T-Test vs. ANOVA: When to Use Each Statistical Test
A t-test compares the means of exactly two groups, while ANOVA (Analysis of Variance) tests the means of three or more groups in one shot.
Imagine you’re a product manager checking whether iOS or Android users spend more. You instinctively reach for the t-test, but when a third platform—say, WhatsApp Web—enters, the same instinct screams ANOVA; the switch feels abrupt, so many just default to multiple t-tests and muddy their results.
Key Differences
t-test: two groups, one comparison, equal or unequal variances. ANOVA: ≥3 groups, single F-test controls family-wise error, followed by post-hoc checks if significant.
Which One Should You Choose?
If your question involves exactly two samples, use a t-test. The moment you have three or more independent groups, ANOVA prevents inflated Type I error and keeps your CEO happy with cleaner dashboards.
Examples and Daily Life
Testing caffeine impact on focus: two coffee brands → t-test. Comparing focus across four caffeine doses → ANOVA. Same lab, same data, just one extra group flips the test.
Can I run several t-tests instead of ANOVA?
Yes, but every extra test raises the chance of a false positive; ANOVA keeps the overall error rate at 5%.
Does ANOVA need equal sample sizes?
No, it tolerates unequal n, yet power drops as imbalance grows.
What post-hoc test follows ANOVA?
Tukey’s HSD or Bonferroni correction pinpoints which groups actually differ.