Which Statistical Test Should I Use?

Answer a few questions about your variables and find the right test for your analysis. Follow the interactive decision tree below, or jump to the static lookup table if you already know what you're looking for.

Variable Types: A Quick Reference

Before starting, make sure you can classify your own variables. Here are the four types:

Nominal (categorical)
Categories with no natural order. E.g., blood type (A, B, AB, O), major (biology, history, engineering), gender (male, female, non-binary).
Ordinal (ranked)
Categories in a meaningful order, but intervals between them are not equal. E.g., survey responses (strongly disagree, disagree, neutral, agree, strongly agree), education level (high school, bachelor's, master's, PhD).
Interval
Numerical data where the intervals are equal, but there is no true zero. E.g., temperature in Celsius (0°C is just a point, not "no temperature"), year (there is no year zero in common usage).
Ratio
Numerical data with equal intervals and a true zero point. E.g., height (0 cm means no height), weight (0 kg means no weight), age (0 years is birth), test score out of 100.

Tip: Interval and ratio data are often treated the same in practice and called "continuous" or "numeric" data. If you have a true zero, it's ratio; if not, it's interval.

Interactive Decision Tree

What are you trying to do?

Main analysis goal

How many groups or conditions are you comparing?

Number of groups

Are the groups independent or dependent?

Group structure

What type of outcome variable do you have?

Outcome type

Is your numeric outcome roughly normally distributed?

Normality assumption

What types are your two variables?

Variable types for relationship analysis

What type is your outcome variable?

Outcome type for prediction

§ The Static Lookup Table

If you know your variable types, find your test here. Rows represent your outcome type and group structure; columns show the recommended parametric test and its non-parametric fallback.

Analysis Type Outcome Type Parametric Test Non-Parametric Alternative
One sample vs. known value Numeric One-sample t-test One-sample median (Wilcoxon signed-rank)
Categorical Binomial test or chi-square goodness-of-fit
Two independent groups Numeric Two-sample t-test Mann-Whitney U test
Ordinal Mann-Whitney U test
Categorical Chi-square or Fisher's exact
Two dependent groups (paired/repeated) Numeric Paired t-test Wilcoxon signed-rank test
Ordinal Wilcoxon signed-rank test
Categorical (binary) McNemar test
3+ independent groups Numeric One-way ANOVA Kruskal-Wallis test
Ordinal Kruskal-Wallis test
Categorical Chi-square test of independence
3+ dependent groups (repeated measures) Numeric Repeated measures ANOVA Friedman test
Ordinal Friedman test
Relationship between two variables Both numeric, linear Pearson correlation Spearman correlation
At least one ordinal or non-linear Spearman correlation
Both categorical Chi-square test of independence
Predict numeric outcome Numeric (continuous) Linear regression (simple or multiple)
Predict binary outcome Binary (yes/no) Logistic regression (simple or multiple)
Describe one sample Numeric Mean, standard deviation, and confidence interval
Categorical Proportion and confidence interval

§ Parametric vs. Non-Parametric in One Paragraph

Parametric tests (t-test, ANOVA, Pearson correlation) assume your outcome is normally distributed and may assume equal variances across groups. They are more powerful (better at detecting real effects) when assumptions hold. Non-parametric tests (Mann-Whitney U, Wilcoxon, Spearman, Kruskal-Wallis) make fewer assumptions and work on ranks or categories, so they're safer when your data is skewed, has outliers, or is ordinal. However, they're slightly less powerful when your data is truly normal. A modern rule of thumb: use the parametric test if your outcome is numeric and either the data is roughly normal or you have at least ~30 observations per group (so the Central Limit Theorem saves you). Otherwise, use the non-parametric version.

§ What to Do When Your Assumptions Fail

Non-normal data? Check the sample size. If n ≥ 30 per group, proceed with the parametric test—the Central Limit Theorem makes the test robust. If n < 30, make a plot (histogram, Q-Q plot) to decide: if it's only slightly skewed, parametric is usually still fine; if it's heavily skewed or has extreme outliers, use the non-parametric alternative.

Unequal variances? For t-tests, use Welch's t-test (which doesn't assume equal variances) instead of Student's t-test. For ANOVA, the same idea applies (Welch's ANOVA). These are the modern default.

Categorical outcome? Chi-square tests require at least 5 observations in each cell. If you have cells with expected counts < 5, use Fisher's exact test (for 2×2 tables) or consider collapsing categories if it makes scientific sense.

Dependent observations? Never ignore dependence (e.g., repeated measures, matched pairs, clustered data). Using an independent test on dependent data will underestimate uncertainty and give false confidence. Always use the matched or repeated-measures version of the test.

§ Frequently Asked Questions

How do I know if my data is normal?

Make a histogram or Q-Q plot. A histogram should look roughly bell-shaped; a Q-Q plot should show points close to a diagonal line. You can also run a Shapiro-Wilk test or Kolmogorov-Smirnov test, but these are sensitive to sample size—with huge samples, trivial deviations from normality will "reject" normality, and with small samples, the test has low power. Use the plot plus your sample size as a guide. If n ≥ 30, mild departures from normality are okay.

What's the difference between ordinal and nominal data?

Ordinal data has a meaningful order (e.g., 1 = strongly disagree, 5 = strongly agree). Nominal data does not (e.g., red, blue, green—no order). The test you choose depends on whether order matters. For ordinal data, Mann-Whitney or Spearman are often better than chi-square. For nominal data, chi-square is the standard.

Do I have to test the assumptions first?

No formal "assumption test" is required before running your analysis. Instead, (1) think about your design (are observations independent?), (2) look at the data (is it roughly normal, are there outliers?), and (3) know your sample size. Run the parametric test if it's reasonable; if you're uncertain, compare it to the non-parametric version. Modern practice focuses less on formal assumption tests and more on visual inspection and robustness.

What if I'm comparing two groups and I'm not sure whether they're independent or dependent?

They are independent if each person contributes one observation, and different people are in group A vs. group B. They are dependent if the same person (or matched pairs) appear in both groups (e.g., before and after treatment). If you're still unsure, ask: "Could I match observation A to observation B?" If yes, they're dependent; if not, they're independent.

Why does my textbook recommend test X, but this tool says test Y?

Different sources may emphasize different tests based on their discipline and when they were written. For example, some fields traditionally use one-way ANOVA for 3+ groups, while others prefer Kruskal-Wallis by default. This tool follows modern consensus from sources like UCLA OARC and emphasizes the best choice for your actual data type and assumptions. When in doubt, discuss your choice with your instructor.

Can I use this tool for multivariate analyses (multiple outcomes or predictors)?

This tool focuses on univariate tests (one outcome). If you have multiple outcomes, you would use MANOVA. If you have multiple predictors and one numeric outcome, use multiple regression; for binary outcomes, use multiple logistic regression. These are beyond the scope of this decision tree, but the same principle applies: think about your outcome type and predictors, then choose the test.

§ Sources

This tool was developed using the following sources: