questions about anova

"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

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.