sure to consider the following: a. Assumptions Assessment. b. Analysis with the covariate included. c. Compare to previous analysis (without the covariate). What changes? What stays the same? ANOVA MODEL The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F trt 2 1.55555556 0.77777778 0.04 0.9604 Error 6 114.6666667 19.1111111 Corrected Total 8 116.2222222 R-Square Coeff Var Root MSE y Mean 0.013384 37.83138 4.371626 11.55556 t Tests (LSD) for y NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 6 Error Mean Square 19.11111 Critical Value of t 2.44691 Least Significant Difference 8.734 Means with the same letter are not significantly different. GRP Mean N trt A 12.000 3 1 A 11.667 3 3 A 11.000 3 2 ANCOVA Interaction Model Sum of Source DF Squares Mean Square F Value Pr > F x 1 9.66896458 9.66896458 1.97 0.2554 trt 2 87.46642860 43.73321430 8.89 0.0548 x*trt 2 4.33686046 2.16843023 0.44 0.6793 Error 3 14.7499686 4.9166562 Corrected Total 8 116.2222222 R-Square Coeff Var Root MSE y Mean 0.873088 19.18864 2.217353 11.55556 t r t 1 2 3 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 D i s e a s e S t a g e 1 2 3 4 5 6 7 8 9 1 1 1 2 2 2 3 3 3
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- 1 . 5 - 1 - 0 . 5 0 0 . 5 1 1 . 5 - 3 - 2 - 1 0 1 2 3 r e s i d N o r ma l Qu a n t i l e s r e s i d - 3 - 2 - 1 0 1 2 3 p r e d 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 ANCOVA MODEL Sum of Source DF Squares Mean Square F Value Pr > F Model 3 97.1353932 32.3784644 8.48 0.0209 Error 5 19.0868290 3.8173658 Corrected Total 8 116.2222222 R-Square Coeff Var Root MSE y Mean 0.835773 16.90795 1.953808 11.55556 Source DF Type I SS Mean Square F Value Pr > F x 1 9.66896458 9.66896458 2.53 0.1724 trt 2 87.46642860 43.73321430 11.46 0.0136 Source DF Type III SS Mean Square F Value Pr > F x 1 95.57983762 95.57983762 25.04 0.0041 trt 2 87.46642860 43.73321430 11.46 0.0136 Least Squares Means Adjustment for Multiple Comparisons: Tukey-Kramer Standard LSMEAN trt y LSMEAN Error Pr > |t| Number 1 -1.1648624 2.8625918 0.7009 1 2 10.3148399 1.1363118 0.0003 2 3 25.5166892
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CLG Topic 10 - Topic 10 Handout: ANCOVA & RCBD Designs...

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