[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.
> >>
> >>
> 
> ______________________________________________
> 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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