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Maths Skills Centre: a practical guide to maths & statistics

Which statistical test?

Which statistical test?

There are many statistical tests for different data and situations. Use this guide to identify the appropriate statistical test to analyse your data.

Getting started

Not sure which variables or data types you have? Work through our guide before choosing your test:

You can also view our workshop materials on choosing a statistical test to walk you through using the tool:

Personalise this page

Many different words can be used to describe types of variables, data and statistical tests. If our words don't look familiar, you can change them to your preferred terminology:

variables you measure
variables you control
numerical variables
ordered variables
variables with groups/levels
study design

Some statistical tests also have alternative names. You can choose to show or hide these test name synonyms:

Choose a statistical test

  • scale dependent variable

    • 1 nominal independent variable

      • independent variable has 2 groups
        • t-test if data is normally distributed

          also called: Student's t-test, 2-sample t-test, independent t-test

        • Mann Whitney U if data is not normally distributed

          also called: Wilcoxon-Mann Whitney U

        • paired t-test if data is matched and normally distributed

          also called: dependent t-test, match t-test

        • Wilcoxon if data is matched but not normally distributed

          also called: Wilcoxon signed rank test

      • independent variable has 3+ groups
        • 1 way ANOVA if data is normally distributed
        • Kruskal-Wallis if data is not normally distributed
        • repeated measures ANOVA if data is matched

          also called: within-subjects ANOVA, one-way ANOVA with repeated measures

    • 2 nominal independent variables

      • independent variable has 2+ groups
        • 2 way ANOVA

          also called: factorial ANOVA

    • 1 scale independent variable

      • simple regression

        also called: simple linear regression, regression, linear model

    • 1 ordinal independent variable

      • simple regression if assumptions are met

        also called: simple linear regression, regression, linear model

    • 2+ independent variables

      • independent variables are scale, ordinal or nominal
        • multiple regression
      • 1 independent variable is matched
        • mixed effect regression

          also called: mixed effects model, mixed effect regression, multiple regression with random variable, multiple regression with winthin subjects variable

  • ordinal dependent variable

    • 1 nominal independent variable

      • independent variable has 2 groups
        • Mann Whitney U

          also called: Wilcoxon-Mann Whitney U

        • Wilcoxon if data is matched

          also called: Wilcoxon signed rank test

      • independent variable has 3+ groups
        • Kruskal Wallis

    • 2+ independent variables

      • independent variables are scale, ordinal or nominal
        • ordinal regression (more advanced test)

          also called: ordinal logistic regression

  • nominal dependent variable

    • 1 nominal independent variable

      • Chi square for association is commonly used

    • 1+ independent variable

      • dependent variable has 2 groups
        • binary logistic regression (more advanced test)

          also called: binomial regression, binary regression

      • dependent variable has 2+ nominal groups
        • multinomial regression (more advanced test)

  • no obvious dependent variable

    • 2 nominal variables

      • Chi square for association
      • Fisher's Exact test

    • 2 ordinal variables

      • Spearman's rank correlation

        also called: Spearman's rho

      • Chi square for association if few ordinal categories

    • 1 ordinal and 1 scale variable

      • Spearman's rank correlation

        also called: Spearman's rho

    • 2 scale variables

      • Pearson's correlation

        also called: Pearson's r

Tips

  • If you have more than 1 dependent variable, usually a statistical test is run on each dependent variable separately. If you're sure you want to put multiple dependent variables into the same statistical test, you'll need to do some research on using multivariate analyses such as MANOVA, PCA, factor analysis or cluster analysis.
  • Likert-style questions are ordinal data and should probably not be treated as scale data. Totals and means derived from several Likert-style questions are more commonly treated as scale data.
  • Always check that your data meets any assumptions of a test you use.