library(readxl)
A6Q4 <- read_excel("C:/Users/SHRUTI/Downloads/A6Q4.xlsx")

names(A6Q4)

## [1] "Exercise" "Weight"

head(A6Q4)

## # A tibble: 6 × 2
##   Exercise Weight
##   <chr>     <dbl>
## 1 nolift    25.8 
## 2 nolift    30.1 
## 3 nolift     7.17
## 4 nolift    88.7 
## 5 nolift    66.1 
## 6 nolift     3.29

table(A6Q4$Exercise)

## 
##   lift nolift 
##     25     25

# install.packages("dplyr")
# install.packages("effectsize")
# install.packages("effsize")

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(dplyr)

## 
## 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

library(effectsize)
library(effsize)

# Descriptive statistics by group
A6Q4 %>%
  group_by(Exercise) %>%
  summarise(
    Mean = mean(Weight, na.rm = TRUE),
    Median = median(Weight, na.rm = TRUE),
    SD = sd(Weight, na.rm = TRUE),
    N = n()
  )

## # A tibble: 2 × 5
##   Exercise  Mean Median    SD     N
##   <chr>    <dbl>  <dbl> <dbl> <int>
## 1 lift     120.   116.   53.3    25
## 2 nolift    33.0   40.8  56.7    25

# Histograms
hist(A6Q4$Weight[A6Q4$Exercise == "lift"],
     breaks = 15,
     col = "skyblue",
     border = "white")

hist(A6Q4$Weight[A6Q4$Exercise == "nolift"],
     breaks = 15,
     col = "firebrick",
     border = "white")

# Boxplot
ggboxplot(A6Q4, x = "Exercise", y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

# Shapiro-Wilk for each group
shapiro.test(A6Q4$Weight[A6Q4$Exercise == "lift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4$Weight[A6Q4$Exercise == "lift"]
## W = 0.78786, p-value = 0.0001436

shapiro.test(A6Q4$Weight[A6Q4$Exercise == "nolift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4$Weight[A6Q4$Exercise == "nolift"]
## W = 0.70002, p-value = 7.294e-06

# Data for the lift group appears abnormally distributed (positively skewed, with a long right tail).
# Data for the nolift group appears abnormally distributed (negatively skewed, with one extreme low value).

# The lift boxplot has outliers.
# The nolift boxplot has an outlier (a negative weight of about -200, which is impossible and likely a data error; it was kept because the Mann-Whitney U test is based on ranks).

# The lift group is abnormally distributed, (p < .001).
# The nolift group is abnormally distributed, (p < .001).
# Both Shapiro-Wilk tests were abnormal, so a Mann-Whitney U Test is appropriate.

wilcox.test(Weight ~ Exercise, data = A6Q4)

## 
##  Wilcoxon rank sum exact test
## 
## data:  Weight by Exercise
## W = 603, p-value = 7.132e-11
## alternative hypothesis: true location shift is not equal to 0

cliff.delta(Weight ~ Exercise, data = A6Q4)

## 
## Cliff's Delta
## 
## delta estimate: 0.9296 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.7993841 0.9764036

# A Mann-Whitney U Test was conducted to determine if there was a difference in weight between the lift and nolift groups.
# Lift scores (Mdn = 116) were significantly different from Nolift scores (Mdn = 40.8), W = 603, p < .001.
# The effect size was large, Cliff's delta = 0.93.