Paired sample t test

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 = "Paired sample t test", col_types = c("text", 
         "numeric"))
View(Data)
attach(Data)
require(dplyr)

## Loading required package: dplyr

## Warning: package 'dplyr' was built under R version 4.0.4

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

require(ggplot2)

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 4.0.3

h=ggplot(Data,aes(x=Group,y=Weight),order = c("Before", "After"))
h+geom_boxplot()+theme_bw()+theme_classic()

Assumption 1: Are the two samples paired?

Assumption 2: Is this a large sample? (n>30)

Assumption 3: Normal distribution

d= with(Data, 
        Weight[Group == "Before"] - Weight[Group == "After"])
shapiro.test(d)

## 
##  Shapiro-Wilk normality test
## 
## data:  d
## W = 0.94545, p-value = 0.6151

Run paired sample t test

res=t.test(Weight ~ Group, data = Data, paired = TRUE)
res

## 
##  Paired t-test
## 
## data:  Weight by Group
## t = 20.886, df = 9, p-value = 6.192e-09
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  173.3717 215.4883
## sample estimates:
## mean of the differences 
##                  194.43

Conclusion: p-value = 6.192e-09 => significantly different mean weight before and after using treatment