Thanks for your replies,
but unfortunately none of them seem to help.
I do get p-values in the output, but can't seem to locate them anywhere
in these objects via the str() function. I also get very different
output using str() than you obtained from the lm help page
Here's my output:
> A <- factor( rep(1:2,each=3) )
> B <- factor( rep(1:3,times=2) )
> idata <- data.frame(A,B)
> idata
A B
1 1 1
2 1 2
3 1 3
4 2 1
5 2 2
6 2 3
>
> fit <- lm( cbind(a1_b1,a1_b2,a1_b3,a2_b1,a2_b2,a2_b3) ~ sex,
data=Data.wide)
> result <- Anova(fit, type="III", test="Wilks", idata=idata, idesign=~A*B)
> result
Type III Repeated Measures MANOVA Tests: Wilks test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.02863 610.81 1 18 2.425e-15
sex 1 0.76040 5.67 1 18 0.02849
A 1 0.91390 1.70 1 18 0.20925
sex:A 1 0.99998 0.00 1 18 0.98536
B 1 0.26946 23.05 2 17 1.443e-05
sex:B 1 0.98394 0.14 2 17 0.87140
A:B 1 0.27478 22.43 2 17 1.704e-05
sex:A:B 1 0.98428 0.14 2 17 0.87397
> summary(result)
Type III Repeated Measures MANOVA Tests:
------------------------------------------
Term: (Intercept)
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 1169345
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.97137 610.8117 1 18 2.425e-15
Wilks 1 0.02863 610.8117 1 18 2.425e-15
Hotelling-Lawley 1 33.93399 610.8117 1 18 2.425e-15
Roy 1 33.93399 610.8117 1 18 2.425e-15
------------------------------------------
Term: sex
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 10857.8
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: sex
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.2395956 5.671614 1 18 0.028486
Wilks 1 0.7604044 5.671614 1 18 0.028486
Hotelling-Lawley 1 0.3150896 5.671614 1 18 0.028486
Roy 1 0.3150896 5.671614 1 18 0.028486
------------------------------------------
Term: A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 980
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0861024 1.695860 1 18 0.20925
Wilks 1 0.9138976 1.695860 1 18 0.20925
Hotelling-Lawley 1 0.0942145 1.695860 1 18 0.20925
Roy 1 0.0942145 1.695860 1 18 0.20925
------------------------------------------
Term: sex:A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 0.2
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: sex:A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0000192 0.0003460939 1 18 0.98536
Wilks 1 0.9999808 0.0003460939 1 18 0.98536
Hotelling-Lawley 1 0.0000192 0.0003460939 1 18 0.98536
Roy 1 0.0000192 0.0003460939 1 18 0.98536
------------------------------------------
Term: B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 3618.05 3443.2
B2 3443.20 3276.8
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.730544 23.04504 2 17 1.4426e-05
Wilks 1 0.269456 23.04504 2 17 1.4426e-05
Hotelling-Lawley 1 2.711181 23.04504 2 17 1.4426e-05
Roy 1 2.711181 23.04504 2 17 1.4426e-05
------------------------------------------
Term: sex:B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 26.45 23
B2 23.00 20
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: sex:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0160644 0.1387764 2 17 0.8714
Wilks 1 0.9839356 0.1387764 2 17 0.8714
Hotelling-Lawley 1 0.0163266 0.1387764 2 17 0.8714
Roy 1 0.0163266 0.1387764 2 17 0.8714
------------------------------------------
Term: A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 5152.05 738.3
A1:B2 738.30 105.8
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.7252156 22.43334 2 17 1.7039e-05
Wilks 1 0.2747844 22.43334 2 17 1.7039e-05
Hotelling-Lawley 1 2.6392162 22.43334 2 17 1.7039e-05
Roy 1 2.6392162 22.43334 2 17 1.7039e-05
------------------------------------------
Term: sex:A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 26.45 2.3
A1:B2 2.30 0.2
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: sex:A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0157232 0.1357821 2 17 0.87397
