A6Q1

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effectsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

## The following objects are masked from 'package:effectsize':
## 
##     cohens_d, eta_squared

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

data <- read_excel("C:/Users/kvpra/Documents/spring 2026/rlaanguage/A6Q1.xlsx")

Before <- data$Before
After  <- data$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 = "weight in kgs",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

#Histogram of Difference Scores
#The difference scores look [abnormally]distributed.
#The data is [ negatively skewed ].
#The data [does not have] a proper bell curve.

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

# Boxplot
# There is one outlier present below the lower whisker.
# The outlier is far from the rest of the data.
# The distribution appears negatively skewed.
# Based on these findings, the data does not appear to be normally distributed.

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 the diet versus after the diet.
#Before scores (M = 76.99, SD = 8.17) were not significantly different from after scores (M = 70.36, SD = 7.47), t(19) = 1.90, p > .05.