ANOVA

library(tidyverse)

## Warning: package 'tidyverse' was built under R version 3.6.3

## -- Attaching packages ------------------------------------------------------------------- tidyverse 1.3.0 --

## v ggplot2 3.3.1     v purrr   0.3.2
## v tibble  3.0.1     v dplyr   0.8.3
## v tidyr   1.0.0     v stringr 1.4.0
## v readr   1.3.1     v forcats 0.4.0

## Warning: package 'ggplot2' was built under R version 4.0.0

## Warning: package 'tibble' was built under R version 4.0.0

## -- Conflicts ---------------------------------------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

library(ggpubr)

## Warning: package 'ggpubr' was built under R version 3.6.3

library(rstatix)

## Warning: package 'rstatix' was built under R version 3.6.3

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:stats':
## 
##     filter

library(readxl)
weight <- read_excel("~/weight.xlsx")

Descriptive Statistics

Identical variances between groups indicating equal variance assumptions is satisfied

weight %>%
    group_by(Treatment, Time) %>%
    get_summary_stats(Weight, type = "mean_sd")

## # A tibble: 6 x 6
##   Treatment Time     variable     n  mean    sd
##   <chr>     <chr>    <chr>    <dbl> <dbl> <dbl>
## 1 C         Final    Weight       5 0.022 0.001
## 2 C         Starting Weight       5 0.022 0.001
## 3 W         Final    Weight       5 0.023 0.001
## 4 W         Starting Weight       5 0.023 0.001
## 5 WS        Final    Weight       5 0.022 0.001
## 6 WS        Starting Weight       5 0.022 0.001

bxp <- ggboxplot(
    weight, x = "Time", y = "Weight",
    color = "Treatment", palette = "jco"
)
bxp

Normality assumptions

Large p-values (p > 0.05) implies no issue in normality

weight %>%
    group_by(Treatment, Time) %>%
    shapiro_test(Weight)

## # A tibble: 6 x 5
##   Treatment Time     variable statistic     p
##   <chr>     <chr>    <chr>        <dbl> <dbl>
## 1 C         Final    Weight       0.950 0.734
## 2 C         Starting Weight       0.950 0.734
## 3 W         Final    Weight       0.987 0.966
## 4 W         Starting Weight       0.963 0.826
## 5 WS        Final    Weight       0.833 0.148
## 6 WS        Starting Weight       0.858 0.220

Anova

Let see if you can infer from the following result hahaha

res.aov <- anova_test(
    data = weight, dv = Weight, wid = ID,
    within = c(Treatment, Time)
)
get_anova_table(res.aov)

## ANOVA Table (type III tests)
## 
##           Effect DFn DFd      F     p p<.05      ges
## 1      Treatment   2   8  3.857 0.067       0.334000
## 2           Time   1   4 16.000 0.016     * 0.000432
## 3 Treatment:Time   2   8  1.000 0.410       0.000216

Pairwise comparison

To check which group is different from one to another

pwc <- weight %>%
    group_by(Time) %>%
    pairwise_t_test(
        Weight ~ Treatment, paired = TRUE,
        p.adjust.method = "bonferroni"
    )
pwc

## # A tibble: 6 x 11
##   Time  .y.   group1 group2    n1    n2 statistic    df     p p.adj p.adj.signif
## * <chr> <chr> <chr>  <chr>  <int> <int>     <dbl> <dbl> <dbl> <dbl> <chr>       
## 1 Final Weig~ C      W          5     5    -2.44      4 0.071 0.214 ns          
## 2 Final Weig~ C      WS         5     5     0.402     4 0.709 1     ns          
## 3 Final Weig~ W      WS         5     5     3.10      4 0.036 0.109 ns          
## 4 Star~ Weig~ C      W          5     5    -2.45      4 0.071 0.212 ns          
## 5 Star~ Weig~ C      WS         5     5     0.322     4 0.764 1     ns          
## 6 Star~ Weig~ W      WS         5     5     3.19      4 0.033 0.1   ns