Hello, R experts, If I understand Ted's anwser correctly, then I can not contrast the mean yields between sections 1-8 and 9-11 under "Trt" but I can contrast mean yields for sections 1-3 and 6-11 because there exists significant interaction between two factors (Trt:section4, Trt:section5). Could I use the commands below to test the difference between sections 1-3 and 6-11 ? > contrasts(section)<-c(-2,-2,-2,0,0,1,1,1,1,1,1) > newobj<-lm(log2(yield)~treat*section) How can I infer that there is significant difference between sections 1-3 and sections 6-11 for the "Trt" from the output below?
> summary(newobj) Call: lm(formula = log2(yield) ~ treat * section) Residuals: Min 1Q Median 3Q Max -0.49647 -0.14913 -0.01521 0.17471 0.51105 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 6.28840 0.05003 125.682 < 2e-16 *** treatTrt 1.22122 0.07076 17.259 < 2e-16 *** section1 0.17831 0.03911 4.559 4.08e-05 *** section2 -0.23102 0.16595 -1.392 0.17087 section3 2.38170 0.16595 14.352 < 2e-16 *** section4 3.36834 0.16595 20.298 < 2e-16 *** section5 -1.56873 0.16595 -9.453 3.67e-12 *** section6 -0.41522 0.16595 -2.502 0.01613 * section7 -0.89943 0.16595 -5.420 2.38e-06 *** section8 0.09522 0.16595 0.574 0.56901 section9 -0.78784 0.16595 -4.748 2.21e-05 *** section10 0.74821 0.16595 4.509 4.79e-05 *** treatTrt:section1 0.10101 0.05532 1.826 0.07461 . treatTrt:section2 0.27270 0.23468 1.162 0.25151 treatTrt:section3 -1.22210 0.23468 -5.207 4.85e-06 *** treatTrt:section4 -1.39187 0.23468 -5.931 4.26e-07 *** treatTrt:section5 -0.76137 0.23468 -3.244 0.00225 ** treatTrt:section6 0.07320 0.23468 0.312 0.75658 treatTrt:section7 0.33108 0.23468 1.411 0.16535 treatTrt:section8 -0.13686 0.23468 -0.583 0.56276 treatTrt:section9 0.22086 0.23468 0.941 0.35180 treatTrt:section10 -0.14476 0.23468 -0.617 0.54054 --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Residual standard error: 0.2874 on 44 degrees of freedom Multiple R-Squared: 0.973, Adjusted R-squared: 0.9601 F-statistic: 75.55 on 21 and 44 DF, p-value: < 2.2e-16 Joshua Quoting "(Ted Harding)" <[EMAIL PROTECTED]>: > On 24-Aug-06 [EMAIL PROTECTED] wrote: >> Hello, R users, >> I have two factors (treat, section) anova design experiment where >> there are 3 replicates. The objective of the experiment is to test if >> there is significant difference of yield between top (section 9 to 11) >> and bottom (section 9 to 11) > [I think you mean sections 1 to 8] > >> of the fruit tree under treatment. I found that there are interaction >> between two factors. I wonder if I can contrast means from levels of >> one factor (section) under another factor (treat)? if so, how to do >> it in R and how to interpret the output? > > I think you would be well advised to look at a plot of the data. > For example, let Y stand for yield, R for replicate, T for treat > and S for section. > > ix<-(T=="Trt");plot(S[ix],Y[ix],col="red",ylim=c(0,1000)) > ix<-(T=="Ctl");points(S[ix],Y[ix],col="blue") > >> From this it is clear that sections 4 and 5 are in a class of > their own. Also, in sections 1-3 and 6-11 the "Ctl" yields > are not only lower, but have smaller (in some cases hardly any) > variance, compared with the "Trt" yields. The