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
 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
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 =
>             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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