[R-sig-eco] ANOVA Output

[tyler]

Apologies if I'm beating a dead horse here, but this is exactly the
problem I raised in the thread on classical statistics in R. If Katrina
is using a textbook like Sokal and Rohlf, it is indeed completely
unexpected to find that changing the order of explanatory variables in
an anova will produce different results. Thierry points out that this is
because R produces Type I SS by default. Unfortunately, nowhere in S&R
is this distinction explained, so for this problem a book widely
regarded as a comprehensive reference for biologists provides absolutely
no help.

These questions come up all the time on the r-help list, and I think
it's a sign of a real disconnect between the presentation of classical
statistics in many undergrad programs and the way the tests are actually
implemented in R.

Anyways, that's a bigger issue. It may be helpful to know that the 'car'
package includes a function Anova (not to be confused with the anova
function) that allows you to calculate type II or type III sums of
squares. 

Cheers,

Tyler

"ONKELINX, Thierry" <Thierry.ONKELINX at inbo.be>
writes:

> Dear Katrina,
>
> The F-value are different because you test different hypotheses since
> anova yields Type I SS. It looks like you expect Type III SS.
>
> HTH,
>
> Thierry
>
>
> ------------------------------------------------------------------------
> ----
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature
> and Forest
> Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
> methodology and quality assurance
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium 
> tel. + 32 54/436 185
> Thierry.Onkelinx at inbo.be 
> www.inbo.be 
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to
> say what the experiment died of.
> ~ Sir Ronald Aylmer Fisher
>
> The plural of anecdote is not data.
> ~ Roger Brinner
>
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of
> data.
> ~ John Tukey
>
> -----Oorspronkelijk bericht-----
> Van: r-sig-ecology-bounces at r-project.org
> [mailto:r-sig-ecology-bounces at r-project.org] Namens Katrina W. Chu
> Verzonden: woensdag 12 november 2008 22:27
> Aan: r-sig-ecology at r-project.org
> Onderwerp: [R-sig-eco] ANOVA Output
>
> I have a question about my R-output when I run a three-way ANOVA.  I
> just plugged in the
> interaction term into the formula and presto!  ANOVA!  But I noticed
> that if I change
> the order of the formula (or interaction term), I get slightly different
> ANOVA outputs.
>  I've pasted the output at the bottom of this message.  I didn't think
> that this should
> happen, so I would appreciate if anyone had any feedback on this
> problem.
>
> Thanks in advance, Kat.
>
>> ANOVA <- aov(Chlorophyll.a~Treatment*SamplingPeriod*Site)
>> summary(ANOVA)
>                                Df  Sum Sq Mean Sq F value    Pr(>F)    
> Treatment                       3   356.5   118.8  4.2878  0.005276 ** 
> SamplingPeriod                  3   374.7   124.9  4.5069  0.003911 ** 
> Site                            1  1016.5  1016.5 36.6791 2.629e-09 ***
> Treatment:SamplingPeriod        9   467.6    52.0  1.8747  0.053284 .  
> Treatment:Site                  3   167.8    55.9  2.0176  0.110424    
> SamplingPeriod:Site             3  1670.2   556.7 20.0884 2.383e-12 ***
> Treatment:SamplingPeriod:Site   9   277.2    30.8  1.1115  0.352455    
> Residuals                     534 14799.5    27.7                      
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
>
>> ANOVA <- aov(Chlorophyll.a~SamplingPeriod*Treatment*Site)
>> summary(ANOVA)
>                                Df  Sum Sq Mean Sq F value    Pr(>F)    
> SamplingPeriod                  3   369.5   123.2  4.4437  0.004264 ** 
> Treatment                       3   361.8   120.6  4.3510  0.004840 ** 
> Site                            1  1016.5  1016.5 36.6791 2.629e-09 ***
> SamplingPeriod:Treatment        9   467.6    52.0  1.8747  0.053284 .  
> SamplingPeriod:Site             3  1662.0   554.0 19.9894 2.718e-12 ***
> Treatment:Site                  3   176.0    58.7  2.1166  0.097111 .  
> SamplingPeriod:Treatment:Site   9   277.2    30.8  1.1115  0.352455    
> Residuals                     534 14799.5    27.7                      
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
>
>> ANOVA <- aov(Chlorophyll.a~Site*SamplingPeriod*Treatment)
>> summary(ANOVA)
>                                Df  Sum Sq Mean Sq F value    Pr(>F)    
> Site                            1  1008.9  1008.9 36.4050 2.998e-09 ***
> SamplingPeriod                  3   374.1   124.7  4.4990  0.003953 ** 
> Treatment                       3   364.8   121.6  4.3871  0.004607 ** 
> Site:SamplingPeriod             3  1654.8   551.6 19.9026 3.050e-12 ***
> Site:Treatment                  3   172.6    57.5  2.0761  0.102364    
> SamplingPeriod:Treatment        9   478.2    53.1  1.9172  0.047282 *  
> Site:SamplingPeriod:Treatment   9   277.2    30.8  1.1115  0.352455    
> Residuals                     534 14799.5    27.7                      
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

-- 
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