[R] extracting p-values from Anova objects (from the car library)
John Fox
jfox at mcmaster.ca
Tue Aug 24 00:01:09 CEST 2010
Dear Johan and Dennis,
I believe that the source of confusion is the difference between Anova.lm(),
the Anova method for a linear-model object, which indeed has a summary
method that returns an object from which you can extract p-values, and
Anova.mlm(), which passes the multivariate-linear-model object through (as I
explained in a previous response).
Best,
John
--------------------------------
John Fox
Senator William McMaster
Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of Johan Steen
> Sent: August-23-10 5:36 PM
> To: Dennis Murphy
> Cc: r-help at r-project.org
> Subject: Re: [R] extracting p-values from Anova objects (from the car
> library)
>
> 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.steen at gmail.com
> >> <mailto:johan.steen at 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
> >>
> >> ______________________________________________
> >> R-help at r-project.org <mailto:R-help at r-project.org> 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.
> >>
> >>
>
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