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Jean-Paul Maalouf

2009-Jul-21 14:38 UTC

[R] Split plot analysis problems

Hello,

I would be very grateful if someone could give me a hand with my split  
plot design problems.

So here is my design :
I am studying the crossed-effects of water (wet/dry) and mowing  
(mowed/not-mowed = nm) on plant height (PH) within 2 types of plant  
communities (Xerobromion and Mesobromion) :
- Within each type of communities, I have localised 4 blocks
- In each block, I have defined 4 plots in order to have the 4  
possible treatments of both the water and mowing factors : nm/dry ;  
mowed/dry ; mowed/wet ; nm/wet.

Here is my data table :

    Community Block Mowing Water    PH
1       Meso    b1  Mowed   Wet  7.40
2       Meso    b1     nm   Wet 13.10
3       Meso    b1  Mowed   Dry  5.55
4       Meso    b1     nm   Dry 10.35
5       Meso    b2     nm   Dry 10.70
6       Meso    b2  Mowed   Dry  6.38
7       Meso    b2     nm   Wet  9.75
8       Meso    b2  Mowed   Wet  6.35
9       Meso    b3     nm   Wet  9.60
10      Meso    b3  Mowed   Dry  5.10
11      Meso    b3     nm   Dry 10.05
12      Meso    b3  Mowed   Wet  6.25
13      Meso    b4     nm   Wet  9.00
14      Meso    b4  Mowed   Wet  6.50
15      Meso    b4     nm   Dry  7.75
16      Meso    b4  Mowed   Dry  5.90
17      Xero    b5     nm   Wet  7.69
18      Xero    b5  Mowed   Wet  8.11
19      Xero    b5     nm   Dry  3.98
20      Xero    b5  Mowed   Dry  3.69
21      Xero    b6     nm   Wet  5.24
22      Xero    b6  Mowed   Wet  4.22
23      Xero    b6     nm   Dry  6.55
24      Xero    b6  Mowed   Dry  4.40
25      Xero    b7  Mowed   Dry  3.79
26      Xero    b7     nm   Dry  3.91
27      Xero    b7     nm   Wet  9.00
28      Xero    b7  Mowed   Wet  8.50
29      Xero    b8  Mowed   Dry  3.33
30      Xero    b8     nm   Wet  6.25
31      Xero    b8  Mowed   Wet  8.00
32      Xero    b8     nm   Dry  6.33

I actually have 2 questions :
I wrote my model in two different ways, and there were differences in  
P-Values according to the model written :

First model : summary(aov(PH~Community*Mowing*Water + Error(Block)))
Error: Block
           Df Sum Sq Mean Sq F value   Pr(>F)
Community  1 42.182  42.182  24.407 0.002603 **
Residuals  6 10.370   1.728
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Error: Within
                        Df Sum Sq Mean Sq F value    Pr(>F)
Mowing                  1 40.007  40.007 21.1747 0.0002215 ***
Water                   1 23.120  23.120 12.2370 0.0025673 **
Community:Mowing        1 21.060  21.060 11.1467 0.0036554 **
Community:Water         1  6.901   6.901  3.6524 0.0720478 .
Mowing:Water            1  1.611   1.611  0.8527 0.3680090
Community:Mowing:Water  1  0.858   0.858  0.4542 0.5089331
Residuals              18 34.008   1.889
---

- Second model (assuming that Mowing*Water are nested inside the Block  
factor) :
summary(aov(PH~Community*Mowing*Water + Error(Block/(Mowing*Water))))

Error: Block
           Df Sum Sq Mean Sq F value   Pr(>F)
Community  1 42.182  42.182  24.407 0.002603 **
Residuals  6 10.370   1.728
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Error: Block:Mowing
                  Df Sum Sq Mean Sq F value    Pr(>F)
Mowing            1 40.007  40.007  37.791 0.0008489 ***
Community:Mowing  1 21.060  21.060  19.893 0.0042820 **
Residuals         6  6.352   1.059
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Error: Block:Water
                 Df  Sum Sq Mean Sq F value  Pr(>F)
Water            1 23.1200 23.1200  6.0725 0.04884 *
Community:Water  1  6.9006  6.9006  1.8125 0.22685
Residuals        6 22.8439  3.8073
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Error: Block:Mowing:Water
                        Df Sum Sq Mean Sq F value Pr(>F)
Mowing:Water            1 1.6110  1.6110  2.0085 0.2062
Community:Mowing:Water  1 0.8581  0.8581  1.0697 0.3409
Residuals               6 4.8126  0.8021

Both models give me interesting (but different!) results. Which one  
would be the most appropriate?

