aov.car: Convenience wrappers for car::Anova using either a formula or...
In afe: Analysis of Factorial Experiments
Description
Usage
Arguments
Details
Value
Note
Author(s)
See Also
Examples
Description
These functions allow convenient access to
Anova (from the car package) for
data in the long format (i.e., one observation
per row), possibly aggregating the data if there is more
than one obersvation per individuum and cell. Hence,
mixed between-within ANOVAs can be calculated
conveniently without using the rather unhandy format of
car::Anova. aov.car can be called using a
formula similar to aov specifying an error
strata for the within-subject factor(s). ez.glm is
called specifying the factors as character vectors.
Usage
1
2
3
4
5
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7
8
Arguments
formula
A formula specifying the ANOVA model
similar to aov. Should include an error
term (i.e., Error( / )). Note that the
within-subject factors do not need to be outside the
Error term (this contrasts with aov). See
Details.
id
character vector (of length 1)
indicating the subject identifier column in data.
dv
character vector (of length 1)
indicating the column containing the dependent
variable in data.
between
character vector indicating the
between-subject(s) factor(s)/column(s) in
data. Default is NULL indicating no
between-subjects factors.
within
character vector indicating the
within-subject(s) factor(s)/column(s) in
data. Default is NULL indicating no
within-subjects factors.
covariate
character vector indicating the
between-subject(s) covariate(s) (i.e., column(s)) in
data. Default is NULL indicating no
covariates.
data
A data.frame containing the data.
Mandatory.
fun.aggregate
The function for aggregating the
data before running the ANOVA if there is more than one
obervation per individuum and cell of the design. The
default NULL issues a warning if aggregation is
necessary and uses mean.
type
The type of sums of squares for the ANOVA.
Defaults to 3. Passed to
Anova. Possible values are
"II", "III", 2, or 3.
print.formula
ez.glm is a wrapper for
aov.car. This boolean argument indicates whether
the formula in the call to car.aov should be
printed.
...
Further arguments passed to
fun.aggregate.
object
An object of class Anova.mlm as
returned by aov.car, ez.glm, or
Anova.
Details
Type 3 sums of squares are default in afe.
Note that type 3 sums of squares are said to be dangerous
and/or problematic. On the other side they are the
default in in SPSS and SAS and recommended by e.g.
Maxwell and Delaney (2003). For a brief discussion see
here.
However, note that lower order effects (e.g., main
effects) in type 3 ANOVAs are only meaningful with
effects
coding. That is, contrasts should be set to
contr.sum via
options(contrasts=c('contr.sum','contr.poly')).
This should be done automatically when loading afe
and afe will issue a warning when running type 3 SS
and
other
coding schemes. You can check the coding with
options("contrasts").
The formula for aov.car must contain a
single Error term specyfying the ID column
and potential within-subject factors. Factors outside the
Error term are treated as between-subject factors
(the within-subject factors specified in the Error
term are ignored outside the Error term, i.e., it
is not necessary to specify them outside the Error
term, see Examples). Suppressing the intercept (i.e, via
0 + or - 1) is ignored. Specific
specifications of effects (e.g., excluding terms with
- or using ^) should be functional. Using
the I or poly function within
the formula is not tested and not supported!
For ez.glm either between or within
must not be NULL.
ez.glm will concatante all between-subject factors
using * (i.e., producing all main effects and
interactions) and all covariates by + (i.e.,
adding only the main effects to the existing
between-subject factors). The within-subject factors do
fully interact with all between-subject factors and
covariates. This is essentially identical to the behavior
of SPSS's glm function.
Value
aov.car and ez.glm are wrappers and
therfore return the same as Anova.
Usually an object of class "Anova.mlm" (with
within-subjects factors) or c("anova",
"data.frame").
univariate returns a list of
data.frames containing the univariate results
(i.e., the classical ANOVA results) from an object of
class "Anova.mlm". This is essentially the output
from summary.Anova.mlm with multivariate =
FALSE, e.g. summary(aov.car(...), multivriate =
FALSE), as a list instead of printed to the console.
For objects of class "anova" (i.e., the object
returned by car::Anova for a purely
between-subjects ANOVA) the object is returned unaltered.
The elements of the list returned by univariate
are: anova, mauchly, and
spehricity.correction (containing both,
Greenhouse-Geisser and Hyundt-Feldt correction).
Note
Variables entered as within-subjects (i.e., repeated
measures) factors are silently converted to factors and
unused levels dropped.
