Statistics

Statistical Test Finder

Answer a few questions about what you want to find out, how your variables are measured and how your groups are structured. The finder suggests tests that are commonly used for that situation and explains why each may fit. It never decides for you.

Free, no account

Describe your study

Answer from your research question and variables. Each answer brings up the next question that matters.

What are you trying to find out?

Start from your research question or objective. The purpose narrows the family of tests before anything about the data does.

Describe a variableSummarise its typical value and how spread out it is, without testing anything.Compare groups, times or a target valueAsk whether an outcome differs between groups, changes over time in the same people, or differs from a known value.Examine a relationship between two variablesAsk whether two measured variables go together, and how strongly.Predict or explain an outcomeEstimate an outcome from one or more other variables.Examine categoriesAsk whether two categorical variables are associated, or whether one variable's categories match expected shares.

Candidate tests

What the finder still needs to know

No test is suggested until these are answered, so nothing is guessed.

What are you trying to find out? The purpose of the analysis decides which family of tests to consider.

Apply it to your research

The finder helps you choose; it doesn't save anything. Your analysis plan is kept by the Data Analysis Recommender, which reads your whole project.

Before you choose

The same reasoning the finder uses, laid out so you can follow it yourself.

Independent or paired?

Independent groups

Group A

Participant 1
Participant 2
Participant 3

Group B

Participant 4
Participant 5
Participant 6

Six different people: each appears in one group only, so the two sets of scores are unrelated.

Paired observations

Participant 1 measured Before then After
Participant 2 measured Before then After
Participant 3 measured Before then After

Three people, each measured twice: every “after” score belongs with one “before” score.

Independent groups and paired observationsPaired scores are related: a person who scores high before usually scores high after. Paired tests use that link by analysing each person's change, which removes differences between people from the comparison. Treating paired data as independent ignores the link; treating independent groups as paired invents one. Either way the test answers the wrong question.

The decision tree

Choosing a statistical test: a decision treeFollow the questions from the top. Each path ends in the tests commonly used for that situation. It shows common practice, not the only valid choice.

What are you trying to find out?

Describe a variable
How is the variable measured?
- Nominal (categories)
  Commonly used: Mode, Frequency
  May also fit: Percentage
- Ordinal (ordered categories)
  Commonly used: Median
  May also fit: Frequency, Mode
- Interval or ratio, roughly symmetric
  Commonly used: Mean, Standard deviation
  May also fit: Median
- Interval or ratio, skewed
  Commonly used: Median
  May also fit: Mean, Standard deviation
Compare groups, times or a target value
What are you comparing?
- One group with a stated value
  How is the outcome measured?
  Interval or ratio
  Commonly used: One-sample t-test
  Nominal (categories)
  Commonly used: Chi-square goodness-of-fit test
- Separate groups of different people (independent)
  How is the outcome measured?
  Interval or ratio
  How are the groups arranged?
  Two groups, one grouping variable
  Commonly used: Independent-samples t-test
  Three or more groups, one grouping variable
  Commonly used: One-way ANOVA
  Two grouping variables together
  Commonly used: Two-way ANOVA
  May also fit: Independent-samples t-test, Multiple regression
  Each grouping variable can have two or more categories.
  Groups compared while controlling for a numeric covariate
  Commonly used: ANCOVA
  May also fit: Independent-samples t-test
  Ordinal
  How many groups?
  Two
  Commonly used: Mann–Whitney U test
  Three or more
  Commonly used: Kruskal–Wallis test
  Nominal (categories)
  Commonly used: Chi-square test of independence
  May also fit: Fisher's exact test
  The same test applies with more groups or categories.
- The same people measured more than once (paired)
  How is the outcome measured, and how many times?
  Interval or ratio, twice
  Commonly used: Paired-samples t-test
  Interval or ratio, three or more times
  Commonly used: Repeated measures ANOVA
  Ordinal, twice
  Commonly used: Wilcoxon signed-rank test
Examine a relationship between two variables
How are the two variables measured?
- Both interval or ratio, roughly normal
  Commonly used: Pearson correlation
  May also fit: Simple linear regression
- At least one ordinal
  Commonly used: Spearman's rank correlation
Predict or explain an outcome
How is the outcome measured, and how many predictors?
- Interval or ratio, one quantitative predictor
  Commonly used: Simple linear regression
  May also fit: Pearson correlation
- Interval or ratio, two or more predictors
  Commonly used: Multiple regression
- Two categories, such as yes or no
  Commonly used: Logistic regression
Examine categories
How many categorical variables?
- One, compared with expected shares
  Commonly used: Chi-square goodness-of-fit test
- Two, examined together
  Commonly used: Chi-square test of independence
  May also fit: Fisher's exact test

