ANCOVA - UC Davis Plants

ANCOVA - UC Davis Plants

ANCOVA One continuous Y variable. One or more continuous X variables (covariates). One or more class variables (treatments). Model: (Y-GMY) = (Y-Y) + B (X-GMX) + Y = j + B (X- GMX) + 25-Apr-00 AGR206 1 Use of ANCOVA

25-Apr-00 Increase sensitivity of ANOVA. Adjust the treatment means to what they would be if all were at the average value of X. In MANOVA (not considered any further). AGR206 2 Assumptions 25-Apr-00 Normal, independent and equalvariance errors. X is not affected by treatments. Relationship between Y and Xs does not need to be linear. Homogeneity of slopes. The model that relates Y to Xs must be the

same for all groups (except for intercept). AGR206 3 Example: 3 treatments 50 New sales 45 40 Y 35 30 25 20 15 20

25 X 30 35 Previous sales 25-Apr-00 AGR206 4 Uncorrected ANOVA Analysis of Variance Source Model Error C Total DF 2 12 14

Sum of Squares 338.80000 307.60000 646.40000 Mean Square 169.400 25.633 46.171 F Ratio 6.6086 Prob>F 0.0116 Means for Oneway Anova Level Number Mean Std Error 1 5 38.2000 2.2642 2 5 36.0000

2.2642 3 5 27.2000 2.2642 Std Error uses a pooled estimate of error variance 25-Apr-00 AGR206 5 ANCOVA Effect Test Source X trt X*trt Nparm 1 2 2 DF 1

2 2 Sum of Squares 243.14124 1.26328 7.05047 F Ratio 69.4230 0.1803 1.0065 Prob>F <.0001 0.8379 0.4032 DF 1 2 Sum of Squares 269.02869 417.15091 F Ratio

76.7232 59.4828 Prob>F <.0001 <.0001 Effect Test Source X trt Nparm 1 2 Least Squares Means Level 1 2 3 25-Apr-00 Least Sq Mean 39.81740696 34.74201681

26.84057623 Std Error 0.8575506796 0.8496604538 0.8384392070 AGR206 Mean 38.2000 36.0000 27.2000 6 HW06 Solution 25-Apr-00 AGR206 7 HW06 Solution 25-Apr-00

AGR206 8 HW06 Solution 25-Apr-00 AGR206 9 HW06 Solution 25-Apr-00 AGR206 10

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