Contrasts attached to a factor as an attribute are
probably not preserved and not supported.
Author(s)
univariate is basically a copy of
summary.Anova.mlm written by John
Fox.
The other functions were written by Henrik
Singmann.
See Also
nice.anova is a function for creating nice
ANOVA tables (including sphercitiy corrections) from
objects returned by ez.glm and aov.car.
obk.long describes the long version of the
OBrienKaiser dataset used in the examples.
Examples
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# exampel using obk.long (see ?obk.long), a long version of the OBrienKaiser dataset from car.
data(obk.long)
# run univariate mixed ANCOVA for the full design:
univariate(aov.car(value ~ treatment * gender + age + Error(id/phase*hour), data = obk.long))
univariate(ez.glm("id", "value", obk.long, c("treatment", "gender"), c("phase", "hour"), "age"))
# both calls return the same:
## $anova
## SS num Df Error SS den Df F Pr(>F)
## (Intercept) 6454.236987 1 215.65658 9 269.3547893 5.152317e-08
## treatment 171.399953 2 215.65658 9 3.5765187 7.193619e-02
## gender 94.598340 1 215.65658 9 3.9478742 7.818280e-02
## age 12.398975 1 215.65658 9 0.5174466 4.901885e-01
## treatment:gender 61.531858 2 215.65658 9 1.2839551 3.231798e-01
## phase 134.586005 2 59.72439 18 20.2810632 2.448505e-05
## treatment:phase 80.604542 4 59.72439 18 6.0732385 2.826803e-03
## gender:phase 1.634246 2 59.72439 18 0.2462681 7.843036e-01
## age:phase 20.553392 2 59.72439 18 3.0972362 6.982439e-02
## treatment:gender:phase 21.254421 4 59.72439 18 1.6014379 2.170946e-01
## hour 108.513510 4 47.59543 36 20.5192290 7.001584e-09
## treatment:hour 7.547869 8 47.59543 36 0.7136275 6.779072e-01
## gender:hour 3.746135 4 47.59543 36 0.7083708 5.915285e-01
## age:hour 14.904567 4 47.59543 36 2.8183608 3.926421e-02
## treatment:gender:hour 6.235198 8 47.59543 36 0.5895186 7.798264e-01
## phase:hour 9.762579 8 88.62706 72 0.9913814 4.501348e-01
## treatment:phase:hour 6.579092 16 88.62706 72 0.3340505 9.915014e-01
## gender:phase:hour 8.851396 8 88.62706 72 0.8988515 5.222336e-01
## age:phase:hour 7.539611 8 88.62706 72 0.7656409 6.339004e-01
## treatment:gender:phase:hour 12.822199 16 88.62706 72 0.6510416 8.307936e-01
##
## $mauchly
## Test statistic p-value
## phase 0.8217571566 0.45600959
## treatment:phase 0.8217571566 0.45600959
## gender:phase 0.8217571566 0.45600959
## age:phase 0.8217571566 0.45600959
## treatment:gender:phase 0.8217571566 0.45600959
## hour 0.0966749877 0.04923980
## treatment:hour 0.0966749877 0.04923980
## gender:hour 0.0966749877 0.04923980
## age:hour 0.0966749877 0.04923980
## treatment:gender:hour 0.0966749877 0.04923980
## phase:hour 0.0002379741 0.08651564
## treatment:phase:hour 0.0002379741 0.08651564
## gender:phase:hour 0.0002379741 0.08651564
## age:phase:hour 0.0002379741 0.08651564
## treatment:gender:phase:hour 0.0002379741 0.08651564
##
## $sphericity.correction
## GG eps Pr(>F[GG]) HF eps Pr(>F[HF])
## phase 0.8487215 8.383485e-05 1.0252867 2.448505e-05
## treatment:phase 0.8487215 5.159591e-03 1.0252867 2.826803e-03
## gender:phase 0.8487215 7.493990e-01 1.0252867 7.843036e-01
## age:phase 0.8487215 8.073373e-02 1.0252867 6.982439e-02
## treatment:gender:phase 0.8487215 2.279698e-01 1.0252867 2.170946e-01
## hour 0.5341747 1.302016e-05 0.7054545 8.046331e-07
## treatment:hour 0.5341747 6.010781e-01 0.7054545 6.342676e-01
## gender:hour 0.5341747 5.137213e-01 0.7054545 5.478398e-01
## age:hour 0.5341747 8.155027e-02 0.7054545 6.211130e-02
## treatment:gender:hour 0.5341747 6.843526e-01 0.7054545 7.263729e-01
## phase:hour 0.4355822 4.186799e-01 0.7444364 4.402119e-01
