You cannot legitimately apply anova() to two models applied to different
sets of data. You do have two sets of data, of different sizes.
Cp is Mallow's C_p statistic. It is not a `test', rather a close relative
of AIC. Small Cp is good (and Googling will find you more). Once again,
it applies to multiple models and one set of data.
On Wed, 27 Apr 2005, Thompson, David (MNR) wrote:
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.
**********************************************************
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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Brian D. Ripley, ripley@stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
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