Repeated measures 1 way ANOVA

Input data

library(readxl)

## Warning: package 'readxl' was built under R version 4.0.3

Data= read_excel("C:/Users/Admin/Desktop/R/Data.xlsx", 
     sheet = "Repeated measures 1 way ANOVA", 
     col_types = c("text", "numeric", "numeric"))
attach(Data)
require(lsmeans)

## Loading required package: lsmeans

## Warning: package 'lsmeans' was built under R version 4.0.3

## Loading required package: emmeans

## Warning: package 'emmeans' was built under R version 4.0.3

## The 'lsmeans' package is now basically a front end for 'emmeans'.
## Users are encouraged to switch the rest of the way.
## See help('transition') for more information, including how to
## convert old 'lsmeans' objects and scripts to work with 'emmeans'.

require(multcomp)

## Loading required package: multcomp

## Warning: package 'multcomp' was built under R version 4.0.3

## Loading required package: mvtnorm

## Warning: package 'mvtnorm' was built under R version 4.0.3

## Loading required package: survival

## Loading required package: TH.data

## Warning: package 'TH.data' was built under R version 4.0.3

## Loading required package: MASS

## Warning: package 'MASS' was built under R version 4.0.3

## 
## Attaching package: 'TH.data'

## The following object is masked from 'package:MASS':
## 
##     geyser

Define factor

Treatment=factor(Treatment)
Time=factor(Measured_time)

Run repeated anova

anova= aov(Weight_Gain~Time+Error(Treatment/Time))
summary(anova)

## 
## Error: Treatment
##           Df Sum Sq Mean Sq F value Pr(>F)
## Residuals  5  6.895   1.379               
## 
## Error: Treatment:Time
##           Df Sum Sq Mean Sq F value   Pr(>F)    
## Time       3 28.561   9.520    27.4 2.47e-06 ***
## Residuals 15  5.212   0.347                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Plot

plot=tapply(Weight_Gain,Time,mean)
plot(plot,type="o",xlab="Time",ylab="Weight_gain")

Conclusion: the p value in cage of running repeated more powerful than one way anova when the dependent variable (Weight gain) repeated by time. There are significant different between treatment.

Pairwise.t.test

pairwise.t.test(Weight_Gain,Time,p.adjust.method = "bonferroni")

## 
##  Pairwise comparisons using t tests with pooled SD 
## 
## data:  Weight_Gain and Time 
## 
##   1       2      3     
## 2 0.1501  -      -     
## 3 0.0074  1.0000 -     
## 4 9.1e-06 0.0021 0.0456
## 
## P value adjustment method: bonferroni