Research Question

Is there a relationship between age and years of education?

Import the Data

q1 <- read_excel("A4Q1.xlsx")
head(q1)
## # A tibble: 6 × 2
##     age education
##   <dbl>     <dbl>
## 1  42.0      13.2
## 2  38.0      12.6
## 3  16.4      10.3
## 4  33.8      16.2
## 5  33.4      14.0
## 6  14.3      11.4

Test Selection

A Pearson correlation was selected because age and years of education are continuous variables and both variables met the normality assumption.

Normality Tests

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

The Shapiro-Wilk tests were not statistically significant for age and education, indicating that both variables were approximately normally distributed.

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 showed a statistically significant moderate positive relationship between age and years of education, r(148) = .52, p < .001. This means that, in this dataset, older participants tended to report more years of education.