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(effsize)
library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(ggpubr)
A6Q3 <- read_excel("C:/Users/giuli/OneDrive - Saint Louis University/AA 5221/Assignment 6/A6Q3.xlsx")

A6Q3 %>%
  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 cardio    74.7   73.3  7.57    25
## 2 nocardio  70.8   69.5  7.35    25

hist(A6Q3$Weight[A6Q3$Exercise == "cardio"],
     breaks = 15,
     col = "skyblue",
     border = "white")

hist(A6Q3$Weight[A6Q3$Exercise == "nocardio"],
     breaks = 15,
     col = "firebrick",
     border = "white")

#Data for cardio appears normally distributed.
#Data for nocardio appears abnormally distributed.

ggboxplot(A6Q3, x = "Exercise", y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

# The cardio boxplot does not have outliers.
# The nocardio boxplot does not have outliers.

shapiro.test(A6Q3$Weight[A6Q3$Exercise == "cardio"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q3$Weight[A6Q3$Exercise == "cardio"]
## W = 0.96745, p-value = 0.5812

shapiro.test(A6Q3$Weight[A6Q3$Exercise == "nocardio"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q3$Weight[A6Q3$Exercise == "nocardio"]
## W = 0.97686, p-value = 0.8166

#The cardio group is normally distributed, (p > .05).
#The nocardio group is normally distributed, (p > .05).
t.test(Weight ~ Exercise, data = A6Q3, var.equal = TRUE)

## 
##  Two Sample t-test
## 
## data:  Weight by Exercise
## t = 1.8552, df = 48, p-value = 0.06971
## alternative hypothesis: true difference in means between group cardio and group nocardio is not equal to 0
## 95 percent confidence interval:
##  -0.3280454  8.1605622
## sample estimates:
##   mean in group cardio mean in group nocardio 
##               74.73336               70.81710

wilcox.test(Weight ~ Exercise, data = A6Q3)

## 
##  Wilcoxon rank sum exact test
## 
## data:  Weight by Exercise
## W = 399, p-value = 0.09541
## alternative hypothesis: true location shift is not equal to 0

mw_effect <- cliff.delta(Weight ~ Exercise, data = A6Q3); print(mw_effect)

## 
## Cliff's Delta
## 
## delta estimate: 0.2768 (small)
## 95 percent confidence interval:
##       lower       upper 
## -0.05295739  0.55212525

#A Mann-Whitney U test was conducted to determine if there was a difference in Weight between cardio and nocardio.
#cardio scores (Mdn = 73.3) were significantly different from nocardio scores (Mdn = 69.5), W = 0.967, p = 0.581.
#The effect size was small / medium Cliff's Delta = 0.277.