Univariateな被験者内計画の二元配置分散分析をやってみる．以下の式でよいらしい．
# afex package読み込み
> library(afex)
#afexパッケージの中のデータを呼び出す．今回はサンプルデータとして活用
> data("md_12.1")
#データはこんな感じ
> head(md_12.1)
id noise angle rt
1 1 absent 0 420
2 2 absent 0 420
3 3 absent 0 480
4 4 absent 0 420
5 5 absent 0 540
6 6 absent 0 360
> aov0<-aov_car(rt ~ noise * angle + Error(id/noise*angle), data = md_12.1, return = "univariate")
#ここでrtは従属変数，noiseとangleは要因，Errorで被験者内計画となるデータを定義．idは被験者．
> aov0
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
Sum Sq num Df Error SS den Df F value Pr(>F)
(Intercept) 19425660 1 292140 9 598.449 1.527e-09 ***
noise 285660 1 76140 9 33.766 0.000256 ***
angle 289920 2 64080 18 40.719 2.087e-07 ***
noise:angle 105120 2 20880 18 45.310 9.424e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Mauchly Tests for Sphericity
Test statistic p-value
angle 0.96011 0.84972
noise:angle 0.89378 0.63814
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
angle 0.96164 3.402e-07 ***
noise:angle 0.90398 3.454e-07 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
HF eps Pr(>F[HF])
angle 1.217564 2.086763e-07
noise:angle 1.117870 9.424093e-08
MANOVAもやってみる．maultvariateだけじゃなくunivariateも一括で出るけど．
> library(afex)
#afexパッケージの中のデータを呼び出す．今回はサンプルデータとして活用
> data("md_12.1")
#データはこんな感じ
> head(md_12.1)
id noise angle rt
1 1 absent 0 420
2 2 absent 0 420
3 3 absent 0 480
4 4 absent 0 420
5 5 absent 0 540
6 6 absent 0 360
#ANOVAのモデルを作る．
> aov1<-aov_ez(id = "id", dv = "rt", data = md_12.1, within = c("noise", "angle"))
> summary(aov1$Anova)
Type III Repeated Measures MANOVA Tests:
------------------------------------------
Term: (Intercept)
Response transformation matrix:
(Intercept)
absent_X0 1
absent_X4 1
absent_X8 1
present_X0 1
present_X4 1
present_X8 1
Sum of squares and products for the hypothesis:
(Intercept)
(Intercept) 116553960
Multivariate Tests: (Intercept)
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.98518 598.4492 1 9 1.5266e-09 ***
Wilks 1 0.01482 598.4492 1 9 1.5266e-09 ***
Hotelling-Lawley 1 66.49435 598.4492 1 9 1.5266e-09 ***
Roy 1 66.49435 598.4492 1 9 1.5266e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
------------------------------------------
Term: noise
Response transformation matrix:
noise1
absent_X0 1
absent_X4 1
absent_X8 1
present_X0 -1
present_X4 -1
present_X8 -1
Sum of squares and products for the hypothesis:
noise1
noise1 1713960
Multivariate Tests: noise
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.789552 33.76596 1 9 0.00025597 ***
Wilks 1 0.210448 33.76596 1 9 0.00025597 ***
Hotelling-Lawley 1 3.751773 33.76596 1 9 0.00025597 ***
Roy 1 3.751773 33.76596 1 9 0.00025597 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
------------------------------------------
Term: angle
Response transformation matrix:
angle1 angle2
absent_X0 1 0
absent_X4 0 1
absent_X8 -1 -1
present_X0 1 0
present_X4 0 1
present_X8 -1 -1
Sum of squares and products for the hypothesis:
angle1 angle2
angle1 1128960 403200
angle2 403200 144000
Multivariate Tests: angle
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.887597 31.58624 2 8 0.00015963 ***
Wilks 1 0.112403 31.58624 2 8 0.00015963 ***
Hotelling-Lawley 1 7.896559 31.58624 2 8 0.00015963 ***
Roy 1 7.896559 31.58624 2 8 0.00015963 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
------------------------------------------
Term: noise:angle
Response transformation matrix:
noise1:angle1 noise1:angle2
absent_X0 1 0
absent_X4 0 1
absent_X8 -1 -1
present_X0 -1 0
present_X4 0 -1
present_X8 1 1
Sum of squares and products for the hypothesis:
noise1:angle1 noise1:angle2
noise1:angle1 416160 171360
noise1:angle2 171360 70560
Multivariate Tests: noise:angle
Df test stat approx F num Df den Df Pr(>F)
Pillai 1 0.918223 44.91353 2 8 4.4722e-05 ***
Wilks 1 0.081777 44.91353 2 8 4.4722e-05 ***
Hotelling-Lawley 1 11.228381 44.91353 2 8 4.4722e-05 ***
Roy 1 11.228381 44.91353 2 8 4.4722e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Univariate Type III Repeated-Measures ANOVA Assuming Sphericity
Sum Sq num Df Error SS den Df F value Pr(>F)
(Intercept) 19425660 1 292140 9 598.449 1.527e-09 ***
noise 285660 1 76140 9 33.766 0.000256 ***
angle 289920 2 64080 18 40.719 2.087e-07 ***
noise:angle 105120 2 20880 18 45.310 9.424e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Mauchly Tests for Sphericity
Test statistic p-value
angle 0.96011 0.84972
noise:angle 0.89378 0.63814
Greenhouse-Geisser and Huynh-Feldt Corrections
for Departure from Sphericity
GG eps Pr(>F[GG])
angle 0.96164 3.402e-07 ***
noise:angle 0.90398 3.454e-07 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
HF eps Pr(>F[HF])
angle 1.217564 2.086763e-07
noise:angle 1.117870 9.424093e-08
Warning message:
In summary.Anova.mlm(aov1$Anova) : HF eps > 1 treated as 1
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