Choosing statistical tests is usually the actual hard part of a statistics assignment — once you know which test to run, the calculation (or the software) does most of the work. Here's a decision process that works for almost every intro-level question.
Start with your question
Before touching any formula, ask what you're actually trying to find out. Most intro stats questions fall into one of three buckets: comparing groups, testing a relationship between variables, or testing a single sample against a known value.
Step 1: How many groups are you comparing?
- One sample vs. a known value — one-sample t-test
- Two groups — independent samples t-test (different people in each group) or paired t-test (same people, measured twice)
- Three or more groups — ANOVA, not repeated t-tests (running multiple t-tests inflates your error rate)
Step 2: Is your data categorical or continuous?
A t-test and ANOVA both compare continuous data (like scores, heights, or times) across groups. If instead you're comparing categories or proportions (like "pass/fail" or "yes/no" responses across groups), you need a chi-square test instead — this is one of the most common mix-ups in an intro course.
Step 3: Are you testing a relationship, not a difference?
If your question is about whether two continuous variables move together (like study hours and exam score), you're looking at correlation or regression, not a t-test or ANOVA at all.
Quick reference: t-test vs chi-square vs ANOVA
Comparing average test scores between 2 teaching methods? Independent samples t-test.
Comparing average test scores across 4 teaching methods? ANOVA.
Comparing pass/fail rates across 4 teaching methods? Chi-square test.
Testing if study hours predict exam score? Regression.
Common mistakes
Running multiple t-tests instead of one ANOVA. Comparing 4 groups with six separate t-tests inflates your chance of a false positive well beyond 5% — ANOVA exists specifically to handle this correctly.
Using a t-test on categorical data. If your outcome is "which category," not "what number," you need chi-square, not a t-test or ANOVA.
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