[R] questions about anova
Spencer Graves
spencer.graves at pdf.com
Sat Feb 28 21:31:04 CET 2004
"Pr(>F)" = probability of obtaining by chance alone an "F value"
at least as large as what was computed. If this probability is small
(as in this case), it is not credible to believe the null hypothesis.
That is typically taken as evidence that there is a "statistically
significant" trend surface. However, it could also mean that some other
assumption, such as independent observations, is violated. I don't know
"surf.ls", but from my cursory review of the documentation, it may
assume independence, which may not be realistic in this case.
I'm not familiar with Davis, but to test increasing orders of
trend surfaces, consider the following:
> data(topo, package="MASS")
> topo.kr <- surf.ls(2, topo)
> topo.kr3 <- surf.ls(3, topo)
> anova(topo.kr, topo.kr3)
Analysis of Variance Table
Model 1: surf.ls(np = 2, x = topo)
Model 2: surf.ls(np = 3, x = topo)
Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
1 46 39958
2 42 21577 4 18381 8.9447 2.558e-05
> p.23 <- anova(topo.kr, topo.kr3)[2, "Pr(>F)"]
Analysis of Variance Table
Model 1: surf.ls(np = 2, x = topo)
Model 2: surf.ls(np = 3, x = topo)
Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
1 46 39958
2 42 21577 4 18381 8.9447 2.558e-05
> p.23
[1] 2.558186e-05
You can put this in a "for" loop to fit and evaluate increasing
orders of surfaces and put that inside a function. If you need help
with that, please consult the substantial documentation provided with R
or downloadable from "www.r-project.org" or in other references such as
Venables and Ripley (2002) Modern Applied Statistics with S, 4th ed.
(Springer).
Hope this helps. spencer graves
Carlos Henrique Grohmann wrote:
>Hello all,
>
>I have two questions about anova (one is probably VERY basic...)
>
>1 - when one asks for a summary of a trend surface created with surf.ls, he/she
>gets:
>
>
>
>>summary(g3r)
>>
>>
>Analysis of Variance Table
> Model: surf.ls(np = 3, x = gradiente$east, y = gradiente$north, z =
>gradiente$num1)
> Sum Sq Df Mean Sq F value Pr(>F)
>Regression 215.7182 9 23.968693976 2686.508 < 2.22e-16
>Deviation 480.1218 53814 0.008921876
>Total 695.8401 53823
>Multiple R-Squared: 0.31, Adjusted R-squared: 0.3099
>AIC: (df = 53814) -146390.9
>Fitted:
> Min 1Q Median 3Q Max
>0.007852 0.075619 0.100498 0.139042 0.338186
>Residuals:
> Min 1Q Median 3Q Max
>-0.29758 -0.04418 -0.01411 0.02536 0.51484
>
>
>
>So, what's the meaning of the "Pr(>F)?
>
>
>
>2 - I have six trend surfaces, and I like to make a anova for the significance
>of increasing the degree of polynomial (like in Davis, 1986, p.422, Statistics
>and data analysis in geology).
>
>is there a way I can do it automatically or should I do it manually?
>
>
>Thanks all.
>
>
>
>
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