Wilks 1 0.9842768 0.1357821 2 17 0.87397
Hotelling-Lawley 1 0.0159744 0.1357821 2 17 0.87397
Roy 1 0.0159744 0.1357821 2 17 0.87397
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 194891 1 5743.2 18 610.8117 2.425e-15
sex 1810 1 5743.2 18 5.6716 0.02849
A 163 1 1733.6 18 1.6959 0.20925
sex:A 0 1 1733.6 18 0.0003 0.98536
B 1151 2 711.0 36 29.1292 2.990e-08
sex:B 8 2 711.0 36 0.1979 0.82134
A:B 1507 2 933.4 36 29.0532 3.078e-08
sex:A:B 8 2 933.4 36 0.1565 0.85568
Mauchly Tests for Sphericity
Test statistic p-value
B 0.57532 0.0091036
sex:B 0.57532 0.0091036
A:B 0.45375 0.0012104
sex:A:B 0.45375 0.0012104
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
B 0.70191 2.143e-06
sex:B 0.70191 0.7427
A:B 0.64672 4.838e-06
sex:A:B 0.64672 0.7599
HF eps Pr(>F[HF])
B 0.74332 1.181e-06
sex:B 0.74332 0.7560
A:B 0.67565 3.191e-06
sex:A:B 0.67565 0.7702
> str(result)
List of 13
$ SSP :List of 8
..$ (Intercept): num [1, 1] 1169345
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 10858
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 980
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 3618 3443 3443 3277
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 26.4 23 23 20
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 5152 738 738 106
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 26.4 2.3 2.3 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ SSPE :List of 8
..$ (Intercept): num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ P :List of 8
..$ (Intercept): num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ sex:A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ df : Named num [1:8] 1 1 1 1 1 1 1 1
..- attr(*, "names")= chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ error.df : int 18
$ terms : chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ repeated : logi TRUE
$ type : chr "III"
$ test : chr "Wilks"
$ idata :'data.frame': 6 obs. of 2 variables:
..$ A: Factor w/ 2 levels "1","2": 1 1 1 2 2 2
.. ..- attr(*, "contrasts")= chr "contr.sum"
..$ B: Factor w/ 3 levels "1","2","3": 1 2 3 1 2 3
.. ..- attr(*, "contrasts")= chr "contr.sum"
$ idesign :Class 'formula' length 2 ~A * B
.. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
$ icontrasts: chr [1:2] "contr.sum" "contr.poly"
$ imatrix : NULL
- attr(*, "class")= chr "Anova.mlm"
> str(summary(result))
Type III Repeated Measures MANOVA Tests:
------------------------------------------
Term: (Intercept)
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 1169345
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.97137 610.8117 1 18 2.425e-15
Wilks 1 0.02863 610.8117 1 18 2.425e-15
Hotelling-Lawley 1 33.93399 610.8117 1 18 2.425e-15
Roy 1 33.93399 610.8117 1 18 2.425e-15
------------------------------------------
Term: sex
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 10857.8
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: sex
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.2395956 5.671614 1 18 0.028486
Wilks 1 0.7604044 5.671614 1 18 0.028486
Hotelling-Lawley 1 0.3150896 5.671614 1 18 0.028486
Roy 1 0.3150896 5.671614 1 18 0.028486
------------------------------------------
Term: A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 980
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0861024 1.695860 1 18 0.20925
Wilks 1 0.9138976 1.695860 1 18 0.20925
Hotelling-Lawley 1 0.0942145 1.695860 1 18 0.20925
Roy 1 0.0942145 1.695860 1 18 0.20925
------------------------------------------
Term: sex:A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 0.2
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: sex:A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0000192 0.0003460939 1 18 0.98536
Wilks 1 0.9999808 0.0003460939 1 18 0.98536
Hotelling-Lawley 1 0.0000192 0.0003460939 1 18 0.98536
Roy 1 0.0000192 0.0003460939 1 18 0.98536
------------------------------------------
