25-Apr-00 AGR206 1 ANCOVA One continuous Y variable. One or more continuous X variables (covariates). One or more class variables (treatments). Model: (Y-GM Y ) = (Y-Y’) + B (X-GM X ) + Y = j + B (X- GM X ) +
ANCOVA
Feb 13, 2016
ANCOVA. One continuous Y variable. One or more continuous X variables (covariates). One or more class variables (treatments). Model: (Y-GM Y ) = (Y-Y’) + B (X-GM X ) + e Y = m j + B (X- GM X ) + e. Use of ANCOVA. Increase sensitivity of ANOVA. - PowerPoint PPT Presentation
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25-Apr-00 AGR206 1
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 2
Use of ANCOVA 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).
25-Apr-00 AGR206 3
Assumptions Normal, independent and equal-
variance errors. X is not affected by treatments. Relationship between Y and X’s does
not need to be linear. Homogeneity of slopes. The model
that relates Y to X’s must be the same for all groups (except for intercept).
25-Apr-00 AGR206 4
Example: 3 treatments
Y
20
25
30
35
40
45
50
15 20 25 30 35X
Previous sales
New sales
25-Apr-00 AGR206 5
Uncorrected ANOVAAnalysis of VarianceSourceModelErrorC Total
DF 2
12 14
Sum of Squares 338.80000 307.60000 646.40000
Mean Square 169.400 25.633 46.171
F Ratio 6.6086Prob>F 0.0116
Means for Oneway AnovaLevel123
Number 5 5 5
Mean 38.2000 36.0000 27.2000
Std Error 2.2642 2.2642 2.2642
Std Error uses a pooled estimate of error variance
25-Apr-00 AGR206 6
ANCOVAEffect TestSourceXtrtX*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
Effect TestSourceXtrt
Nparm 1 2
DF 1 2
Sum of Squares 269.02869 417.15091
F Ratio 76.7232 59.4828
Prob>F <.0001 <.0001
Least Squares MeansLevel123
Least Sq Mean 39.81740696 34.74201681 26.84057623
Std Error0.85755067960.84966045380.8384392070
Mean 38.2000 36.0000 27.2000
25-Apr-00 AGR206 7
HW06 Solution
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HW06 Solution
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HW06 Solution
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HW06 Solution
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