klebyn klebyn at yahoo.com.br
Fri Jan 27 04:00:04 CET 2006

```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???????

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
###############################

## NOT a Scheffé Model:

x.lm <- lm( y ~ (z1+z2+z3):(x1+x2+x3), data=x)
summary(x.lm)
anova(x.lm)

## Scheffé 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)

```