Term: B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 3618.05 3443.2
B2 3443.20 3276.8
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.730544 23.04504 2 17 1.4426e-05
Wilks 1 0.269456 23.04504 2 17 1.4426e-05
Hotelling-Lawley 1 2.711181 23.04504 2 17 1.4426e-05
Roy 1 2.711181 23.04504 2 17 1.4426e-05
------------------------------------------
Term: sex:B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 26.45 23
B2 23.00 20
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: sex:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0160644 0.1387764 2 17 0.8714
Wilks 1 0.9839356 0.1387764 2 17 0.8714
Hotelling-Lawley 1 0.0163266 0.1387764 2 17 0.8714
Roy 1 0.0163266 0.1387764 2 17 0.8714
------------------------------------------
Term: A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 5152.05 738.3
A1:B2 738.30 105.8
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.7252156 22.43334 2 17 1.7039e-05
Wilks 1 0.2747844 22.43334 2 17 1.7039e-05
Hotelling-Lawley 1 2.6392162 22.43334 2 17 1.7039e-05
Roy 1 2.6392162 22.43334 2 17 1.7039e-05
------------------------------------------
Term: sex:A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 26.45 2.3
A1:B2 2.30 0.2
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: sex:A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0157232 0.1357821 2 17 0.87397
Wilks 1 0.9842768 0.1357821 2 17 0.87397
Hotelling-Lawley 1 0.0159744 0.1357821 2 17 0.87397
Roy 1 0.0159744 0.1357821 2 17 0.87397
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 194891 1 5743.2 18 610.8117 2.425e-15
sex 1810 1 5743.2 18 5.6716 0.02849
A 163 1 1733.6 18 1.6959 0.20925
sex:A 0 1 1733.6 18 0.0003 0.98536
B 1151 2 711.0 36 29.1292 2.990e-08
sex:B 8 2 711.0 36 0.1979 0.82134
A:B 1507 2 933.4 36 29.0532 3.078e-08
sex:A:B 8 2 933.4 36 0.1565 0.85568
Mauchly Tests for Sphericity
Test statistic p-value
B 0.57532 0.0091036
sex:B 0.57532 0.0091036
A:B 0.45375 0.0012104
sex:A:B 0.45375 0.0012104
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
B 0.70191 2.143e-06
sex:B 0.70191 0.7427
A:B 0.64672 4.838e-06
sex:A:B 0.64672 0.7599
HF eps Pr(>F[HF])
B 0.74332 1.181e-06
sex:B 0.74332 0.7560
A:B 0.67565 3.191e-06
sex:A:B 0.67565 0.7702
List of 13
$ SSP :List of 8
..$ (Intercept): num [1, 1] 1169345
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 10858
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 980
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 3618 3443 3443 3277
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 26.4 23 23 20
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 5152 738 738 106
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 26.4 2.3 2.3 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ SSPE :List of 8
..$ (Intercept): num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ P :List of 8
..$ (Intercept): num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ sex:A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ df : Named num [1:8] 1 1 1 1 1 1 1 1
..- attr(*, "names")= chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ error.df : int 18
$ terms : chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ repeated : logi TRUE
$ type : chr "III"
$ test : chr "Wilks"
$ idata :'data.frame': 6 obs. of 2 variables:
..$ A: Factor w/ 2 levels "1","2": 1 1 1 2 2 2
.. ..- attr(*, "contrasts")= chr "contr.sum"
..$ B: Factor w/ 3 levels "1","2","3": 1 2 3 1 2 3
.. ..- attr(*, "contrasts")= chr "contr.sum"
$ idesign :Class 'formula' length 2 ~A * B
.. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
$ icontrasts: chr [1:2] "contr.sum" "contr.poly"
$ imatrix : NULL
- attr(*, "class")= chr "Anova.mlm"
> result$`Pr(>F)`
NULL
> result[[4]]
(Intercept) sex A sex:A B sex:B
1 1 1 1 1 1
A:B sex:A:B
1 1
>
Op 23/08/2010 22:23, Johan Steen schreef:
Thanks for your replies,
but unfortunately none of them seem to help.
