A6Q4

Question 4 Is there a difference in body weight (kg) between participants who lift weights versus participants who do not lift weights?

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)

A6Q4_2 <- read_excel("A6Q4-2.xlsx")

Descriptive statistics

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

Create histogram

hist(A6Q4_2$Weight[A6Q4_2$Exercise == "nolift"],
     main = "Histogram of nolift Weight",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

hist(A6Q4_2$Weight[A6Q4_2$Exercise == "lift"],
     main = "Histogram of lift weight",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

Correction to the colors of the histograms to switch them Group 1: nonlift The first variable looks abnormally distributed. The data is negatively skewed. The data does not have a proper bell curve.

Group 2: lift The second variable looks abnormally distributed. The data is positively skewed. The data does not have a proper bell curve.

Create boxplot to check normality and outliers

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

Boxplot 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: 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.

Statistical normality test

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

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

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

Group 2: lift The second group is abnormally distributed, (p < .001).

Correction to rounding

Mann-Whitney U Test

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

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

A Mann-Whitney U test was conducted to determine if there was a difference in Weight between nolift and lift nolift scores (Mdn = 40.80) were significantly different from lift scores (Mdn = 116 U = 603, p < .001 The effect size was large, Cliff’s Delta = .9296. Correction to rounding