Second question : How can I verify preliminary assumptions (normality  
of residuals and variance homogeneity) in this kind of models?
When I ask R to extract residuals, the answer is "NULL":
> residuals(aov(PH~Community*Mowing*Water + Error(Block/(Mowing*Water))))
NULL> residuals(aov(PH~Community*Mowing*Water + Error(Block)))NULL

A huge thanks to the one who will rescue (or at least try to rescue) my PhD!

Sincerely,


-- 
Jean-Paul Maalouf
UMR 1202 BIOGECO
Inra - Universit? Bordeaux 1
B?timent B8, Avenue des Facult?s
33405 Talence, France
Tel : 05 40008772

Kevin W

2009-Jul-21 20:21 UTC

head link

[R] Split plot analysis problems

I don't think you are clear enough about the layout within each block.  If
the four treatments are randomized, I would choose the first model.

KW


On Tue, Jul 21, 2009 at 9:38 AM, Jean-Paul Maalouf <
jean-paul.maalouf@u-bordeaux1.fr> wrote:
> Hello,
>
> I would be very grateful if someone could give me a hand with my split plot
> design problems.
>
> So here is my design :
> I am studying the crossed-effects of water (wet/dry) and mowing
> (mowed/not-mowed = nm) on plant height (PH) within 2 types of plant
> communities (Xerobromion and Mesobromion) :
> - Within each type of communities, I have localised 4 blocks
> - In each block, I have defined 4 plots in order to have the 4 possible
> treatments of both the water and mowing factors : nm/dry ; mowed/dry ;
> mowed/wet ; nm/wet.
>
> Here is my data table :
>
>   Community Block Mowing Water    PH
> 1       Meso    b1  Mowed   Wet  7.40
> 2       Meso    b1     nm   Wet 13.10
> 3       Meso    b1  Mowed   Dry  5.55
> 4       Meso    b1     nm   Dry 10.35
> 5       Meso    b2     nm   Dry 10.70
> 6       Meso    b2  Mowed   Dry  6.38
> 7       Meso    b2     nm   Wet  9.75
> 8       Meso    b2  Mowed   Wet  6.35
> 9       Meso    b3     nm   Wet  9.60
> 10      Meso    b3  Mowed   Dry  5.10
> 11      Meso    b3     nm   Dry 10.05
> 12      Meso    b3  Mowed   Wet  6.25
> 13      Meso    b4     nm   Wet  9.00
> 14      Meso    b4  Mowed   Wet  6.50
> 15      Meso    b4     nm   Dry  7.75
> 16      Meso    b4  Mowed   Dry  5.90
> 17      Xero    b5     nm   Wet  7.69
> 18      Xero    b5  Mowed   Wet  8.11
> 19      Xero    b5     nm   Dry  3.98
> 20      Xero    b5  Mowed   Dry  3.69
> 21      Xero    b6     nm   Wet  5.24
> 22      Xero    b6  Mowed   Wet  4.22
> 23      Xero    b6     nm   Dry  6.55
> 24      Xero    b6  Mowed   Dry  4.40
> 25      Xero    b7  Mowed   Dry  3.79
> 26      Xero    b7     nm   Dry  3.91
> 27      Xero    b7     nm   Wet  9.00
> 28      Xero    b7  Mowed   Wet  8.50
> 29      Xero    b8  Mowed   Dry  3.33
> 30      Xero    b8     nm   Wet  6.25
> 31      Xero    b8  Mowed   Wet  8.00
> 32      Xero    b8     nm   Dry  6.33
>
> I actually have 2 questions :