I do get p-values in the output, but can't seem to locate them anywhere
in these objects via the str() function. I also get very different
output using str() than you obtained from the lm help page
Here's my output:
> A <- factor( rep(1:2,each=3) )
> B <- factor( rep(1:3,times=2) )
> idata <- data.frame(A,B)
> idata
A B
1 1 1
2 1 2
3 1 3
4 2 1
5 2 2
6 2 3
>
> fit <- lm( cbind(a1_b1,a1_b2,a1_b3,a2_b1,a2_b2,a2_b3) ~ sex,
data=Data.wide)
> result <- Anova(fit, type="III", test="Wilks", idata=idata,
idesign=~A*B)
> result
Type III Repeated Measures MANOVA Tests: Wilks test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.02863 610.81 1 18 2.425e-15
sex 1 0.76040 5.67 1 18 0.02849
A 1 0.91390 1.70 1 18 0.20925
sex:A 1 0.99998 0.00 1 18 0.98536
B 1 0.26946 23.05 2 17 1.443e-05
sex:B 1 0.98394 0.14 2 17 0.87140
A:B 1 0.27478 22.43 2 17 1.704e-05
sex:A:B 1 0.98428 0.14 2 17 0.87397
> summary(result)
Type III Repeated Measures MANOVA Tests:
------------------------------------------
Term: (Intercept)
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 1169345
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.97137 610.8117 1 18 2.425e-15
Wilks 1 0.02863 610.8117 1 18 2.425e-15
Hotelling-Lawley 1 33.93399 610.8117 1 18 2.425e-15
Roy 1 33.93399 610.8117 1 18 2.425e-15
------------------------------------------
Term: sex
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 10857.8
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: sex
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.2395956 5.671614 1 18 0.028486
Wilks 1 0.7604044 5.671614 1 18 0.028486
Hotelling-Lawley 1 0.3150896 5.671614 1 18 0.028486
Roy 1 0.3150896 5.671614 1 18 0.028486
------------------------------------------
Term: A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 980
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0861024 1.695860 1 18 0.20925
Wilks 1 0.9138976 1.695860 1 18 0.20925
Hotelling-Lawley 1 0.0942145 1.695860 1 18 0.20925
Roy 1 0.0942145 1.695860 1 18 0.20925
------------------------------------------
Term: sex:A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 0.2
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: sex:A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0000192 0.0003460939 1 18 0.98536
Wilks 1 0.9999808 0.0003460939 1 18 0.98536
Hotelling-Lawley 1 0.0000192 0.0003460939 1 18 0.98536
Roy 1 0.0000192 0.0003460939 1 18 0.98536
------------------------------------------
Term: B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 3618.05 3443.2
B2 3443.20 3276.8
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.730544 23.04504 2 17 1.4426e-05
Wilks 1 0.269456 23.04504 2 17 1.4426e-05
Hotelling-Lawley 1 2.711181 23.04504 2 17 1.4426e-05
Roy 1 2.711181 23.04504 2 17 1.4426e-05
------------------------------------------
Term: sex:B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 26.45 23
B2 23.00 20
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: sex:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0160644 0.1387764 2 17 0.8714
Wilks 1 0.9839356 0.1387764 2 17 0.8714
Hotelling-Lawley 1 0.0163266 0.1387764 2 17 0.8714
Roy 1 0.0163266 0.1387764 2 17 0.8714
------------------------------------------
Term: A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 5152.05 738.3
A1:B2 738.30 105.8
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.7252156 22.43334 2 17 1.7039e-05
Wilks 1 0.2747844 22.43334 2 17 1.7039e-05
Hotelling-Lawley 1 2.6392162 22.43334 2 17 1.7039e-05
Roy 1 2.6392162 22.43334 2 17 1.7039e-05
