library(readxl)

A5Q1 <- read_excel("C:/Users/eboni/Downloads/A5Q1.xlsx")

View(A5Q1)

Create a Scatterplot

plot(A5Q1$age,
     A5Q1$education,
     xlab = "Age",
     ylab = "Years of Education",
     main = "Relationship Between Age and Education")

Interpret the Scatterplot

# The relationship is linear.
# The relationship is positive.
# There are outliers.

Calculate Descriptive Statistics

# Descriptive statistics for Age
mean(A5Q1$age)

## [1] 35.32634

sd(A5Q1$age)

## [1] 11.45344

median(A5Q1$age)

## [1] 35.79811

# Descriptive statistics for Education
mean(A5Q1$education)

## [1] 13.82705

sd(A5Q1$education)

## [1] 2.595901

median(A5Q1$education)

## [1] 14.02915

# Age: M = 35.33, SD = 11.45, Median = 35.80
# Education: M = 13.83, SD = 2.60, Median = 14.03

Check Normality Visually: Histograms

hist(A5Q1$age,
     main = "Age",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

hist(A5Q1$education,
     main = "Education",
     breaks = 20,
     col = "lightcoral",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

Interpret the Histograms

# Variable 1: Age
# The variable looks normally distributed.
# The data is symmetrical.
# The data has a proper bell curve.

# Variable 2: Education
# The variable looks normally distributed.
# The data is symmetrical.
# The data has a proper bell curve.

Check Normality Statistically: Shapiro-Wilk Test

# Shapiro-Wilk Test for Age
shapiro.test(A5Q1$age)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q1$age
## W = 0.99194, p-value = 0.5581

# Shapiro-Wilk Test for Education
shapiro.test(A5Q1$education)

## 
##  Shapiro-Wilk normality test
## 
## data:  A5Q1$education
## W = 0.9908, p-value = 0.4385

Interpret the Shapiro-Wilk Test

# Variable 1: Age
# The variable is normally distributed (p = .56).

# Variable 2: Education
# The variable is normally distributed (p = .44).

Determine Which Correlation to Use

# A Pearson Correlation should be used because Age and Education are both
# approximately normally distributed based on the histograms and
# Shapiro-Wilk tests.

Conduct the Pearson Correlation

cor.test(
  A5Q1$age,
  A5Q1$education,
  method = "pearson"
)

## 
##  Pearson's product-moment correlation
## 
## data:  A5Q1$age and A5Q1$education
## t = 7.4066, df = 148, p-value = 9.113e-12
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3924728 0.6279534
## sample estimates:
##       cor 
## 0.5200256

Report the Results

# A Pearson correlation was conducted to test the relationship between Age (M = 35.33, SD = 11.45) and Education (M = 13.83, SD = 2.60).

# There was a statistically significant relationship between the two variables, r(148) = .52, p < .001.

# The relationship was positive and moderate.

# As Age increased, Education increased.