Assignment 4_Question 1

#Question 1: Age vs. Education

#Question 1
q1 <- read_excel("A4Q1.xlsx")
#Create scatterplot
ggscatter(
  q1,
  x = "age",
  y = "education",
  add = "reg.line",
  xlab = "Age",
  ylab = "Education"
)

#Relationship is linear, positive, moderate, and with no outliers.

#Descriptive statistics (mean, standard deviation, median)

#Age
mean(q1$age)

## [1] 35.32634

sd(q1$age)

## [1] 11.45344

median(q1$age)

## [1] 35.79811

#Education
mean(q1$education)

## [1] 13.82705

sd(q1$education)

## [1] 2.595901

median(q1$education)

## [1] 14.02915

#Histograms for age and education.

#Histogram for age
hist(q1$age,
     main = "Age",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

#Histogram for education
hist(q1$education,
     main = "Education",
     breaks = 20,
     col = "lightcoral",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
)

# Test for normality
shapiro.test(q1$age)

## 
##  Shapiro-Wilk normality test
## 
## data:  q1$age
## W = 0.99194, p-value = 0.5581

shapiro.test(q1$education)

## 
##  Shapiro-Wilk normality test
## 
## data:  q1$education
## W = 0.9908, p-value = 0.4385

Normality Assessment:
A Shapiro-Wilk normality test was conducted for both variables.Age (p = 0.5581) and education (p = 0.4385) were both normally distributed (p > 0.05). Therefore, the Pearson correlation test was selected.

# Pearson Correlation
cor.test(q1$age,q1$education,method = "pearson")

## 
##  Pearson's product-moment correlation
## 
## data:  q1$age and q1$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

Interpretation:
A pearson correlation task was conducted to examine the relationship between age and years of education (M = 35.33, SD = 11.45) and education level (M = 13.83, SD = 2.60). The results showed a statistically significant positive relationship between age and education, r(148) = .52, p < .001. This indicates a strong association. Older people tended to have higher levels of education. As age increased, education levels generally increased as well.

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