Assignment 4, Question 2

Open packages

library (readxl)

## Warning: package 'readxl' was built under R version 4.6.1

library (ggpubr)

## Warning: package 'ggpubr' was built under R version 4.6.1

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 4.6.1

library(rmarkdown)

Import Dataset

A4Q2 <-read_excel("C:/Users/rteno/OneDrive - Saint Louis University/AA 5221-11_Assignment 4/A4Q2.xlsx")

Create scatterplot

ggscatter(A4Q2, 
          x="phone", 
          y="sleep", 
          add = "reg.line", 
          xlab = "Phone (hours)", 
          ylab = "Sleep (hours)")

# The relationship is linear.
# The relationship is negative.
# The relationship is moderate.
# There are outliers

Calculate descriptive Statistics

mean(A4Q2$phone)

## [1] 3.804609

sd(A4Q2$phone)

## [1] 2.661866

median(A4Q2$phone)

## [1] 3.270839

mean(A4Q2$sleep)

## [1] 7.559076

sd(A4Q2$sleep)

## [1] 1.208797

median(A4Q2$sleep)

## [1] 7.524099

Create histograms

# Histogram for phone
hist(A4Q2$phone, 
     main = "Phone (hours)",
     breaks = 20 , 
     col = "lightblue",
     border = "white",
     cex.main=1,
     cex.axis=1,
     cex.lab=1)

# Phone is abnormally distributed. 
# The data is positively skewed. 
# The data does not have a proper bell curve.

# Histogram for sleep
hist(A4Q2$sleep, 
     main = "Sleep (hours)", 
     breaks = 20 , 
     col = "lightcoral",
     border = "white",
     cex.main=1,
     cex.axis=1,
     cex.lab=1)

# Sleep is abnormally distributed. 
# The data is negatively skewed. 
# The data has a proper bell curve.

Normality Tests

shapiro.test(A4Q2$phone)

## 
##  Shapiro-Wilk normality test
## 
## data:  A4Q2$phone
## W = 0.89755, p-value = 9.641e-09

shapiro.test(A4Q2$sleep)

## 
##  Shapiro-Wilk normality test
## 
## data:  A4Q2$sleep
## W = 0.91407, p-value = 8.964e-08

# Phone is abnormal
# Sleep is abnormal

Conduct inferential test (Spearman Correlation)

cor.test(A4Q2$phone,A4Q2$sleep,method = "spearman")

## 
##  Spearman's rank correlation rho
## 
## data:  A4Q2$phone and A4Q2$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 (Mdn = 7.52).There was a statistically significant relationship between the two variables, ρ = -.615, p < .001.The relationship was negative and strong.As phone use increased, sleep decreased.