> I wrote my model in two different ways, and there were differences in
> P-Values according to the model written :
>
> First model : summary(aov(PH~Community*Mowing*Water + Error(Block)))
> Error: Block
>          Df Sum Sq Mean Sq F value   Pr(>F)
> Community  1 42.182  42.182  24.407 0.002603 **
> Residuals  6 10.370   1.728
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> Error: Within
>                       Df Sum Sq Mean Sq F value    Pr(>F)
> Mowing                  1 40.007  40.007 21.1747 0.0002215 ***
> Water                   1 23.120  23.120 12.2370 0.0025673 **
> Community:Mowing        1 21.060  21.060 11.1467 0.0036554 **
> Community:Water         1  6.901   6.901  3.6524 0.0720478 .
> Mowing:Water            1  1.611   1.611  0.8527 0.3680090
> Community:Mowing:Water  1  0.858   0.858  0.4542 0.5089331
> Residuals              18 34.008   1.889
> ---
>
> - Second model (assuming that Mowing*Water are nested inside the Block
> factor) :
> summary(aov(PH~Community*Mowing*Water + Error(Block/(Mowing*Water))))
>
> Error: Block
>          Df Sum Sq Mean Sq F value   Pr(>F)
> Community  1 42.182  42.182  24.407 0.002603 **
> Residuals  6 10.370   1.728
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> Error: Block:Mowing
>                 Df Sum Sq Mean Sq F value    Pr(>F)
> Mowing            1 40.007  40.007  37.791 0.0008489 ***
> Community:Mowing  1 21.060  21.060  19.893 0.0042820 **
> Residuals         6  6.352   1.059
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> Error: Block:Water
>                Df  Sum Sq Mean Sq F value  Pr(>F)
> Water            1 23.1200 23.1200  6.0725 0.04884 *
> Community:Water  1  6.9006  6.9006  1.8125 0.22685
> Residuals        6 22.8439  3.8073
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
>
> Error: Block:Mowing:Water
>                       Df Sum Sq Mean Sq F value Pr(>F)
> Mowing:Water            1 1.6110  1.6110  2.0085 0.2062
> Community:Mowing:Water  1 0.8581  0.8581  1.0697 0.3409
> Residuals               6 4.8126  0.8021
>
> Both models give me interesting (but different!) results. Which one would
> be the most appropriate?
>
> Second question : How can I verify preliminary assumptions (normality of
> residuals and variance homogeneity) in this kind of models?
> When I ask R to extract residuals, the answer is "NULL":
>
>  residuals(aov(PH~Community*Mowing*Water + Error(Block/(Mowing*Water))))
>>
> NULL
>
>> residuals(aov(PH~Community*Mowing*Water + Error(Block)))
>>
> NULL
>
> A huge thanks to the one who will rescue (or at least try to rescue) my
> PhD!
>
> Sincerely,
>
>
> --
> Jean-Paul Maalouf
> UMR 1202 BIOGECO
> Inra - Université Bordeaux 1
> Bâtiment B8, Avenue des Facultés
> 33405 Talence, France
> Tel : 05 40008772
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
	[[alternative HTML version deleted]]