## treatment:phase:hour 0.4355822 9.317848e-01 0.7444364 9.787985e-01
## gender:phase:hour 0.4355822 4.651930e-01 0.7444364 5.020890e-01
## age:phase:hour 0.4355822 5.395151e-01 0.7444364 5.992844e-01
## treatment:gender:phase:hour 0.4355822 7.100921e-01 0.7444364 7.878433e-01
##
## Warning message:
## In univariate(aov.car(value ~ treatment * gender + age + Error(id/phase * :
## HF eps > 1 treated as 1
# To get a nicer ANOVA table use function nice.anova (see ?noce.anova):
nice.anova(ez.glm("id", "value", obk.long, c("treatment", "gender"), c("phase", "hour"), "age"))
## Effect df MSE F p
## 1 treatment 2, 9 23.96 3.58 + .07
## 2 gender 1, 9 23.96 3.95 + .08
## 3 age 1, 9 23.96 0.52 .49
## 4 treatment:gender 2, 9 23.96 1.28 .32
## 5 phase 1.7, 15.28 3.91 20.28 *** <.001
## 6 treatment:phase 3.39, 15.28 3.91 6.07 ** .005
## 7 gender:phase 1.7, 15.28 3.91 0.25 .75
## 8 age:phase 1.7, 15.28 3.91 3.10 + .08
## 9 treatment:gender:phase 3.39, 15.28 3.91 1.60 .23
## 10 hour 2.14, 19.23 2.48 20.52 *** <.001
## 11 treatment:hour 4.27, 19.23 2.48 0.71 .60
## 12 gender:hour 2.14, 19.23 2.48 0.71 .51
## 13 age:hour 2.14, 19.23 2.48 2.82 + .08
## 14 treatment:gender:hour 4.27, 19.23 2.48 0.59 .68
## 15 phase:hour 3.48, 31.36 2.83 0.99 .42
## 16 treatment:phase:hour 6.97, 31.36 2.83 0.33 .93
## 17 gender:phase:hour 3.48, 31.36 2.83 0.90 .47
## 18 age:phase:hour 3.48, 31.36 2.83 0.77 .54
## 19 treatment:gender:phase:hour 6.97, 31.36 2.83 0.65 .71
# replicating ?Anova using aov.car:
aov.car(value ~ treatment * gender + Error(id/phase*hour), data = obk.long, type = 2)
# in contrast to aov you do not need the within-subject factors outside Error()
# replicating ?Anova using ez.glm:
ez.glm("id", "value", obk.long, c("treatment", "gender"), c("phase", "hour"), type = 2)
#both return:
## Type II Repeated Measures MANOVA Tests: Pillai test statistic
## Df test stat approx F num Df den Df Pr(>F)
## (Intercept) 1 0.970 318 1 10 0.0000000065 ***
## treatment 2 0.481 5 2 10 0.03769 *
## gender 1 0.204 3 1 10 0.14097
## treatment:gender 2 0.364 3 2 10 0.10447
## phase 1 0.851 26 2 9 0.00019 ***
## treatment:phase 2 0.685 3 4 20 0.06674 .
## gender:phase 1 0.043 0 2 9 0.82000
## treatment:gender:phase 2 0.311 1 4 20 0.47215
## hour 1 0.935 25 4 7 0.00030 ***
## treatment:hour 2 0.301 0 8 16 0.92952
## gender:hour 1 0.293 1 4 7 0.60237
## treatment:gender:hour 2 0.570 1 8 16 0.61319
## phase:hour 1 0.550 0 8 3 0.83245
## treatment:phase:hour 2 0.664 0 16 8 0.99144
## gender:phase:hour 1 0.695 1 8 3 0.62021
## treatment:gender:phase:hour 2 0.793 0 16 8 0.97237
## ---
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# aggregating over one within-subjects factor (phase) with warning:
aov.car(value ~ treatment * gender + age + Error(id/hour), data = obk.long)
ez.glm("id", "value", obk.long, c("treatment", "gender"), "hour", "age")
# runs with "numeric" factors
obk.long$hour2 <- as.numeric(as.character(obk.long$hour))
aov.car(value ~ treatment * gender + Error(id/hour2), data = obk.long, type = 2)
# only between
aov.car(value ~ treatment * gender + age + Error(id), data = obk.long, type = 2)
aov.car(value ~ treatment * gender + Error(id), data = obk.long, type = 2)
ez.glm("id", "value", obk.long, c("treatment", "gender"), within = NULL, covariate = "age", type = 2, print.formula = TRUE)
ez.glm("id", "value", obk.long, c("treatment", "gender"), within = NULL, type = 2, print.formula = TRUE)
# only within
univariate(aov.car(value ~ Error(id/phase*hour), data = obk.long, type = 2))
univariate(ez.glm("id", "value", obk.long, NULL, c("phase", "hour"), type = 2, print.formula = TRUE))
afe documentation built on May 2, 2019, 4:48 p.m.
