This preview shows pages 1–6. Sign up to view the full content.

Chapter 17 Analysis of Covariance 1 Analysis of Covariance Analysis of covariance can be summarized as a technique to reduce experimental error by utilizing additional factor(s) which are not part of the treatments but were in place prior to imposing treatments and are affecting the measure in the experimental units. This technique removes the influence of the covariates on the treatment comparisons. data a; input Group \$ Age Change @@; cards; A 31 17.05 A 23 4.96 A 27 10.40 A 28 11.05 A 22 0.26 A 24 2.51 R 23 -0.87 R 22 -10.74 R 22 -3.27 R 25 -1.97 R 27 7.50 R 20 -7.25 ;;;; Proc GLM data=a; class group; model change = group; lsmeans group; run;

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 17 Analysis of Covariance 2 Class Level Information Class Levels Values Group 2 A R Number of observations 12 Dependent Variable: Change Sum of Source DF Squares Mean Square F Value Pr > F Model 1 328.9674083 328.9674083 8.45 0.0156 Error 10 389.2962833 38.9296283 Corrected Total 11 718.2636917 R-Square Coeff Var Root MSE Change Mean 0.458004 252.6910 6.239361 2.469167 Source DF Type I SS Mean Square F Value Pr > F Group 1 328.9674083 328.9674083 8.45 0.0156 Source DF Type III SS Mean Square F Value Pr > F Group 1 328.9674083 328.9674083 8.45 0.0156 Least Squares Means Change Group LSMEAN A 7.70500000 R -2.76666667
Chapter 17 Analysis of Covariance 3 * This allows us to look at the data in an overlay graph. A good way to start all such problems. We will see that there is a clear relationship between age and change, but there also appears to be evidence that the aerobic training has a larger mean change than the flat running. The question is how does the age effect come into play when comparing training methods?. That is what the Analysis of Covariance (ANCOVA) does.; data aerobic; set a; if group ne "A" then delete; a_change = change; drop change; run; data runners; set a; if group ne "R" then delete; r_change = change; drop change; run; data combined; set aerobic runners; run; proc print data=combined;

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 17 Analysis of Covariance 4 proc plot data=combined; plot a_change*age = "A" r_change*age = "R" / overlay; run; The SAS System Obs Group Age a_change r_change 1 A 31 17.05 . 2 A 23 4.96 . 3 A 27 10.40 . 4 A 28 11.05 . 5 A 22 0.26 . 6 A 24 2.51 . 7 R 23 . -0.87 8 R 22 . -10.74 9 R 22 . -3.27 10 R 25 . -1.97 11 R 27 . 7.50 12 R 20 . -7.25
Chapter 17 Analysis of Covariance 5 Plot of a_change*Age. Symbol used is 'A'. Plot of r_change*Age. Symbol used is 'R'. 20 ˆ A A 10 ˆ A R a_change ‚ A A 0 ˆ A R R R ‚R -10 ˆ R Šˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒ 20 25 30 35 Age NOTE: 12 obs had missing values. The mean age of the Aerobic group is 25.83

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.