What is ANOVA (Analysis of Variance)?
ANOVA (Analysis of Variance) is a statistical method for testing whether the average (mean) of a numeric variable differs across three or more groups. It tells you if group differences are unlikely to be due to random chance.
ANOVA compares the variation between group means to the variation within groups to decide whether observed differences are statistically meaningful. For example, a one-way ANOVA tests whether the mean satisfaction score differs across language groups; a two-way ANOVA tests the effects of two factors (e.g., language and school) and their interaction; repeated-measures ANOVA is used when the same people are measured multiple times. ANOVA itself indicates whether at least one group differs from the others; follow-up (post-hoc) tests identify which specific groups differ.
Usage example
We ran a one-way ANOVA to check whether average survey satisfaction scores differed between respondents answering in English, Spanish and Arabic. The ANOVA showed a significant difference, so we followed up with pairwise comparisons to see which language groups differed.
Practical application
ANOVA matters because it helps you decide if observed differences across groups (languages, locations, age bands, treatment vs control) are likely real or just noise. In practical terms, it guides decisions such as where to target improvements, whether a new program had an impact, or whether different language communities are experiencing services differently. For survey teams using Hearo, ANOVA is useful for comparing numeric outcomes (scores, counts, ratings) across groups defined by language, school, neighbourhood or other categories — but open-text answers must first be coded or scored numerically.
FAQ
What does a 'significant' ANOVA result mean?
A significant result means there is statistical evidence that not all group means are equal — at least one group differs from the others. It does not tell you which groups differ; you need post-hoc tests (for example Tukey) to locate specific differences.
What assumptions does ANOVA make and why do they matter?
Common assumptions are independence of observations, roughly normal distribution of the outcome within groups, and similar variances across groups. Violations can affect the reliability of results; if assumptions fail, alternatives like Welch’s ANOVA (for unequal variances) or non-parametric tests (Kruskal–Wallis) may be better.
Can I use ANOVA with survey data collected in different languages?
Yes — provided the outcome is a numeric variable (e.g., a rating or a coded score). You can compare means across language groups to see if experiences differ. Make sure translations are consistent and that you code open-text responses carefully before analysis.
How many groups or respondents do I need for ANOVA?
ANOVA can handle three or more groups, but statistical power depends on group sizes and the size of differences you expect. Small groups make it harder to detect real differences; aim for balanced and sufficiently large samples when possible.