How to Perform ANOVA in R: Simple Guide with Example

To perform ANOVA in R, use the aov() function with a formula like response ~ group and your data frame. Then apply summary() to the result to see the ANOVA table showing if group means differ significantly.

Syntax

The basic syntax for ANOVA in R uses the aov() function with a formula and data frame. The formula is response ~ group, where response is the numeric outcome and group is the categorical factor.

• aov(): Runs the ANOVA test.
• formula: Defines the relationship between response and groups.
• data: The data frame containing your variables.
• summary(): Displays the ANOVA results.

r

anova_result <- aov(response ~ group, data = your_data)
summary(anova_result)

Example

This example shows how to perform a one-way ANOVA to test if three groups have different average values.

r

data <- data.frame(
  response = c(5, 6, 7, 8, 5, 6, 7, 9, 10),
  group = factor(c('A', 'A', 'A', 'B', 'B', 'B', 'C', 'C', 'C'))
)
anova_result <- aov(response ~ group, data = data)
summary(anova_result)

Output

            Df Sum Sq Mean Sq F value  Pr(>F)  
group        2  14.22   7.111   6.222 0.04157 *
Residuals    6  6.86    1.143                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Common Pitfalls

Common mistakes when performing ANOVA in R include:

• Not converting the grouping variable to a factor, which can cause errors or wrong results.
• Using lm() instead of aov() without understanding the difference in output.
• Ignoring assumptions like normality and equal variances before running ANOVA.

r

## Wrong: group is numeric, not factor
wrong_data <- data.frame(response = c(5,6,7,8,5,6), group = c(1,1,1,2,2,2))
aov(response ~ group, data = wrong_data) # May give incorrect results

## Right: convert group to factor
right_data <- data.frame(response = c(5,6,7,8,5,6), group = factor(c(1,1,1,2,2,2)))
aov(response ~ group, data = right_data)

Quick Reference

Remember these tips when performing ANOVA in R:

• Use aov() with a formula and data frame.
• Always convert grouping variables to factors.
• Check assumptions before interpreting results.
• Use summary() to view the ANOVA table.

Key Takeaways

Use aov(response ~ group, data) to perform ANOVA in R.

Always convert grouping variables to factors before analysis.

Use summary() on the aov result to see the ANOVA table.

Check assumptions like normality and equal variance before trusting results.

ANOVA tests if group means differ significantly.