From: Anita Narwani <anitanarwani_at_gmail.com>

Date: Thu, 03 Jun 2010 17:19:09 -0700

Date: Thu, 03 Jun 2010 17:19:09 -0700

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) andReceived on Fri 04 Jun 2010 - 00:24:46 GMT

> 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_at_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_at_gmail.com>> wrote:> >> > You have everything right except that there are only 2 zooplankton> species (C & D, which stand for Ceriodaphnia and Daphnia).> >>

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