Research Question

Is there a relationship between age and years of education?

Null Hypothesis: There is no relationship between age and years of education.

Alternate Hypothesis: There is a relationship between age and years of education.

Step 1-2: Load Packages

library(readxl)
library(ggpubr)
## Loading required package: ggplot2

Step 3: Import Dataset

DatasetQ1 <- read_excel("A4Q1.xlsx")

Step 4: Scatterplot

ggscatter(
  DatasetQ1,
  x = "age",
  y = "education",
  add = "reg.line",
  xlab = "Age",
  ylab = "Years of Education"
)

Step 5: Interpret the Scatterplot

The relationship is linear.

The relationship is positive.

The relationship is strong.

There are no outliers.

Step 6: Descriptive Statistics

mean(DatasetQ1$age)
## [1] 35.32634
sd(DatasetQ1$age)
## [1] 11.45344
median(DatasetQ1$age)
## [1] 35.79811
mean(DatasetQ1$education)
## [1] 13.82705
sd(DatasetQ1$education)
## [1] 2.595901
median(DatasetQ1$education)
## [1] 14.02915

Step 7: Histograms

hist(DatasetQ1$age,
     main = "Age",
     breaks = 20,
     col = "lightblue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

hist(DatasetQ1$education,
     main = "Years of Education",
     breaks = 20,
     col = "lightcoral",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

Step 8: Interpret the Histograms

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

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

Step 9: Shapiro-Wilk Test

shapiro.test(DatasetQ1$age)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetQ1$age
## W = 0.99194, p-value = 0.5581
shapiro.test(DatasetQ1$education)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetQ1$education
## W = 0.9908, p-value = 0.4385

Step 10: Interpret the Shapiro-Wilk Test

Variable 1: Age The first variable is normally distributed (p = .558).

Variable 2: Years of Education The second variable is normally distributed (p = .439).

Step 11: Determine Normality

Both histograms are normal AND both Shapiro-Wilk tests are normal. Overall data is normal. Use Pearson Correlation.

Step 12: Pearson Correlation

cor.test(DatasetQ1$age, DatasetQ1$education, method = "pearson")
## 
##  Pearson's product-moment correlation
## 
## data:  DatasetQ1$age and DatasetQ1$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

Step 13: Report the Results

A Pearson correlation was conducted to test the relationship between a person’s age (M = 35.33, SD = 11.45) and a person’s years of 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 strong.

As age increased, years of education increased.