SPSS uses a different calculation. As far as I understood, they test main
effects without the covariate. Regarding the difference between my and your
results, did you use sum contrasts?
options(contrasts=c("contr.sum","contr.poly"))

On Fri, Jun 4, 2010 at 2:19 AM, Anita Narwani <anitanarwani@gmail.com>wrote:

> Hi Joris,
> That seems to have worked and the contrasts look correct.
> I have tried comparing the results to what SPSS produces for the same
> model. The two programs produce very different results, although the model F
> statistics, R squared and adjusted R squared values are identical. The
> results are so different that I don't know what to trust.
>
> For the same model you coded I got:
>
> test <- lm(C.Mean~  Mean.richness + Diversity + Zoop + Diversity/Phyto +
> + Zoop*Diversity/Phyto)
> > Anova(test,type="III")
> Anova Table (Type III tests)
>
> Response: C.Mean
>                        Sum Sq Df F value    Pr(>F)
> (Intercept)          28223311  1 11.8056  0.001701 **
> Mean.richness        49790403  1 20.8269 7.471e-05 ***
> Diversity            31055477  1 12.9903  0.001082 **
> Zoop                  2736238  1  1.1445  0.292953
> Diversity:Phyto      27943313  6  1.9481  0.104103
> Diversity:Zoop         168184  1  0.0703  0.792584
> Diversity:Zoop:Phyto 61710145  6  4.3021  0.002879 **
> Residuals            74110911 31
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> (Also sightly different from your result)
>
> and
>
> > summary(test)
>
> Call:
> lm(formula = C.Mean ~ Mean.richness + Diversity + Zoop + Diversity/Phyto +
>     +Zoop * Diversity/Phyto)
>
> Residuals:
>      Min       1Q   Median       3Q      Max
> -3555.26  -479.53    49.94   423.49  4073.20
>
> Coefficients:
>                          Estimate Std. Error t value Pr(>|t|)
> (Intercept)               -8562.9     2492.2  -3.436  0.00170 **
> Mean.richness              4605.7     1009.2   4.564 7.47e-05 ***
> DiversityL                 6576.9     1824.8   3.604  0.00108 **
> ZoopD                     -1414.4     1322.1  -1.070  0.29295
> DiversityH:PhytoP2        -4307.5     1824.8  -2.361  0.02472 *
> DiversityL:PhytoP2         -268.4     1262.5  -0.213  0.83300
> DiversityH:PhytoP3        -2233.4     1393.0  -1.603  0.11900
> DiversityL:PhytoP3        -1571.4     1262.5  -1.245  0.22257
> DiversityH:PhytoP4        -7914.8     2647.2  -2.990  0.00543 **
> DiversityL:PhytoP4        -1612.8     1262.5  -1.277  0.21092
> DiversityL:ZoopD            484.9     1828.0   0.265  0.79258
> DiversityH:ZoopD:PhytoP2    683.9     1855.3   0.369  0.71493
> DiversityL:ZoopD:PhytoP2   6346.4     1785.4   3.555  0.00124 **
> DiversityH:ZoopD:PhytoP3   4922.8     1786.3   2.756  0.00971 **
> DiversityL:ZoopD:PhytoP3   1085.4     1785.4   0.608  0.54766
> DiversityH:ZoopD:PhytoP4   3261.8     1985.6   1.643  0.11055
> DiversityL:ZoopD:PhytoP4    681.9     1785.4   0.382  0.70513
> ---
> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 1546 on 31 degrees of freedom
> Multiple R-squared: 0.7858,     Adjusted R-squared: 0.6753
> F-statistic: 7.109 on 16 and 31 DF,  p-value: 1.810e-06
>
> From SPSS I got
>     Tests of Between-Subjects Effects
>
>
>
>
>  Dependent Variable:C Mean
>
>
>
>
>  Source Type III Sum of Squares df Mean Square F Sig.  Corrected Model
> 2.719E+08 16 1.700E+07 7.109 .000  Intercept 2.394E+07 1 2.394E+07 10.012
> .003  Meanrichness 4.979E+07 1 4.979E+07 20.827 .000  Diversity 3.581E+07
> 1 3.581E+07 14.978 .001  Zoop 1.079E+07 1 1.079E+07 4.515 .042  Diversity
> * Zoop 261789.172 1 261789.172 .110 .743  Phyto(Diversity) 1.186E+08 6
> 1.976E+07 8.265 .000  Phyto * Zoop(Diversity) 6.171E+07 6 1.029E+07 4.302
> .003  Error 7.411E+07 31 2.391E+06
>
>  Total 7.959E+08 48
>
>
>  Corrected Total 3.460E+08 47
>
>
>
>
> Which, gives some similar results, but a completely different F statistic
> and P-value for the main effect of Zoop and the nested effect of Phyto.
> Obviously SPSS is not necessarily the perfect reference, but when using the
> Type I SS, the results did agree. Any thoughts on why this might be? Could
> the two programs be calculating the Type III SS differently? Might it be
> wise to stick to Type I SS?
>
> Thanks very much for your time and effort. It has been very helpful.
> Anita.
>
>
> On Thu, Jun 3, 2010 at 4:25 PM, Joris Meys <jorismeys@gmail.com> wrote:
>
>> I see where my confusion comes from. I counted 4 levels of Phyto, but
>> you have 8, being 4 in every level of Diversity. There's your
>> aliasing.
>>
>> > table(Diversity,Phyto)
>>          Phyto
>> Diversity M1 M2 M3 M4 P1 P2 P3 P4
>>         H  0  0  0  0  6  6  6  6
>>         L  6  6  6  6  0  0  0  0
>>
>> There's no need to code them differently for every level of Diversity.
>> If you don't, all is fine :
>>
>> > Phyto <- gsub("M","P",as.character(Phyto))
>> > Phyto <- as.factor(Phyto)
>> >
>> > test <- lm(C.Mean~  Mean.richness + Diversity + Zoop + Diversity/Phyto +
>> + Zoop*Diversity/Phyto)
>> >
>> > Anova(test,type="III")
>> Anova Table (Type III tests)
>>
>> Response: C.Mean
>>                         Sum Sq Df F value    Pr(>F)
>> (Intercept)           23935609  1 10.0121 0.0034729 **
>> Mean.richness         49790385  1 20.8269 7.471e-05 ***
>> Diversity             35807205  1 14.9779 0.0005234 ***
>> Zoop                  10794614  1  4.5153 0.0416688 *
>> Diversity:Phyto      118553464  6  8.2650 2.184e-05 ***
>> Diversity:Zoop          261789  1  0.1095 0.7429356
>> Diversity:Zoop:Phyto  61710162  6  4.3021 0.0028790 **
>> Residuals             74110938 31
>> ---
>> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>> >
>>
>> You can check with summary(test) that the model is fitted correctly.
>>
>> On Fri, Jun 4, 2010 at 12:48 AM, Anita Narwani <anitanarwani@gmail.com>
>> wrote:
>> >
>> > You have everything right except that there are only 2 zooplankton
>> species (C & D, which stand for Ceriodaphnia and Daphnia).
>> >
>>
>
>


-- 
Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

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