Intro statistics · Choosing a test
Which statistical test should I use?
Pick the test from two things: what kind of variable you measured (numbers or categories) and how many groups you compare. This chart covers the tests in a typical intro course.
The chart
| Your question | Data | Test |
|---|---|---|
| Is one mean different from a set value? | One quantitative sample | One-sample t-test |
| Do two separate groups have different means? | Quantitative, two independent groups | Two-sample t-test (often Welch) |
| Did the same subjects change? | Before and after, or matched pairs | Paired t-test |
| Do three or more groups differ? | Quantitative, 3+ groups | One-way ANOVA |
| Is a proportion different from a value, or are two proportions different? | Yes/no outcome | One- or two-proportion z-test |
| Are two categorical variables related? | Two-way table of counts | Chi-square test of independence |
| Do counts match expected shares? | One categorical variable | Chi-square goodness-of-fit |
| Is there a linear relationship between two numbers? | Two quantitative variables | Correlation and linear regression (t-test on the slope) |
Practice scenarios
1. You measure the same 20 students' scores before and after a review session.
Show answer
Paired t-test, because each student is measured twice.
2. You compare average sleep hours for nursing, biology and chemistry majors.
Show answer
One-way ANOVA: one quantitative variable, three independent groups.
3. You ask 300 students their year (first to fourth) and whether they use flashcards (yes or no).
Show answer
Chi-square test of independence: two categorical variables in a 4 × 2 table.
4. You test whether hours studied predict exam score.
Show answer
Linear regression, testing whether the slope differs from 0.
Frequently asked questions
What if my data are very skewed and the sample is small?
t-procedures assume roughly normal data or a large enough sample. With small, skewed samples, many courses use a nonparametric test such as the Wilcoxon or Mann-Whitney test.
Why use Welch's t-test?
It does not assume the two groups have equal variances, so it is a safe default for two independent means.
Reference: OpenStax Introductory Statistics 2e, chapters 9 to 13.