Mathematics and Statistics Support

# ANOVA (between subjects)

Dependent (outcome) variable: Continuous/numerical/scale (some disciplines also test ordinal data)

Independent (predictor/explanatory) variable: A one way ANOVA has only one independent categorical variable with at least 3 groups. Two-way ANOVA has two categorical independent variables each with at least two groups and ANCOVA is when at least one independent variable is continuous

Use: Used to detect the difference in means of 3 or more independent groups. It can be thought of as an extension of the independent t-test for 3 or more independent groups. ANOVA stands for Analysis of Variance as uses the ratio of the between group variance to the within group variance to decide whether there are statistically significant differences between the groups or not.
Example: A basic one way ANOVA could be used to compare exam score for students in one of three research methods tutorial groups using different teaching methods to see which is most effective. If you wished to add another categorical independent variable, such as gender, this would be a two-way ANOVA and you wanted to add a continuous variable such as age or percentage exam score in their last module, you would need an ANCOVA.

Assumptions: The residuals (requested as part of the output) should be approximately normally distributed. If a histogram or QQplot suggests the residuals are vey skewed or the dependent variable is ordinal, a Kruskall-Wallis test (which is based on ranks rather than the raw data) can be used instead of a one-way ANOVA but there is no non-parametric equivalent to two way ANOVA or ANCOVA. Some people use parametric tests for ordinal data if there are quite a few categories but be careful when interpreting differences

Data notes Ensure there is only one row per participant with the dependent variable in one column and each independent variable in it's own column.

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SPSS R Sheet R Script Jamovi SAS Mathematical
Understanding One way ANOVA     Two way ANOVA    Interactions for ANOVA   ANCOVA #### Need help choosing the right statistical test? Use our online test chooser 