[R] anova results?

[David Meyer]

dechao wang wrote:
> 
> Dear R users,
> 
> I did 16 experiments, with 16 responses (yield), and 4
> factors(hidden, theres, lrate, cycl) with each having
> 2 levels as shown below. I want to do analysis of
> variance to see which factor affect the response. The
> coses are as follows:
> 
> hidden<-c(2,2,10,10,2,2,10,10,2,2,10,10,2,2,10,10)
> theres<-c(0.0001, 0.1, 0.0001, 0.1, 0.0001, 0.1,
> 0.0001, 0.1, 0.0001, 0.1, 0.0001, 0.1, 0.0001, 0.1,
> 0.0001, 0.1)
> lrate<-c(0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0.9,0.9,0.9,0.9,0.9,0.9,0.9,0.9)
> cycl<-c(5000,5000,5000,5000,10000,10000,10000,10000,5000,5000,5000,5000,10000,10000,10000,10000)
> yield<-c(0.26, 1.77, 0.29, 1.75, 0.26, 1.77, 0.31,
> 1.75, 0.29, 1.78, 0.35, 1.83, 0.29, 1.79, 0.35, 1.83)
> 
>     npk <- data.frame(H=factor(hidden),
> T=factor(theres),
>                        L=factor(lrate),
> C=factor(cycl), yield=yield)
> 
>      ( npk.aov <- aov(yield ~ H*T*L*C, npk) )
>      summary(npk.aov)
> 
> when I run it, I got the following results: but there
> is no any F values and p-values. Can you please advise
> me what I missed? Many thanks in advance, dechao


Your model is much to complex for only 16 observations.

The following e.g. works:

 tmp <- lm(yield ~ H+T+L+C, npk)
> summary(tmp)

Call:
lm(formula = yield ~ H + T + L + C, data = npk)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.029375 -0.009687 -0.001250  0.011563  0.025625 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.260625   0.010618  24.545 5.88e-11 ***
H10         0.031250   0.009497   3.290 0.007200 ** 
T0.1        1.483750   0.009497 156.228  < 2e-16 ***
L0.9        0.043750   0.009497   4.607 0.000757 ***
C10000      0.003750   0.009497   0.395 0.700503    
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Residual standard error: 0.01899 on 11 degrees of freedom
Multiple R-Squared: 0.9996,	Adjusted R-squared: 0.9994 
F-statistic:  6110 on 4 and 11 DF,  p-value:     0 



> 
>             Df   Sum Sq  Mean Sq
> H            1   0.0039   0.0039
> T            1   8.8061   8.8061
> L            1   0.0077   0.0077
> C            1   0.0001   0.0001
> H:T          1   0.0014   0.0014
> H:L          1   0.0018   0.0018
> H:C          1 6.25e-06 6.25e-06
> T:L          1   0.0001   0.0001
> T:C          1 6.25e-06 6.25e-06
> L:C          1 6.25e-06 6.25e-06
> H:T:L        1   0.0005   0.0005
> H:T:C        1   0.0001   0.0001
> H:L:C        1   0.0001   0.0001
> T:L:C        1   0.0001   0.0001
> H:T:L:C      1 6.25e-06 6.25e-06
> 
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-- 
	Mag. David Meyer		Wiedner Hauptstrasse 8-10
Vienna University of Technology		A-1040 Vienna/AUSTRIA
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Statistics and Probability Theory	mail: david.meyer at ci.tuwien.ac.at
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