variances for > sections 7,8,9,10,11 are greater than for 1,2,3,6 without > great change in mean value. > > While there is an evident difference between "Trt" yields and > "Ctrl" yields for sections 1-3 and 6-11, this is not so for > sections 4 and 5. > > This sort of behaviour no doubt provides some reasons for the > interaction you observed. You seem to have a quite complex > phenomenon here! > > To some extent the problems with variance can be diminished by > working with logarithms. Compare the previous plot with > > ix<-(T=="Trt");plot(S[ix],log10(Y[ix]),col="red",ylim=c(0,3)) > ix<-(T=="Ctl");points(S[ix],log10(Y[ix]),col="blue") > > (you have used log2() in your commands). The above observations > can be seen reflected in R if you look at the output of > > summary(obj) > > where in particular: > > treatTrt:section2 -1.11691 0.33189 -3.365 0.001595 ** > treatTrt:section3 -0.45634 0.33189 -1.375 0.176099 > treatTrt:section4 -1.56627 0.33189 -4.719 2.42e-05 *** > treatTrt:section5 -1.73604 0.33189 -5.231 4.48e-06 *** > treatTrt:section6 -0.91311 0.33189 -2.751 0.008588 ** > treatTrt:section7 -0.07853 0.33189 -0.237 0.814055 > treatTrt:section8 0.17935 0.33189 0.540 0.591654 > treatTrt:section9 -0.28859 0.33189 -0.870 0.389277 > treatTrt:section10 0.06913 0.33189 0.208 0.835972 > treatTrt:section11 -0.29649 0.33189 -0.893 0.376543 > > which, precisely, "contrasts means from levels of one factor > (section) under another factor (treat)", and shows that most > of the "interaction" arises in sections 4 and 5. > > Since sections 4 and 5 (in the middle of sections 1 to 8) are > so exceptional, they will have strong influence on your comparison > between sections 1-8 and sections 9-11. You need to think about > what to do with sections 4 and 5! > >> Here is the data and commands I used to test the differece between >> section 1 to 8 and 9 to 11 under treatment. But I don't know if I was >> right, how to interpret the out and whether there are significant >> difference between section 1 to 8 and section 9 to 11 under treatment. >> >> yield replicate treat section >> 35.55 1 Ctl 1 >> 53.70 1 Ctl 2 >> 42.79 1 Ctl 3 >> 434.81 1 Ctl 4 >> 705.96 1 Ctl 5 >> 25.91 1 Ctl 6 >> 57.53 1 Ctl 7 >> 41.45 1 Ctl 8 >> 85.54 1 Ctl 9 >> 51.23 1 Ctl 10 >> 188.24 1 Ctl 11 >> 35.71 2 Ctl 1 >> 45.15 2 Ctl 2 >> 40.10 2 Ctl 3 >> 312.76 2 Ctl 4 >> 804.05 2 Ctl 5 >> 28.22 2 Ctl 6 >> 68.51 2 Ctl 7 >> 46.15 2 Ctl 8 >> 123.14 2 Ctl 9 >> 33.78 2 Ctl 10 >> 121.28 2 Ctl 11 >> 30.96 3 Ctl 1 >> 36.10 3 Ctl 2 >> 47.19 3 Ctl 3 >> 345.80 3 Ctl 4 >> 644.61 3 Ctl 5 >> 27.73 3 Ctl 6 >> 56.63 3 Ctl 7 >> 42.63 3 Ctl 8 >> 61.25 3 Ctl 9 >> 59.43 3 Ctl 10 >> 109.87 3 Ctl 11 >> 143.50 1 Trt 1 >> 82.76 1 Trt 2 >> 125.03 1 Trt 3 >> 493.76 1 Trt 4 >> 868.48 1 Trt 5 >> 45.09 1 Trt 6 >> 249.43 1 Trt 7 >> 167.28 1 Trt 8 >> 274.72 1 Trt 9 >> 176.40 1 Trt 10 >> 393.10 1 Trt 11 >> 93.75 2 Trt 1 >> 63.83 2 Trt 2 >> 117.50 2 Trt 3 >> 362.68 2 Trt 4 >> 659.40 2 Trt 5 >> 62.10 2 Trt 6 >> 218.24 2 Trt 7 >> 210.98 2 Trt 8 >> 291.48 2 Trt 9 >> 209.36 2 Trt 10 >> 454.68 2 Trt 11 >> 119.62 3 Trt 1 >> 66.50 3 Trt 2 >> 87.37 3 Trt 3 >> 414.01 3 Trt 4 >> 707.70 3 Trt 5 >> 44.40 3 Trt 6 >> 142.59 3 Trt 