Mark Difford

2009-Jul-22 14:47 UTC

head link

[R] Split plot analysis problems

Hi Jean-Paul,
>> ... since R is not able to extract residuals?
R can extract the residuals, but they are a "hidden" in models with an
error
structure

##
str(aov(PH~Community*Mowing*Water + Error(Block)))
residuals(aov(PH~Community*Mowing*Water + Error(Block))$Block)
residuals(aov(PH~Community*Mowing*Water + Error(Block))$Within)

Regards, Mark.


Jean-Paul Maalouf wrote:> 
> Hello,
> 
> I would be very grateful if someone could give me a hand with my split  
> plot design problems.
> 
> So here is my design :
> I am studying the crossed-effects of water (wet/dry) and mowing  
> (mowed/not-mowed = nm) on plant height (PH) within 2 types of plant  
> communities (Xerobromion and Mesobromion) :
> - Within each type of communities, I have localised 4 blocks
> - In each block, I have defined 4 plots in order to have the 4  
> possible treatments of both the water and mowing factors : nm/dry ;  
> mowed/dry ; mowed/wet ; nm/wet.
> 
> Here is my data table :
> 
>     Community Block Mowing Water    PH
> 1       Meso    b1  Mowed   Wet  7.40
> 2       Meso    b1     nm   Wet 13.10
> 3       Meso    b1  Mowed   Dry  5.55
> 4       Meso    b1     nm   Dry 10.35
> 5       Meso    b2     nm   Dry 10.70
> 6       Meso    b2  Mowed   Dry  6.38
> 7       Meso    b2     nm   Wet  9.75
> 8       Meso    b2  Mowed   Wet  6.35
> 9       Meso    b3     nm   Wet  9.60
> 10      Meso    b3  Mowed   Dry  5.10
> 11      Meso    b3     nm   Dry 10.05
> 12      Meso    b3  Mowed   Wet  6.25
> 13      Meso    b4     nm   Wet  9.00
> 14      Meso    b4  Mowed   Wet  6.50
> 15      Meso    b4     nm   Dry  7.75
> 16      Meso    b4  Mowed   Dry  5.90
> 17      Xero    b5     nm   Wet  7.69
> 18      Xero    b5  Mowed   Wet  8.11
> 19      Xero    b5     nm   Dry  3.98
> 20      Xero    b5  Mowed   Dry  3.69
> 21      Xero    b6     nm   Wet  5.24
> 22      Xero    b6  Mowed   Wet  4.22
> 23      Xero    b6     nm   Dry  6.55
> 24      Xero    b6  Mowed   Dry  4.40
> 25      Xero    b7  Mowed   Dry  3.79
> 26      Xero    b7     nm   Dry  3.91
> 27      Xero    b7     nm   Wet  9.00
> 28      Xero    b7  Mowed   Wet  8.50
> 29      Xero    b8  Mowed   Dry  3.33
> 30      Xero    b8     nm   Wet  6.25
> 31      Xero    b8  Mowed   Wet  8.00
> 32      Xero    b8     nm   Dry  6.33
> 
> I actually have 2 questions :
> I wrote my model in two different ways, and there were differences in  
> P-Values according to the model written :
> 
> First model : summary(aov(PH~Community*Mowing*Water + Error(Block)))
> Error: Block
>            Df Sum Sq Mean Sq F value   Pr(>F)
> Community  1 42.182  42.182  24.407 0.002603 **
> Residuals  6 10.370   1.728
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
> 
> Error: Within
>                         Df Sum Sq Mean Sq F value    Pr(>F)
> Mowing                  1 40.007  40.007 21.1747 0.0002215 ***
> Water                   1 23.120  23.120 12.2370 0.0025673 **
> Community:Mowing        1 21.060  21.060 11.1467 0.0036554 **
> Community:Water         1  6.901   6.901  3.6524 0.0720478 .
> Mowing:Water            1  1.611   1.611  0.8527 0.3680090
> Community:Mowing:Water  1  0.858   0.858  0.4542 0.5089331
> Residuals              18 34.008   1.889
> ---
> 
> - Second model (assuming that Mowing*Water are nested inside the Block  
> factor) :
> summary(aov(PH~Community*Mowing*Water + Error(Block/(Mowing*Water))))
> 
> Error: Block
>            Df Sum Sq Mean Sq F value   Pr(>F)
> Community  1 42.182  42.182  24.407 0.002603 **
> Residuals  6 10.370   1.728
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
> 
> Error: Block:Mowing
>                   Df Sum Sq Mean Sq F value    Pr(>F)
> Mowing            1 40.007  40.007  37.791 0.0008489 ***
> Community:Mowing  1 21.060  21.060  19.893 0.0042820 **
> Residuals         6  6.352   1.059
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
> 
> Error: Block:Water
>                  Df  Sum Sq Mean Sq F value  Pr(>F)
> Water            1 23.1200 23.1200  6.0725 0.04884 *
> Community:Water  1  6.9006  6.9006  1.8125 0.22685
> Residuals        6 22.8439  3.8073
> ---
> Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
> 
> Error: Block:Mowing:Water
>                         Df Sum Sq Mean Sq F value Pr(>F)
> Mowing:Water            1 1.6110  1.6110  2.0085 0.2062
> Community:Mowing:Water  1 0.8581  0.8581  1.0697 0.3409
> Residuals               6 4.8126  0.8021
> 
> Both models give me interesting (but different!) results. Which one  
> would be the most appropriate?
> 
> Second question : How can I verify preliminary assumptions (normality  
> of residuals and variance homogeneity) in this kind of models?
> When I ask R to extract residuals, the answer is "NULL":
> 
>> residuals(aov(PH~Community*Mowing*Water + Error(Block/(Mowing*Water))))
> NULL
>> residuals(aov(PH~Community*Mowing*Water + Error(Block)))
> NULL
> 
> A huge thanks to the one who will rescue (or at least try to rescue) my
> PhD!
> 
> Sincerely,
> 
> 
> -- 
> Jean-Paul Maalouf
> UMR 1202 BIOGECO
> Inra - Universit? Bordeaux 1
> B?timent B8, Avenue des Facult?s
> 33405 Talence, France
> Tel : 05 40008772
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
> 
-- 
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