A6Q4

load libraries

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(tidyverse)

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## ✔ lubridate 1.9.5     ✔ tibble    3.3.1
## ✔ purrr     1.2.1     ✔ tidyr     1.3.2
## ✔ readr     2.2.0

## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

load dataset

D4 <- read_excel("A6Q4.xlsx")

Descriptive Statistics

D4 <- pivot_longer(D4,cols = c(nolift, lift), names_to = "label", values_to = "weight") 
D4 %>%
  group_by(label) %>%
  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
##   label   Mean Median    SD     N
##   <chr>  <dbl>  <dbl> <dbl> <int>
## 1 lift    33.0   40.8  56.7    25
## 2 nolift 120.   116.   53.3    25

Histogram Creation

hist(D4$weight[D4$label == "nolift"],
     main = "Histogram of No lift Weights",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "pink",
     breaks = 10)

hist(D4$weight[D4$label == "lift"],
     main = "Histogram of lift weights",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "pink",
     breaks = 10)

Group 1: nolift

The first variable looks abnormally distributed. The data is negatively sqewed. The data has a high kurtosis.

Group 2: Female

The second variable looks abnormally distributed. The data is negatively skewed. The data has a high kurtosis.

Box plots

ggboxplot(D4, x = "label", y = "weight",
          color = "label",
          palette = "jco",
          add = "jitter")

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. Based on these findings, the boxplot is abnormal.

Boxplot 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. Based on these findings, the boxplot is abnormal.

shapiro walk test

shapiro.test(D4$weight[D4$label == "nolift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  D4$weight[D4$label == "nolift"]
## W = 0.78786, p-value = 0.0001436

shapiro.test(D4$weight[D4$label == "lift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  D4$weight[D4$label == "lift"]
## W = 0.70002, p-value = 7.294e-06

Group 1: nolift

The first group is abnormally distributed, (p < 0.001).

Group 2: lift

The second group is abnormally distributed, (p < 0.001).

Mann-Whitney U test

wilcox.test(weight ~ label, data = D4)

## 
##  Wilcoxon rank sum exact test
## 
## data:  weight by label
## W = 22, p-value = 7.132e-11
## alternative hypothesis: true location shift is not equal to 0

effect size

mw_effect <- cliff.delta(weight ~ label, data = D4)
print(mw_effect)

## 
## Cliff's Delta
## 
## delta estimate: -0.9296 (large)
## 95 percent confidence interval:
##      lower      upper 
## -0.9969233 -0.0729899

Report

A Mann-Whitney U test was conducted to determine if there was a difference in body Weight (kg) between weightlifters and non weight lifters. nolift scores (Mdn = 116.000) were significantly different from lifter scores (Mdn =40.800), U = 0.700, p < 0.001. The effect size was LARGE, Cliff’s Delta = -0.93.