Assignment 6 Q4

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)
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

A6Q4_2 <- read_excel("C:/Users/Owner/Documents/Alida/A6Q4-2.xlsx")
A6Q4_2 %>%
  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_2$Weight[A6Q4_2$Exercise == "lift"],
     main = "Histogram of lift ",
     xlab = "Weight",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 25)

hist(A6Q4_2$Weight[A6Q4_2$Exercise == "nolift"],
     main = "Histogram of nolift ",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 25)

#Group 1:lift
#The first variable looks abnormally distributed.
#The data is positive skewed .
#The data does not have proper bell curve.


#Group 2:nolift
#The second variable looks abnormally distributed.
#The data is negative skewed.
#The data does not have proper bell curve.

ggboxplot(A6Q4_2, x = "Exercise", y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

#Boxplot 1: 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

#Boxplot 2: 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

shapiro.test(A6Q4_2$Weight[A6Q4_2$Exercise == "lift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4_2$Weight[A6Q4_2$Exercise == "lift"]
## W = 0.78786, p-value = 0.0001436

shapiro.test(A6Q4_2$Weight[A6Q4_2$Exercise == "nolift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4_2$Weight[A6Q4_2$Exercise == "nolift"]
## W = 0.70002, p-value = 7.294e-06

#Group 1: lift
#The first group is abnormally distributed, (p <.001).

#Group 2: no lift
#The second group is abnormally distributed, (p < .001).

t.test(Weight ~ Exercise, data = A6Q4_2, 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_2)

## 
##  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_2)
print(cohens_d_result)

## # A tibble: 1 × 7
##   .y.    group1 group2 effsize    n1    n2 magnitude
## * <chr>  <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 Weight lift   nolift    1.58    25    25 large

mw_effect <- cliff.delta(Weight ~ Exercise, data = A6Q4_2)
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 OutcomeVariable between lift and nolift.
#lift scores (M = 120, SD = 53.3) were significantly  different from nolift scores (M = 33, SD = 56.7), t(48) = 5.59, p <.001
#The effect size was very large, Cohen's d = .58.

#A Mann-Whitney U test was conducted to determine if there was a difference in OutcomeVariable between  lift and nolift.
#lift scores (Mdn = 116) were significantly  different from nolift scores (Mdn = 40.8) U =0.78, p <.001.
#The effect size was large, Cliff's Delta = .929.