library(readxl)
library(ggpubr)
## Warning: package 'ggpubr' was built under R version 4.6.1
## Loading required package: ggplot2
library(dplyr)
## Warning: package 'dplyr' was built under R version 4.6.1
## 
## 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)
## Warning: package 'effectsize' was built under R version 4.6.1
library(effsize)
## Warning: package 'effsize' was built under R version 4.6.1
library(dplyr)
A6Q4 <- read_excel("C:/Users/Tharu/Downloads/A6Q4.xlsx")
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
hist(A6Q4$Weight[A6Q4$Exercise == "nolift"],
     main = "Histogram of Weight - No lift",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

hist(A6Q4$Weight[A6Q4$Exercise == "lift"],
     main = "Histogram of Weight - lift",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

#Group 1: No lift #The first variable is approximately normally distributed, but not perfectly. #The data is moderately symmetrical, with a slight left-skew due to a low outlier (around -200). #The data shows a general bell-shaped pattern, although there is some deviation caused by the negative extreme value.

#Group 2: Lift #The second variable is not perfectly normally distributed. #The data is clearly right-skewed due to a few high extreme values (around 220 and 300). #The data does not form a perfect bell-shaped pattern because of these outliers, even though most values are clustered between 0 and 100.

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

#Boxplot 1: Group 1 (nolift)

#There are dots outside the boxplot. #The dots are not close to the whiskers. #The dots are very far away from the whiskers. #The outliers are not balanced. #Based on these findings, the boxplot is not normal.

#Boxplot 2: Group 2 (lift)

#There are dots outside the boxplot. #The dots are not close to the whiskers. #The dots are very far away from the whiskers. #The outliers are not balanced. #Based on these findings, the boxplot is not normal

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

#Group 1: nocardio #The first group is abnormally distributed, (p = 7.294e-06).

#Group 2: cardio #The second group is normally distributed, (p = 0.0001436).

t.test(Weight ~ Exercise, data = A6Q4, var.equal = TRUE)
## 
##  Two Sample t-test
## 
## data:  Weight by Exercise
## t = 5.5923, df = 48, p-value = 1.045e-06
## alternative hypothesis: true difference in means between group lift and group nolift is not equal to 0
## 95 percent confidence interval:
##   55.75715 118.35710
## sample estimates:
##   mean in group lift mean in group nolift 
##            120.08238             33.02525
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
cohens_d_result <- cohens_d(Weight ~ Exercise, data = A6Q4)
cohens_d_result
## Cohen's d |       95% CI
## ------------------------
## 1.58      | [0.94, 2.21]
## 
## - Estimated using pooled SD.
mw_effect <- cliff.delta(Weight ~ Exercise, data = A6Q4)
print(mw_effect)
## 
## Cliff's Delta
## 
## delta estimate: 0.9296 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.7993841 0.9764036

#An Independent T-Test was conducted to determine if there was a difference in Weight between lift and nolift. #lift scores (M = 120.00, SD = 53.30) were significantly different from nolift scores (M = 33.00, SD = 56.70), t(48) = 5.59, p < .001. #The effect size was very large, Cohen’s d = 1.58.

#A Mann-Whitney U test was conducted to determine if there was a difference in Weight between lift and nolift. #lift scores (Mdn = 116.0) were significantly different from nolift scores (Mdn = 40.8), U = 603, p < .001.