library(readxl)
library(ggpubr)
## Loading required package: ggplot2
library(effsize)
library(rstatix)
## 
## Attaching package: 'rstatix'
## The following object is masked from 'package:stats':
## 
##     filter
ds1 <- read_excel("~/Downloads/ds1.xlsx")
Before <- ds1$Before
After <- ds1$After
Differences <- After - Before
mean(Before, na.rm = TRUE)
## [1] 76.13299
median(Before, na.rm = TRUE)
## [1] 75.95988
sd(Before, na.rm = TRUE)
## [1] 7.781323
mean(After, na.rm = TRUE)
## [1] 71.58994
median(After, na.rm = TRUE)
## [1] 70.88045
sd(After, na.rm = TRUE)
## [1] 6.639509
hist(Differences,
      main = "Histogram of Difference Scores",
      xlab = "Value",
      ylab = "Frequency",
      col = "blue",
      border = "black",
      breaks = 20)

Histogram of Difference Scores The difference scores look normally distributed. The data is symmetrical. The data has a proper bell curve.

boxplot(Differences,
         main = "Distribution of Score Differences (After - Before)",
         ylab = "Difference in Scores",
         col = "blue",
         border = "darkblue")

Boxplot There are no dots outside the boxplot. Based on these findings, the boxplot is normal.

shapiro.test(Differences)
## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.94757, p-value = 0.3318

Shapiro-Wilk Difference Scores The data is normally distributed, (p = .332).

t.test(Before, After, paired = TRUE, na.action = na.omit)
## 
##  Paired t-test
## 
## data:  Before and After
## t = 1.902, df = 19, p-value = 0.07245
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.4563808  9.5424763
## sample estimates:
## mean difference 
##        4.543048

A Dependent T-Test was conducted to determine if there was a difference in body weight before low calorie diet versus after low calorie diet. Before scores (M = 76.13, SD = 7.78) were not significantly different from after scores (M = 71.59, SD = 6.64), t(19) = 1.90, p > .05.