7 >> 137.37 3 Trt 8 >> 181.03 3 Trt 9 >> 131.65 3 Trt 10 >> 310.18 3 Trt 11 >> >>> dat1<-read.delim("c:/testcontr.txt", header=T) >>> dat1$treat<-as.factor(dat1$treat) >>> dat1$replicate<-as.factor(dat1$replicate) >>> dat1$section<-as.factor(dat1$section) >>> attach(dat1) >>> obj<-lm(log2(yield)~treat*section) >>> anova(obj) >> Analysis of Variance Table >> >> Response: log2(yield) >> Df Sum Sq Mean Sq F value Pr(>F) >> treat 1 24.608 24.608 297.8649 < 2.2e-16 *** >> section 10 99.761 9.976 120.7565 < 2.2e-16 *** >> treat:section 10 6.708 0.671 8.1197 2.972e-07 *** >> Residuals 44 3.635 0.083 >> --- >> Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 >> >>> contrasts(section)<-c(3,3,3,3,3,3,3,3,-8,-8,-8) >>> objnew<-lm(log2(yield)~treat*section) >>> summary(objnew) >> >> Call: >> lm(formula = log2(yield) ~ treat * section) >> >> Residuals: >> Min 1Q Median 3Q Max >> -0.49647 -0.14913 -0.01521 0.17471 0.51105 >> >> Coefficients: >> Estimate Std. Error t value Pr(>|t|) >> (Intercept) 6.288403 0.050034 125.682 < 2e-16 *** >> treatTrt 1.221219 0.070759 17.259 < 2e-16 *** >> section1 -0.008502 0.010213 -0.832 0.409675 >> section2 -0.491175 0.165945 -2.960 0.004942 ** >> section3 2.569427 0.165945 15.484 < 2e-16 *** >> section4 3.556067 0.165945 21.429 < 2e-16 *** >> section5 -1.157069 0.165945 -6.973 1.25e-08 *** >> section6 -0.003562 0.165945 -0.021 0.982971 >> section7 -0.487770 0.165945 -2.939 0.005223 ** >> section8 0.106181 0.165945 0.640 0.525585 >> section9 -0.776882 0.165945 -4.682 2.74e-05 *** >> section10 0.759168 0.165945 4.575 3.87e-05 *** >> treatTrt:section1 -0.049000 0.014444 -3.392 0.001474 ** >> treatTrt:section2 0.160825 0.234682 0.685 0.496757 >> treatTrt:section3 -0.949101 0.234682 -4.044 0.000208 *** >> treatTrt:section4 -1.118870 0.234682 -4.768 2.07e-05 *** >> treatTrt:section5 -0.295937 0.234682 -1.261 0.213950 >> treatTrt:section6 0.538638 0.234682 2.295 0.026549 * >> treatTrt:section7 0.796518 0.234682 3.394 0.001468 ** >> treatTrt:section8 -0.548744 0.234682 -2.338 0.023984 * >> treatTrt:section9 -0.191029 0.234682 -0.814 0.420033 >> treatTrt:section10 -0.556642 0.234682 -2.372 0.022137 * >> --- >> Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 >> >> Residual standard error: 0.2874 on 44 degrees of freedom >> Multiple R-Squared: 0.973, Adjusted R-squared: 0.9601 >> F-statistic: 75.55 on 21 and 44 DF, p-value: < 2.2e-16 >> >> Thanks, >> Joshua >> >> ______________________________________________ >> R-help@stat.math.ethz.ch 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. > > -------------------------------------------------------------------- > E-Mail: (Ted Harding) <[EMAIL PROTECTED]> > Fax-to-email: +44 (0)870 094 0861 > Date: 24-Aug-06 Time: 21:43:57 > ------------------------------ XFMail ------------------------------ > > ______________________________________________ > R-help@stat.math.ethz.ch 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. > ______________________________________________ R-help@stat.math.ethz.ch 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. ______________________________________________ R-help@stat.math.ethz.ch 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.