From: klebyn > > Hello all R-users > > > _question 1_ > > I need to make a statistical model and respective ANOVA table > but I get distinct results for > > the T-test (in summary(lm.object) function) and > the F-test (in anova(lm.object) ) > > shouldn't this two approach give me the same result, i.e > to indicate the same significants terms in both tests???????
No, because they are not the same tests. The t-tests in summary.lm() test whether the coefficient is zero, when all other terms are present in the model. The F-tests in anova.lm() test the terms by sequentially adding them into the model. Here's an example: > set.seed(1) > d <- data.frame(x1=runif(20), x2=runif(20), y=rnorm(20)) > fm <- lm(y ~ ., d) > summary(fm)$coef Estimate Std. Error t value Pr(>|t|) (Intercept) 1.0187254 0.5534310 1.8407452 0.08318123 x1 -1.6914784 0.6377065 -2.6524404 0.01675543 x2 -0.1817831 0.6618875 -0.2746435 0.78689983 > anova(fm) Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) x1 1 4.2341 4.2341 7.0936 0.01638 * x2 1 0.0450 0.0450 0.0754 0.78690 Residuals 17 10.1472 0.5969 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 > anova(fm2 <- lm(y ~ x2 + x1, d)) Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) x2 1 0.0797 0.0797 0.1336 0.71928 x1 1 4.1994 4.1994 7.0354 0.01676 * Residuals 17 10.1472 0.5969 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Notice how the p-value for x1 in the last output matches that of the t-test: because both are testing if the coefficient for x1 is 0 given that x2 is already in the model. (It's the same reason that the p-value for x2 in the first anova() output matches that of the summary.lm(), but not the second anova() output.) I may be off, but I do not think the restrictions you mentioned have any bearing on the analysis. If x + z is restricted to something _for each case_ then you do have to worry, but not the way you have it. You can choose the independent variables to take on any value you like (as in designed experiments), so such restrictions should not matter. Andy > obs. > > The system has two restrictions: > 1) sum( x_i ) = 1 > 2) sum( z_j ) = 1 > > > > *output below* > > _question 2_ > > > Has I to considerate a SST in ANOVA table with: > > 1) N-2 d.f. because of 2 restrictions? > or > 2) N-1 d.f. because of 1 global restriction: sum( x ) + sum( z ) = 2 ? > > > I don't find any paper, book or another reference, > if someone may to indicate references for this type model (with 2 > restrictions), > I would be very grateful. > > > Thanks a lot. > Regards > > > Cleber N. Borges > > > > ############################### > # OUTPUT > ############################### > > > Coefficients: (1 not defined because of singularities) > Estimate Std. Error t value Pr(>|t|) > (Intercept) 15.5000 0.5270 29.409 2.97e-10 *** > z1:x1 -5.0000 0.7454 -6.708 8.77e-05 *** > z1:x2 0.5000 0.7454 0.671 0.519177 > z1:x3 -3.0000 0.7454 -4.025 0.002996 ** > z2:x1 -6.0000 0.7454 -8.050 2.11e-05 *** > z2:x2 -5.0000 0.7454 -6.708 8.77e-05 *** > z2:x3 -4.5000 0.7454 -6.037 0.000193 *** > z3:x1 1.0000 0.7454 1.342 0.212580 > z3:x2 1.5000 0.7454 2.012 0.075029 . > z3:x3 NA NA NA NA > > Analysis of Variance Table > > Response: y > Df Sum Sq Mean Sq F value Pr(>F) > z1:x1 1 16.674 16.674 30.0125 0.0003910 *** > z1:x2 1 13.580 13.580 24.4446 0.0007977 *** > z1:x3 1 1.190 1.190 2.1429 0.1772677 > z2:x1 1 35.267 35.267 63.4800 2.287e-05 *** > z2:x2 1 32.400 32.400 58.3200 3.202e-05 *** > z2:x3 1 42.667 42.667 76.8000 1.061e-05 *** > z3:x1 1 0.083 0.083 0.1500 0.7075349 > z3:x2 1 2.250 2.250 4.0500 0.0750295 . > Residuals 9 5.000 0.556 > --- > > > > > > ############################### > # DATA > ############################### > > z1 z2 z3 x1 x2 x3 y > 1 0 0 1 0 0 10 > 1 0 0 0 1 0 15 > 1 0 0 0 0 1 12 > 0 1 0 1 0 0 10 > 0 1 0 0 1 0 11 > 0 1 0 0 0 1 11 > 0 0 1 1 0 0 16 > 0 0 1 0 1 0 17 > 0 0 1 0 0 1 15 > 1 0 0 1 0 0 11 > 1 0 0 0 1 0 17 > 1 0 0 0 0 1 13 > 0 1 0 1 0 0 9 > 0 1 0 0 1 0 10 > 0 1 0 0 0 1 11 > 0 0 1 1 0 0 17 > 0 0 1 0 1 0 17 > 0 0 1 0 0 1 16 > > > > ############################### > # CODE > ############################### > > > x = read.table(file("clipboard"),h=T) > > ## NOT a Scheffé Model: > > x.lm <- lm( y ~ (z1+z2+z3):(x1+x2+x3), data=x) > summary(x.lm) > anova(x.lm) > > > ## Scheffé Model: <- IS CORRECT the analysis below? > > x.lm <- lm( y ~ -1 + (z1+z2+z3):(x1+x2+x3), data=x) > summary(x.lm) > > x.aov <- aov( y ~ (z1+z2+z3):(x1+x2+x3), data=x) > summary(x.aov) > > ______________________________________________ > 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 > > ______________________________________________ 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