Hello,
I have run the following ANOVA, both with the same model,
a) first with imputed missing cell values,
b) then with missing cells left in place.
Call: aov(formula = ht00 ~ blk + trt * size,
data = morph, projections = T, qr = T, na.action = na.exclude)
a) Df Sum of Sq Mean Sq F Value Pr(F)
blk 2 35.0 17.52 7.10 0.0032
trt 4 165.7 41.43 16.80 0.0000
size 2 9.4 4.70 1.90 0.1677
trt:size 8 15.0 1.88 0.76 0.6393
Residuals 28 69.1 2.47
Residual standard error: 1.571
b) Df Sum of Sq Mean Sq F Value Pr(F)
blk 2 102.5 51.25 18.80 0.0000
trt 4 86.0 21.49 7.88 0.0006
size 2 7.8 3.92 1.44 0.2614
trt:size 8 14.7 1.84 0.67 0.7080
Residuals 20 54.5 2.73
Residual standard error: 1.651
I then use anova() to compare the two aov.objects(?):
> anova(aovht00, aovht00na, test="F")
Response: ht00
Terms Resid. Df RSS Test Df Sum of Sq F Value
Pr(F)
1 blk + trt * size 28 69.06
2 blk + trt * size 20 54.53 = 8 14.53 0.6662
0.7148
> anova(aovht00, aovht00na, test="Chi")
Response: ht00
Terms Resid. Df RSS Test Df Sum of Sq Pr(Chi)
1 blk + trt * size 28 69.06
2 blk + trt * size 20 54.53 = 8 14.53 0.06892
> anova(aovht00, aovht00na, test="Cp")
Response: ht00
Terms Resid. Df RSS Test Df Sum of Sq Cp
1 blk + trt * size 28 69.06 161.8
2 blk + trt * size 20 54.53 = 8 14.53 190.9
Q1. Do I interpret the lack of significance under F and Chi^2 tests
to indicate that the differences are negligible?
Q2. And can I extend this interpretation to mean that the imbalance
has little, or no, impact on the result?
Q3. What is the "Cp" test? and how do I use it?
Thank you, DaveT.
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Silviculture Data Analyst
Ontario Forest Research Institute
Ontario Ministry of Natural Resources
Sault Ste. Marie, Ontario, Canada
david.thompson@mnr.gov.on.ca
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