------------------------------------------
Term: sex:A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 26.45 2.3
A1:B2 2.30 0.2
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: sex:A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0157232 0.1357821 2 17 0.87397
Wilks 1 0.9842768 0.1357821 2 17 0.87397
Hotelling-Lawley 1 0.0159744 0.1357821 2 17 0.87397
Roy 1 0.0159744 0.1357821 2 17 0.87397
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 194891 1 5743.2 18 610.8117 2.425e-15
sex 1810 1 5743.2 18 5.6716 0.02849
A 163 1 1733.6 18 1.6959 0.20925
sex:A 0 1 1733.6 18 0.0003 0.98536
B 1151 2 711.0 36 29.1292 2.990e-08
sex:B 8 2 711.0 36 0.1979 0.82134
A:B 1507 2 933.4 36 29.0532 3.078e-08
sex:A:B 8 2 933.4 36 0.1565 0.85568
Mauchly Tests for Sphericity
Test statistic p-value
B 0.57532 0.0091036
sex:B 0.57532 0.0091036
A:B 0.45375 0.0012104
sex:A:B 0.45375 0.0012104
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
B 0.70191 2.143e-06
sex:B 0.70191 0.7427
A:B 0.64672 4.838e-06
sex:A:B 0.64672 0.7599
HF eps Pr(>F[HF])
B 0.74332 1.181e-06
sex:B 0.74332 0.7560
A:B 0.67565 3.191e-06
sex:A:B 0.67565 0.7702
> str(result)
List of 13
$ SSP :List of 8
..$ (Intercept): num [1, 1] 1169345
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 10858
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 980
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 3618 3443 3443 3277
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 26.4 23 23 20
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 5152 738 738 106
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 26.4 2.3 2.3 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ SSPE :List of 8
..$ (Intercept): num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ P :List of 8
..$ (Intercept): num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ sex:A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ df : Named num [1:8] 1 1 1 1 1 1 1 1
..- attr(*, "names")= chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ error.df : int 18
$ terms : chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ repeated : logi TRUE
$ type : chr "III"
$ test : chr "Wilks"
$ idata :'data.frame': 6 obs. of 2 variables:
..$ A: Factor w/ 2 levels "1","2": 1 1 1 2 2 2
.. ..- attr(*, "contrasts")= chr "contr.sum"
..$ B: Factor w/ 3 levels "1","2","3": 1 2 3 1 2 3
.. ..- attr(*, "contrasts")= chr "contr.sum"
$ idesign :Class 'formula' length 2 ~A * B
.. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
$ icontrasts: chr [1:2] "contr.sum" "contr.poly"
$ imatrix : NULL
- attr(*, "class")= chr "Anova.mlm"
> str(summary(result))
Type III Repeated Measures MANOVA Tests:
------------------------------------------
Term: (Intercept)
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 1169345
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.97137 610.8117 1 18 2.425e-15
Wilks 1 0.02863 610.8117 1 18 2.425e-15
Hotelling-Lawley 1 33.93399 610.8117 1 18 2.425e-15
Roy 1 33.93399 610.8117 1 18 2.425e-15
------------------------------------------
Term: sex
Response transformation matrix:
(Intercept)
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 1
a2_b2 1
a2_b3 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 10857.8
Sum of squares and products for error:
(Intercept)
(Intercept) 34459.4
Multivariate Tests: sex
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.2395956 5.671614 1 18 0.028486
Wilks 1 0.7604044 5.671614 1 18 0.028486
Hotelling-Lawley 1 0.3150896 5.671614 1 18 0.028486
