====== E.g. 1 ======
{{r:rep.meas.anova.csv}}
###################################################
###################################################
###################################################
# data
df <- data.frame(patient=rep(1:5, each=4),
drug=rep(1:4, times=5),
response=c(30, 28, 16, 34,
14, 18, 10, 22,
24, 20, 18, 30,
38, 34, 20, 44,
26, 28, 14, 30))
#view data
df
write.csv(df, file="rep.meas.anova.csv")
#fit repeated measures ANOVA model
df$drug <- factor(df$drug)
df$patient <- factor(df$patient)
# Error(patient) = patient error should be isolated
m.aov <- aov(response ~ drug
+ Error(patient),
data = df)
#view model summary
summary(m.aov)
# check probability level (pr)
1 - pf(24.75886525, 3, 12)
# A one-way repeated measures ANOVA was conducted
# on five individuals to examine the effect that
# four different drugs had on response time.
# Results showed that the type of drug used lead
# to statistically significant differences in
# response time (F(3, 12) = 24.76, p < 0.001).
> ###################################################
> ###################################################
> ###################################################
>
> # data
> df <- data.frame(patient=rep(1:5, each=4),
+ drug=rep(1:4, times=5),
+ response=c(30, 28, 16, 34,
+ 14, 18, 10, 22,
+ 24, 20, 18, 30,
+ 38, 34, 20, 44,
+ 26, 28, 14, 30))
>
> #view data
> df
patient drug response
1 1 1 30
2 1 2 28
3 1 3 16
4 1 4 34
5 2 1 14
6 2 2 18
7 2 3 10
8 2 4 22
9 3 1 24
10 3 2 20
11 3 3 18
12 3 4 30
13 4 1 38
14 4 2 34
15 4 3 20
16 4 4 44
17 5 1 26
18 5 2 28
19 5 3 14
20 5 4 30
> write.csv(df, file="rep.meas.anova.csv")
>
>
> #fit repeated measures ANOVA model
> df$drug <- factor(df$drug)
> df$patient <- factor(df$patient)
>
> # Error(patient) = patient error should be isolated
> m.aov <- aov(response ~ drug
+ + Error(patient),
+ data = df)
> #view model summary
> summary(m.aov)
Error: patient
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 4 680.8 170.2
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
drug 3 698.2 232.7 24.76 1.99e-05 ***
Residuals 12 112.8 9.4
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> # check probability level (pr)
> 1 - pf(24.75886525, 3, 12)
[1] 1.992501e-05
>
> # A one-way repeated measures ANOVA was conducted
> # on five individuals to examine the effect that
> # four different drugs had on response time.
>
> # Results showed that the type of drug used lead
> # to statistically significant differences in
> # response time (F(3, 12) = 24.76, p < 0.001).
>
>
====== E.g. 2 ======
{{:r:rep.meas.anova.eg.movie.review.csv}}
# the second
movrev <- data.frame(reviewer=rep(1:5, each=3),
movie=rep(1:3, times=5),
score=c(88, 84, 92,
76, 78, 90,
78, 94, 95,
80, 83, 88,
82, 90, 99))
#view data
movrev
write.csv(movrev, file="rep.meas.anova.eg.movie.review.csv")
movrev$movie <- factor(movrev$movie)
movrev$reviewer <- factor(movrev$reviewer)
# Error(reviewer) = reviewer error should be isolated
# The above is the same as Error(reviewer/movie)
m.aov <- aov(score ~ movie
+ Error(reviewer),
data = movrev)
#view model summary
summary(m.aov)
# pairwise.t.test(movrev$score, movrev$movie, paired = T, p.adjust.method = "bonf")
attach(movrev)
pairwise.t.test(score, movie, paired = T, p.adjust.method = "bonf")
# or
with(movrev,
pairwise.t.test(score, movie,
paired = T,
p.adjust.method = "bonf"))
> # the second
> movrev <- data.frame(reviewer=rep(1:5, each=3),
+ movie=rep(1:3, times=5),
+ score=c(88, 84, 92,
+ 76, 78, 90,
+ 78, 94, 95,
+ 80, 83, 88,
+ 82, 90, 99))
>
> #view data
> movrev
reviewer movie score
1 1 1 88
2 1 2 84
3 1 3 92
4 2 1 76
5 2 2 78
6 2 3 90
7 3 1 78
8 3 2 94
9 3 3 95
10 4 1 80
11 4 2 83
12 4 3 88
13 5 1 82
14 5 2 90
15 5 3 99
> write.csv(movrev, file="rep.meas.anova.eg.movie.review.csv")
>
> movrev$movie <- factor(movrev$movie)
> movrev$reviewer <- factor(movrev$reviewer)
>
> # Error(reviewer) = reviewer error should be isolated
> # The above is the same as Error(reviewer/movie)
> m.aov <- aov(score ~ movie
+ + Error(reviewer),
+ data = movrev)
> #view model summary
> summary(m.aov)
Error: reviewer
Df Sum Sq Mean Sq F value Pr(>F)
Residuals 4 173.7 43.43
Error: Within
Df Sum Sq Mean Sq F value Pr(>F)
movie 2 363.3 181.67 10.19 0.00632 **
Residuals 8 142.7 17.83
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> # pairwise.t.test(movrev$score, movrev$movie, paired = T, p.adjust.method = "bonf")
> attach(movrev)
The following objects are masked from movrev (pos = 5):
movie, reviewer, score
> pairwise.t.test(score, movie, paired = T, p.adjust.method = "bonf")
Pairwise comparisons using paired t tests
data: score and movie
1 2
2 0.628 -
3 0.029 0.060
P value adjustment method: bonferroni
> # or
> with(movrev,
+ pairwise.t.test(score, movie,
+ paired = T,
+ p.adjust.method = "bonf"))
Pairwise comparisons using paired t tests
data: score and movie
1 2
2 0.628 -
3 0.029 0.060
P value adjustment method: bonferroni
>