A6Q4

Open the Installed Packages

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)

Import and Name the Dataset

A6Q4 <- read_excel("C:/Users/krish/Downloads/A6Q4-2.xlsx")

Calculate the Descriptive Statistics

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

Create Histograms (Normality Check #1)

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

hist(A6Q4$Weight[A6Q4$Exercise == "nolift"],
     main = "Histogram of Male ExamScores",
     xlab = "Value",
     ylab = "Frequency",
     col = "brown",
     border = "black",
     breaks = 10)

Interpret the Histograms

Group 1: lift

The first variable looks abnormally distributed.

The data is positively skewed

The data does not has a proper bell curve.

Group 2: nolift

The second variable looks abnormally distributed.

The data is negatively skewed.

The data does not has a proper bell curve.

Create Boxplots for Outliers (Normality Check #2)

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

Interpret the Boxplots

Boxplot : 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 : nolift

There is one dot outside the boxplot.

The dot is not close to the whisker.

The dots is very far away from the whiskers

The outliers are not balanced.

Based on these findings, the boxplot is not normal.

Shapiro-Wilk Tests (Normality Check #3)

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

Interpret the Shapiro-Wilk Test

#Group 1: lift #The second group is abnormally distributed, (p=0.0001436, p <0.5).

#Group 2: nolift #The first group is abnormally distributed, (p =7.294e-06, p<0.5).

Conduct the Mann-Whitney U

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

Calculate Effect Size for Mann-Whitney U

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

Report the Mann-Whitney U

A Mann-Whitney U test was conducted to determine if there was a difference in Weight between lift and nolift.

lift (Mdn = 116) were [significantly / not significantly] different from nolift (Mdn = 40.8) U = 603, p < .001

The effect size was large, Cliff’s Delta = 0.923.