load data

data <- read.csv("raw.csv", h = T)
head(data)
##   ID Gender T1 T2 T3
## 1  1      2 13  9 13
## 2  2      2 13  8 12
## 3  3      2 11  7  7
## 4  4      2 14  9 10
## 5  5      2  7  6  5
## 6  6      2 13 10 11

convert to long data

library(tidyverse)
## Warning: 套件 'tidyverse' 是用 R 版本 4.1.3 來建造的
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5     v purrr   0.3.4
## v tibble  3.1.6     v dplyr   1.0.8
## v tidyr   1.2.0     v stringr 1.4.0
## v readr   2.1.2     v forcats 0.5.1
## Warning: 套件 'ggplot2' 是用 R 版本 4.1.3 來建造的
## Warning: 套件 'tibble' 是用 R 版本 4.1.3 來建造的
## Warning: 套件 'tidyr' 是用 R 版本 4.1.3 來建造的
## Warning: 套件 'readr' 是用 R 版本 4.1.3 來建造的
## Warning: 套件 'purrr' 是用 R 版本 4.1.3 來建造的
## Warning: 套件 'dplyr' 是用 R 版本 4.1.3 來建造的
## Warning: 套件 'stringr' 是用 R 版本 4.1.3 來建造的
## Warning: 套件 'forcats' 是用 R 版本 4.1.3 來建造的
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
ldata <- pivot_longer(data, cols = c(, 3:5), names_to = "time", values_to = "total")
head(ldata)
## # A tibble: 6 x 4
##      ID Gender time  total
##   <int>  <int> <chr> <int>
## 1     1      2 T1       13
## 2     1      2 T2        9
## 3     1      2 T3       13
## 4     2      2 T1       13
## 5     2      2 T2        8
## 6     2      2 T3       12
str(ldata)
## tibble [63 x 4] (S3: tbl_df/tbl/data.frame)
##  $ ID    : int [1:63] 1 1 1 2 2 2 3 3 3 4 ...
##  $ Gender: int [1:63] 2 2 2 2 2 2 2 2 2 2 ...
##  $ time  : chr [1:63] "T1" "T2" "T3" "T1" ...
##  $ total : int [1:63] 13 9 13 13 8 12 11 7 7 14 ...

convert char to factor variable

ldata$time <- as.factor(ldata$time)
ldata$ID <- as.factor(ldata$ID)

convert to wide data

wdata <- pivot_wider(ldata, names_from = "time", values_from = "total")
str(wdata)
## tibble [21 x 5] (S3: tbl_df/tbl/data.frame)
##  $ ID    : Factor w/ 21 levels "1","2","3","4",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ Gender: int [1:21] 2 2 2 2 2 2 2 2 2 2 ...
##  $ T1    : int [1:21] 13 13 11 14 7 13 8 15 13 15 ...
##  $ T2    : int [1:21] 9 8 7 9 6 10 7 11 9 9 ...
##  $ T3    : int [1:21] 13 12 7 10 5 11 8 15 8 13 ...

visualized

library(gplots)
## Warning: 套件 'gplots' 是用 R 版本 4.1.3 來建造的
## 
## 載入套件：'gplots'
## 下列物件被遮斷自 'package:stats':
## 
##     lowess
plot(total ~ time, data = ldata, frame.plot = FALSE)

plotmeans(total ~ time, data = ldata, frame = F)
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" 不是一個繪圖參數
## Warning in axis(1, at = 1:length(means), labels = legends, ...): "frame" 不是一
## 個繪圖參數
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" 不是一個繪圖參數

aggregate(total ~ time, data = ldata, mean)
##   time     total
## 1   T1 11.857143
## 2   T2  8.285714
## 3   T3  9.333333
aggregate(total ~ time, data = ldata, sd)
##   time    total
## 1   T1 3.054271
## 2   T2 2.552310
## 3   T3 3.022141

run ANOVA

summary(aov(total ~ time, data = ldata))
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## time         2  141.6   70.78   8.501 0.000561 ***
## Residuals   60  499.5    8.33                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

ANOVA for repeated measures

summary(aov(total ~ time + Error(ID), data = ldata))
## 
## Error: ID
##           Df Sum Sq Mean Sq F value Pr(>F)
## Residuals 20  431.1   21.55               
## 
## Error: Within
##           Df Sum Sq Mean Sq F value   Pr(>F)    
## time       2 141.56   70.78   41.36 1.83e-10 ***
## Residuals 40  68.44    1.71                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Because F value and P value, we can say the differences of mean between each time are significant.

data$total <- c(data$T1 + data$T2 + data$T3)
aggregate(total ~ Gender, data = data, mean)
##   Gender    total
## 1      1 19.66667
## 2      2 31.11111
aggregate(total ~ Gender, data = data, sd)
##   Gender    total
## 1      1 10.69268
## 2      2  6.54297
plotmeans(total ~ Gender, data = data, frame = F)
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" 不是一個繪圖參數
## Warning in axis(1, at = 1:length(means), labels = legends, ...): "frame" 不是一
## 個繪圖參數
## Warning in plot.xy(xy.coords(x, y), type = type, ...): "frame" 不是一個繪圖參數

summary(aov(total ~ Gender, data = data))
##             Df Sum Sq Mean Sq F value Pr(>F)  
## Gender       1  336.8   336.8    6.69 0.0181 *
## Residuals   19  956.4    50.3                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

the total answer between gender has significant differences