Roy 1 0.3150896 5.671614 1 18 0.028486
------------------------------------------
Term: A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 980
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0861024 1.695860 1 18 0.20925
Wilks 1 0.9138976 1.695860 1 18 0.20925
Hotelling-Lawley 1 0.0942145 1.695860 1 18 0.20925
Roy 1 0.0942145 1.695860 1 18 0.20925
------------------------------------------
Term: sex:A
Response transformation matrix:
A1
a1_b1 1
a1_b2 1
a1_b3 1
a2_b1 -1
a2_b2 -1
a2_b3 -1
Sum of squares and products for the hypothesis:
A1
A1 0.2
Sum of squares and products for error:
A1
A1 10401.8
Multivariate Tests: sex:A
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0000192 0.0003460939 1 18 0.98536
Wilks 1 0.9999808 0.0003460939 1 18 0.98536
Hotelling-Lawley 1 0.0000192 0.0003460939 1 18 0.98536
Roy 1 0.0000192 0.0003460939 1 18 0.98536
------------------------------------------
Term: B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 3618.05 3443.2
B2 3443.20 3276.8
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.730544 23.04504 2 17 1.4426e-05
Wilks 1 0.269456 23.04504 2 17 1.4426e-05
Hotelling-Lawley 1 2.711181 23.04504 2 17 1.4426e-05
Roy 1 2.711181 23.04504 2 17 1.4426e-05
------------------------------------------
Term: sex:B
Response transformation matrix:
B1 B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 1 0
a2_b2 0 1
a2_b3 -1 -1
Sum of squares and products for the hypothesis:
B1 B2
B1 26.45 23
B2 23.00 20
Sum of squares and products for error:
B1 B2
B1 2304.5 1396.8
B2 1396.8 1225.2
Multivariate Tests: sex:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0160644 0.1387764 2 17 0.8714
Wilks 1 0.9839356 0.1387764 2 17 0.8714
Hotelling-Lawley 1 0.0163266 0.1387764 2 17 0.8714
Roy 1 0.0163266 0.1387764 2 17 0.8714
------------------------------------------
Term: A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 5152.05 738.3
A1:B2 738.30 105.8
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.7252156 22.43334 2 17 1.7039e-05
Wilks 1 0.2747844 22.43334 2 17 1.7039e-05
Hotelling-Lawley 1 2.6392162 22.43334 2 17 1.7039e-05
Roy 1 2.6392162 22.43334 2 17 1.7039e-05
------------------------------------------
Term: sex:A:B
Response transformation matrix:
A1:B1 A1:B2
a1_b1 1 0
a1_b2 0 1
a1_b3 -1 -1
a2_b1 -1 0
a2_b2 0 -1
a2_b3 1 1
Sum of squares and products for the hypothesis:
A1:B1 A1:B2
A1:B1 26.45 2.3
A1:B2 2.30 0.2
Sum of squares and products for error:
A1:B1 A1:B2
A1:B1 3210.5 1334.4
A1:B2 1334.4 924.0
Multivariate Tests: sex:A:B
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.0157232 0.1357821 2 17 0.87397
Wilks 1 0.9842768 0.1357821 2 17 0.87397
Hotelling-Lawley 1 0.0159744 0.1357821 2 17 0.87397
Roy 1 0.0159744 0.1357821 2 17 0.87397
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
SS num Df Error SS den Df F Pr(>F)
(Intercept) 194891 1 5743.2 18 610.8117 2.425e-15
sex 1810 1 5743.2 18 5.6716 0.02849
A 163 1 1733.6 18 1.6959 0.20925
sex:A 0 1 1733.6 18 0.0003 0.98536
B 1151 2 711.0 36 29.1292 2.990e-08
sex:B 8 2 711.0 36 0.1979 0.82134
A:B 1507 2 933.4 36 29.0532 3.078e-08
sex:A:B 8 2 933.4 36 0.1565 0.85568
Mauchly Tests for Sphericity
Test statistic p-value
B 0.57532 0.0091036
sex:B 0.57532 0.0091036
A:B 0.45375 0.0012104
sex:A:B 0.45375 0.0012104
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
B 0.70191 2.143e-06
sex:B 0.70191 0.7427
A:B 0.64672 4.838e-06
sex:A:B 0.64672 0.7599
HF eps Pr(>F[HF])
B 0.74332 1.181e-06
sex:B 0.74332 0.7560
A:B 0.67565 3.191e-06
sex:A:B 0.67565 0.7702
List of 13
