Assignment 5 Question 2

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

A5Q2 <- read_excel("C:/Users/nehab/OneDrive/A5221/Assignment 5/A5Q2.xlsx")

ggscatter(
  A5Q2,
  x = "phone",
  y = "sleep",
  add = "reg.line",
  xlab = "Daily Phone Use",
  ylab = "Nightly Sleep Duration"
)

# The relationship is linear.
# The relationship is negative.
# There are outliers.
# I corrected the scatterplot description.
# I originally described only possible outliers, but the scatterplot shows outliers.

mean(A5Q2$sleep)

## [1] 7.559076

sd(A5Q2$sleep)

## [1] 1.208797

median(A5Q2$sleep)

## [1] 7.524099

mean(A5Q2$phone)

## [1] 3.804609

sd(A5Q2$phone)

## [1] 2.661866

median(A5Q2$phone)

## [1] 3.270839

hist(
  A5Q2$sleep,
  main = "Distribution of Sleep Duration",
  xlab = "Nightly Sleep Duration"
)

hist(
  A5Q2$phone,
  main = "Distribution of Phone Use",
  xlab = "Daily Phone Use"
)

# Sleep has possible outliers and may not be normally distributed.
# Phone use appears right-skewed and is not normally distributed.

shapiro.test(A5Q2$sleep)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q2$sleep
## W = 0.91407, p-value = 8.964e-08

shapiro.test(A5Q2$phone)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q2$phone
## W = 0.89755, p-value = 9.641e-09

# Sleep is not normally distributed because p < .001.
# Phone use is not normally distributed because p < .001.
# Both p-values are less than .05.
# Therefore, a Spearman correlation will be used.

cor.test(
  A5Q2$phone,
  A5Q2$sleep,
  method = "spearman",
  exact = FALSE
)

## 
##  Spearman's rank correlation rho
## 
## data:  A5Q2$phone and A5Q2$sleep
## S = 908390, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.6149873

# A Spearman correlation was conducted to test the relationship between
# phone use (Mdn = 3.27) and sleep duration (Mdn = 7.52).
# There was a statistically significant relationship between the two variables,
# rho = -.61, p < .001.
# The relationship was negative and strong.
# As phone use increased, sleep duration decreased.
# Therefore, the null hypothesis was rejected.

# I corrected the interpretation by adding the medians for both variables.
# I clearly explained that the relationship was negative and strong.