t-test vs ANOVA: when to use which (with R)

A t-test compares two groups; ANOVA compares three or more. See in R why they’re the same test for two groups, and why you shouldn’t run many t-tests instead of one ANOVA.

They feel like different tools, but a t-test and one-way ANOVA are the same idea at different scales. Knowing the relationship keeps you from a classic mistake. (Not sure which test fits your design? Try our which-test tool.)

The rule

• Two groups → two-sample t-test.
• Three or more groups → one-way ANOVA.

They agree for two groups

For exactly two groups, ANOVA’s F equals the t statistic squared — same p-value, same conclusion:

set.seed(10)
g <- factor(rep(c("A", "B"), each = 30))
y <- c(rnorm(30, 0), rnorm(30, 0.6))

t_res <- t.test(y ~ g, var.equal = TRUE)
a_res <- summary(aov(y ~ g))

c(t_squared = unname(t_res$statistic^2),
  F_value   = a_res[[1]][["F value"]][1])

t_squared   F_value 
 12.58062  12.58062 

The two numbers match — a t-test is just ANOVA with two groups.

Why not many t-tests?

With three groups you might be tempted to run A-vs-B, A-vs-C, B-vs-C. Don’t: each test carries a 5% false-positive risk, so three tests push your overall error rate well above 5%. ANOVA asks “is there any difference?” in a single test at the right error rate.

library(ggplot2)
ggplot(PlantGrowth, aes(group, weight, fill = group)) +
  geom_boxplot(alpha = 0.7, show.legend = FALSE) +
  scale_fill_manual(values = c("#2f6fed", "#17a2b8", "#5aa0ff")) +
  labs(title = "One-way ANOVA compares 3+ groups at once",
       x = NULL, y = "Weight") +
  theme_minimal(base_family = "sans") +
  theme(plot.title = element_text(face = "bold", colour = "#1b2a4a"))

Figure 1

After a significant ANOVA

ANOVA tells you a difference exists, not which. Follow up with a post-hoc test that controls for multiple comparisons — see one-way ANOVA with post-hoc tests in R.

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Comparing groups in your own data? We’ll pick the right test and defend it.