$ SSP :List of 8
..$ (Intercept): num [1, 1] 1169345
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 10858
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 980
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 3618 3443 3443 3277
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 26.4 23 23 20
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 5152 738 738 106
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 26.4 2.3 2.3 0.2
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ SSPE :List of 8
..$ (Intercept): num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1, 1] 34459
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "(Intercept)"
.. .. ..$ : chr "(Intercept)"
..$ A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ sex:A : num [1, 1] 10402
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr "A1"
.. .. ..$ : chr "A1"
..$ B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:2, 1:2] 2304 1397 1397 1225
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "B1" "B2"
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:2, 1:2] 3210 1334 1334 924
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ P :List of 8
..$ (Intercept): num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ sex : num [1:6, 1] 1 1 1 1 1 1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "(Intercept)"
..$ A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ sex:A : num [1:6, 1] 1 1 1 -1 -1 -1
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr "A1"
..$ B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ sex:B : num [1:6, 1:2] 1 0 -1 1 0 -1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "B1" "B2"
..$ A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
..$ sex:A:B : num [1:6, 1:2] 1 0 -1 -1 0 1 0 1 -1 0 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : chr [1:6] "a1_b1" "a1_b2" "a1_b3" "a2_b1" ...
.. .. ..$ : chr [1:2] "A1:B1" "A1:B2"
$ df : Named num [1:8] 1 1 1 1 1 1 1 1
..- attr(*, "names")= chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ error.df : int 18
$ terms : chr [1:8] "(Intercept)" "sex" "A" "sex:A" ...
$ repeated : logi TRUE
$ type : chr "III"
$ test : chr "Wilks"
$ idata :'data.frame': 6 obs. of 2 variables:
..$ A: Factor w/ 2 levels "1","2": 1 1 1 2 2 2
.. ..- attr(*, "contrasts")= chr "contr.sum"
..$ B: Factor w/ 3 levels "1","2","3": 1 2 3 1 2 3
.. ..- attr(*, "contrasts")= chr "contr.sum"
$ idesign :Class 'formula' length 2 ~A * B
.. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
$ icontrasts: chr [1:2] "contr.sum" "contr.poly"
$ imatrix : NULL
- attr(*, "class")= chr "Anova.mlm"
> result$`Pr(>F)`
NULL
> result[[4]]
(Intercept) sex A sex:A B sex:B
1 1 1 1 1 1
A:B sex:A:B
1 1
>
Op 23/08/2010 21:56, Dennis Murphy schreef:
Hi:
Look at
result$`Pr(>F)`
(with backticks around Pr(>F) ), or more succinctly, result[[4]].
HTH,
Dennis
On Mon, Aug 23, 2010 at 12:01 PM, Johan Steen <johan.st...@gmail.com
<mailto:johan.st...@gmail.com>> wrote:
Dear all,
is there anyone who can help me extracting p-values from an Anova
object from the car library? I can't seem to locate the p-values
using str(result) or str(summary(result)) in the example below
> A <- factor( rep(1:2,each=3) )
> B <- factor( rep(1:3,times=2) )
> idata <- data.frame(A,B)
> fit <- lm( cbind(a1_b1,a1_b2,a1_b3,a2_b1,a2_b2,a2_b3) ˜ sex,
data=Data.wide)
> result <- Anova(fit, type="III", test="Wilks", idata=idata,
idesign=˜A*B)
Any help would be much appreciated!
Many thanks,
Johan
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