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Description Usage Arguments Details Value Note Author(s) See Also Examples
Description
These functions allow convenient access to
Anova (from the car package) for
data in the long format (i.e., one observation
per row), possibly aggregating the data if there is more
than one obersvation per individuum and cell. Hence,
mixed between-within ANOVAs can be calculated
conveniently without using the rather unhandy format of
car::Anova. aov.car can be called using a
formula similar to aov specifying an error
strata for the within-subject factor(s). ez.glm is
called specifying the factors as character vectors.
Usage
1 2 3 4 5 6 7 8 |
Arguments
formula |
A formula specifying the ANOVA model
similar to |
id |
|
dv |
|
between |
|
within |
|
covariate |
|
data |
A |
fun.aggregate |
The function for aggregating the
data before running the ANOVA if there is more than one
obervation per individuum and cell of the design. The
default |
type |
The type of sums of squares for the ANOVA.
Defaults to 3. Passed to
|
print.formula |
|
... |
Further arguments passed to
|
object |
An object of class |
Details
Type 3 sums of squares are default in afe. Note that type 3 sums of squares are said to be dangerous and/or problematic. On the other side they are the default in in SPSS and SAS and recommended by e.g. Maxwell and Delaney (2003). For a brief discussion see here.
However, note that lower order effects (e.g., main
effects) in type 3 ANOVAs are only meaningful with
effects
coding. That is, contrasts should be set to
contr.sum via
options(contrasts=c('contr.sum','contr.poly')).
This should be done automatically when loading afe
and afe will issue a warning when running type 3 SS
and
other
coding schemes. You can check the coding with
options("contrasts").
The formula for aov.car must contain a
single Error term specyfying the ID column
and potential within-subject factors. Factors outside the
Error term are treated as between-subject factors
(the within-subject factors specified in the Error
term are ignored outside the Error term, i.e., it
is not necessary to specify them outside the Error
term, see Examples). Suppressing the intercept (i.e, via
0 + or - 1) is ignored. Specific
specifications of effects (e.g., excluding terms with
- or using ^) should be functional. Using
the I or poly function within
the formula is not tested and not supported!
For ez.glm either between or within
must not be NULL.
ez.glm will concatante all between-subject factors
using * (i.e., producing all main effects and
interactions) and all covariates by + (i.e.,
adding only the main effects to the existing
between-subject factors). The within-subject factors do
fully interact with all between-subject factors and
covariates. This is essentially identical to the behavior
of SPSS's glm function.
Value
aov.car and ez.glm are wrappers and
therfore return the same as Anova.
Usually an object of class "Anova.mlm" (with
within-subjects factors) or c("anova",
"data.frame").
univariate returns a list of
data.frames containing the univariate results
(i.e., the classical ANOVA results) from an object of
class "Anova.mlm". This is essentially the output
from summary.Anova.mlm with multivariate =
FALSE, e.g. summary(aov.car(...), multivriate =
FALSE), as a list instead of printed to the console.
For objects of class "anova" (i.e., the object
returned by car::Anova for a purely
between-subjects ANOVA) the object is returned unaltered.
The elements of the list returned by univariate
are: anova, mauchly, and
spehricity.correction (containing both,
Greenhouse-Geisser and Hyundt-Feldt correction).
Note
Variables entered as within-subjects (i.e., repeated measures) factors are silently converted to factors and unused levels dropped.
Contrasts attached to a factor as an attribute are probably not preserved and not supported.
Author(s)
univariate is basically a copy of
summary.Anova.mlm written by John
Fox.
The other functions were written by Henrik
Singmann.
