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)
ds4 <- read_excel("~/Downloads/ds4.xlsx")
ds4 %>%
     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(ds4$Weight[ds4$Exercise == "nolift"],
      main = "Histogram of nolift Weight",
      xlab = "Value",
      ylab = "Frequency",
      col = "lightblue",
      border = "black",
      breaks = 10)

 hist(ds4$Weight[ds4$Exercise == "lift"],
      main = "Histogram of lift Weight",
      xlab = "Value",
      ylab = "Frequency",
      col = "lightgreen",
      border = "black",
      breaks = 10)

Group 1: nolift 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.

ggboxplot(ds4, x = "Exercise", y = "Weight",
           color = "Exercise",
           palette = "jco",
           add = "jitter")

Boxplot 1: nolift There are dots outside the boxplot. There are dots past the whiskers of the boxplot. 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. There are dots past the whiskers of the boxplot. 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(ds4$Weight[ds4$Exercise == "nolift"])
## 
##  Shapiro-Wilk normality test
## 
## data:  ds4$Weight[ds4$Exercise == "nolift"]
## W = 0.70002, p-value = 7.294e-06
shapiro.test(ds4$Weight[ds4$Exercise == "lift"])
## 
##  Shapiro-Wilk normality test
## 
## data:  ds4$Weight[ds4$Exercise == "lift"]
## W = 0.78786, p-value = 0.0001436

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

Group 2: lift The second group is abnormally distributed, (p = 0.0001436).

wilcox.test(Weight ~ Exercise, data = ds4)
## 
##  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 = ds4)
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 no lift and lift. No lift scores (Mdn = 40.8) were significantly different from lift scores (Mdn = 116) U = 603, p < .05. The effect size was large, Cliff’s Delta = .930.