Common tests compared

Common statistical tests compared Scroll sideways to see every column.
Common candidate test	Research purpose	Outcome	Groups or variables	Structure	Key assumptions	Alternative or related method
One-sample t-test	Does the mean of a quantitative outcome differ from a known or hypothesised value?	One quantitative variable (interval or ratio).	None: a comparison value stated in advance. Groups: One.	Not applicable: one measurement per participant.	Interval or ratio measurement Independence of observations Normality No influential outliers	One-sample Wilcoxon signed-rank test
Independent-samples t-test	Do two separate groups differ in the mean of a quantitative outcome?	One quantitative variable (interval or ratio).	One grouping variable with two categories. Groups: Two.	Independent: each participant is in one group only.	Interval or ratio measurement Independence of observations Normality Homogeneity of variance No influential outliers	Mann–Whitney U test
Paired-samples t-test	Does the mean of a quantitative outcome change between two measurements of the same people?	One quantitative variable, measured twice.	Time or condition: two measurements. Groups: One group, two measurements.	Paired: each participant contributes both measurements, or participants are matched in pairs.	Interval or ratio measurement Paired observations Normally distributed differences No influential outliers	Wilcoxon signed-rank test
One-way ANOVA	Do three or more independent groups differ in the mean of a quantitative outcome?	One quantitative variable (interval or ratio).	One grouping variable (factor) with three or more categories. Groups: Three or more.	Independent: each participant is in one group only.	Interval or ratio measurement Independence of observations Normality Homogeneity of variance No influential outliers Adequate group sizes	Kruskal–Wallis test
Two-way ANOVA	Do two grouping variables, separately and together, relate to differences in a quantitative outcome?	One quantitative variable (interval or ratio).	Two grouping variables (factors), each with two or more categories. Groups: Every combination of the two factors' categories.	Independent: each participant is in one combination only.	Interval or ratio measurement Independence of observations Normality Homogeneity of variance No influential outliers Adequate group sizes	Aligned rank transform ANOVA
ANCOVA	Do groups differ in the mean of a quantitative outcome once a quantitative covariate is allowed for?	One quantitative variable (interval or ratio).	One or more grouping variables, plus one or more quantitative covariates. Groups: Two or more.	Independent: each participant is in one group only.	Interval or ratio measurement Independence of observations Normally distributed residuals Homogeneity of variance Linearity Homogeneity of regression slopes Covariate independent of the grouping No influential outliers	Quade's rank analysis of covariance
Chi-square test of independence	Are two categorical variables associated?	One categorical variable.	A second categorical variable. Groups: Two or more categories of each.	Independent: each participant is counted once, in one cell.	Categorical variables Independence of observations Adequate expected counts	Fisher's exact test
Chi-square goodness-of-fit test	Do the counts in one categorical variable's categories match shares stated in advance?	One categorical variable.	None: expected proportions stated in advance. Groups: Two or more categories.	Independent: each participant falls in one category.	Independent observations. Each participant falls in exactly one category. Expected counts of at least 5 in most categories.	Chi-square test of independence
Pearson correlation	Do two quantitative variables go together in a straight line, and how strongly?	First variable: quantitative.	Second variable: quantitative. Neither needs to be the outcome. Groups: Not applicable: one group, a pair of values per participant.	Each participant contributes one value of each variable.	Interval or ratio measurement Independence of observations Linearity Normality No influential outliers	Spearman's rank correlation
Simple linear regression	How well can a quantitative outcome be predicted from one predictor, and how much does it change per unit of the predictor?	One quantitative variable.	One predictor, usually quantitative. Groups: Not applicable.	Each participant contributes one value of each variable.	Interval or ratio measurement Independence of observations Linearity Normally distributed residuals Homoscedasticity Independent errors No influential outliers	Spearman's rank correlation
Multiple regression	How well do several predictors together predict a quantitative outcome, and what does each add while the others are held constant?	One quantitative variable.	Two or more predictors, quantitative or categorical (entered as dummy variables). Groups: Not applicable.	Each participant contributes one value of each variable.	Interval or ratio measurement Independence of observations Linearity Normally distributed residuals Homoscedasticity Independent errors No influential outliers No multicollinearity	Robust (heteroscedasticity-consistent) standard errors

The table scrolls sideways on narrow screens.

Learn the ideas behind the tests

How to choose a statistical test

The finder suggests tests as you answer, which needs JavaScript. The decision tree and comparison table below work without it.

What should I do next?

You have a test to consider. Now plan and check the analysis.

Power Analysis
Plans the sample size a study needs, or the power it will have, for seven common designs, with every assumption stated.
Effect Size Calculator
Calculate selected standardized effects from reported summary statistics, with formulas and assumptions shown.
SPSS Research Lab
Connects a research question and selected analysis to IBM SPSS Statistics procedures, output tables, assumptions and reporting tools.

How to choose a statistical test
A practical, step-by-step guide to matching a research question, variables and study design with statistical tests, assumptions and interpretation.

How the finder works

Test selection starts from the research question: what you want to find out narrows the family of tests before anything about the data does.
The finder then asks only what matters for that purpose: how the outcome is measured, how many groups there are, whether they are independent or paired, and whether normality is expected. Questions appear one at a time.
Which test suits which arrangement of variables comes from the same rules the Data Analysis Recommender uses, so the two tools agree.
Each candidate says why it may fit, what to check before relying on it, why a similar test may not fit, and what else to consider. Labels describe methodological fit; none says a test is right or wrong.
Assumptions come from the Statistical Assumption Checker's guides, which explain how to check each one.

What this tool can't determine

It suggests tests that commonly fit a situation; it can't decide the right analysis for your study. That depends on your design, your data and your field's conventions, and the final choice is yours and your supervisor's.
It reads only the answers you give. If a measurement level or the structure of your groups is described wrongly, the suggestions will be wrong too.
It can't check assumptions such as normality, which need your data. The Statistical Assumption Checker explains how to check each one.
It covers the tests most used in introductory and postgraduate research methods courses. Some situations, such as multinomial outcomes, repeated categorical measurements or multilevel data, need methods it only names or doesn't cover.
It can't tell you whether a result is important, publishable or correct. It helps you choose; the Results Interpretation Assistant helps you read results.

Privacy

Everything you enter stays in your browser. Nothing is sent anywhere or saved, and it is cleared when you leave the page.