See Also
nice.anova is a function for creating nice
ANOVA tables (including sphercitiy corrections) from
objects returned by ez.glm and aov.car.
obk.long describes the long version of the
OBrienKaiser dataset used in the examples.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 | # exampel using obk.long (see ?obk.long), a long version of the OBrienKaiser dataset from car.
data(obk.long)
# run univariate mixed ANCOVA for the full design:
univariate(aov.car(value ~ treatment * gender + age + Error(id/phase*hour), data = obk.long))
univariate(ez.glm("id", "value", obk.long, c("treatment", "gender"), c("phase", "hour"), "age"))
# both calls return the same:
## $anova
## SS num Df Error SS den Df F Pr(>F)
## (Intercept) 6454.236987 1 215.65658 9 269.3547893 5.152317e-08
## treatment 171.399953 2 215.65658 9 3.5765187 7.193619e-02
## gender 94.598340 1 215.65658 9 3.9478742 7.818280e-02
## age 12.398975 1 215.65658 9 0.5174466 4.901885e-01
## treatment:gender 61.531858 2 215.65658 9 1.2839551 3.231798e-01
## phase 134.586005 2 59.72439 18 20.2810632 2.448505e-05
## treatment:phase 80.604542 4 59.72439 18 6.0732385 2.826803e-03
## gender:phase 1.634246 2 59.72439 18 0.2462681 7.843036e-01
## age:phase 20.553392 2 59.72439 18 3.0972362 6.982439e-02
## treatment:gender:phase 21.254421 4 59.72439 18 1.6014379 2.170946e-01
## hour 108.513510 4 47.59543 36 20.5192290 7.001584e-09
## treatment:hour 7.547869 8 47.59543 36 0.7136275 6.779072e-01
## gender:hour 3.746135 4 47.59543 36 0.7083708 5.915285e-01
## age:hour 14.904567 4 47.59543 36 2.8183608 3.926421e-02
## treatment:gender:hour 6.235198 8 47.59543 36 0.5895186 7.798264e-01
## phase:hour 9.762579 8 88.62706 72 0.9913814 4.501348e-01
## treatment:phase:hour 6.579092 16 88.62706 72 0.3340505 9.915014e-01
## gender:phase:hour 8.851396 8 88.62706 72 0.8988515 5.222336e-01
## age:phase:hour 7.539611 8 88.62706 72 0.7656409 6.339004e-01
## treatment:gender:phase:hour 12.822199 16 88.62706 72 0.6510416 8.307936e-01
##
## $mauchly
## Test statistic p-value
## phase 0.8217571566 0.45600959
## treatment:phase 0.8217571566 0.45600959
## gender:phase 0.8217571566 0.45600959
## age:phase 0.8217571566 0.45600959
## treatment:gender:phase 0.8217571566 0.45600959
## hour 0.0966749877 0.04923980
## treatment:hour 0.0966749877 0.04923980
## gender:hour 0.0966749877 0.04923980
## age:hour 0.0966749877 0.04923980
## treatment:gender:hour 0.0966749877 0.04923980
## phase:hour 0.0002379741 0.08651564
## treatment:phase:hour 0.0002379741 0.08651564
## gender:phase:hour 0.0002379741 0.08651564
## age:phase:hour 0.0002379741 0.08651564
## treatment:gender:phase:hour 0.0002379741 0.08651564
##
## $sphericity.correction
## GG eps Pr(>F[GG]) HF eps Pr(>F[HF])
## phase 0.8487215 8.383485e-05 1.0252867 2.448505e-05
## treatment:phase 0.8487215 5.159591e-03 1.0252867 2.826803e-03
## gender:phase 0.8487215 7.493990e-01 1.0252867 7.843036e-01
## age:phase 0.8487215 8.073373e-02 1.0252867 6.982439e-02
## treatment:gender:phase 0.8487215 2.279698e-01 1.0252867 2.170946e-01
## hour 0.5341747 1.302016e-05 0.7054545 8.046331e-07
## treatment:hour 0.5341747 6.010781e-01 0.7054545 6.342676e-01
## gender:hour 0.5341747 5.137213e-01 0.7054545 5.478398e-01
## age:hour 0.5341747 8.155027e-02 0.7054545 6.211130e-02
## treatment:gender:hour 0.5341747 6.843526e-01 0.7054545 7.263729e-01
## phase:hour 0.4355822 4.186799e-01 0.7444364 4.402119e-01
## treatment:phase:hour 0.4355822 9.317848e-01 0.7444364 9.787985e-01
## gender:phase:hour 0.4355822 4.651930e-01 0.7444364 5.020890e-01
## age:phase:hour 0.4355822 5.395151e-01 0.7444364 5.992844e-01
## treatment:gender:phase:hour 0.4355822 7.100921e-01 0.7444364 7.878433e-01
##
## Warning message:
## In univariate(aov.car(value ~ treatment * gender + age + Error(id/phase * :
## HF eps > 1 treated as 1
# To get a nicer ANOVA table use function nice.anova (see ?noce.anova):
nice.anova(ez.glm("id", "value", obk.long, c("treatment", "gender"), c("phase", "hour"), "age"))
## Effect df MSE F p
## 1 treatment 2, 9 23.96 3.58 + .07
## 2 gender 1, 9 23.96 3.95 + .08
## 3 age 1, 9 23.96 0.52 .49
## 4 treatment:gender 2, 9 23.96 1.28 .32
## 5 phase 1.7, 15.28 3.91 20.28 *** <.001
## 6 treatment:phase 3.39, 15.28 3.91 6.07 ** .005
## 7 gender:phase 1.7, 15.28 3.91 0.25 .75
## 8 age:phase 1.7, 15.28 3.91 3.10 + .08
## 9 treatment:gender:phase 3.39, 15.28 3.91 1.60 .23
## 10 hour 2.14, 19.23 2.48 20.52 *** <.001
## 11 treatment:hour 4.27, 19.23 2.48 0.71 .60
## 12 gender:hour 2.14, 19.23 2.48 0.71 .51
## 13 age:hour 2.14, 19.23 2.48 2.82 + .08
## 14 treatment:gender:hour 4.27, 19.23 2.48 0.59 .68
## 15 phase:hour 3.48, 31.36 2.83 0.99 .42
## 16 treatment:phase:hour 6.97, 31.36 2.83 0.33 .93
## 17 gender:phase:hour 3.48, 31.36 2.83 0.90 .47
## 18 age:phase:hour 3.48, 31.36 2.83 0.77 .54
## 19 treatment:gender:phase:hour 6.97, 31.36 2.83 0.65 .71
# replicating ?Anova using aov.car:
aov.car(value ~ treatment * gender + Error(id/phase*hour), data = obk.long, type = 2)
# in contrast to aov you do not need the within-subject factors outside Error()
# replicating ?Anova using ez.glm:
ez.glm("id", "value", obk.long, c("treatment", "gender"), c("phase", "hour"), type = 2)
#both return:
## Type II Repeated Measures MANOVA Tests: Pillai test statistic
## Df test stat approx F num Df den Df Pr(>F)
## (Intercept) 1 0.970 318 1 10 0.0000000065 ***
## treatment 2 0.481 5 2 10 0.03769 *
## gender 1 0.204 3 1 10 0.14097
## treatment:gender 2 0.364 3 2 10 0.10447
## phase 1 0.851 26 2 9 0.00019 ***
## treatment:phase 2 0.685 3 4 20 0.06674 .
## gender:phase 1 0.043 0 2 9 0.82000
## treatment:gender:phase 2 0.311 1 4 20 0.47215
## hour 1 0.935 25 4 7 0.00030 ***
## treatment:hour 2 0.301 0 8 16 0.92952
## gender:hour 1 0.293 1 4 7 0.60237
## treatment:gender:hour 2 0.570 1 8 16 0.61319
## phase:hour 1 0.550 0 8 3 0.83245
## treatment:phase:hour 2 0.664 0 16 8 0.99144
## gender:phase:hour 1 0.695 1 8 3 0.62021
## treatment:gender:phase:hour 2 0.793 0 16 8 0.97237
## ---
## Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# aggregating over one within-subjects factor (phase) with warning:
aov.car(value ~ treatment * gender + age + Error(id/hour), data = obk.long)
ez.glm("id", "value", obk.long, c("treatment", "gender"), "hour", "age")
# runs with "numeric" factors
obk.long$hour2 <- as.numeric(as.character(obk.long$hour))
aov.car(value ~ treatment * gender + Error(id/hour2), data = obk.long, type = 2)
# only between
aov.car(value ~ treatment * gender + age + Error(id), data = obk.long, type = 2)
aov.car(value ~ treatment * gender + Error(id), data = obk.long, type = 2)
ez.glm("id", "value", obk.long, c("treatment", "gender"), within = NULL, covariate = "age", type = 2, print.formula = TRUE)
ez.glm("id", "value", obk.long, c("treatment", "gender"), within = NULL, type = 2, print.formula = TRUE)
# only within
univariate(aov.car(value ~ Error(id/phase*hour), data = obk.long, type = 2))
univariate(ez.glm("id", "value", obk.long, NULL, c("phase", "hour"), type = 2, print.formula = TRUE))
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