Analysis of Variance (ANOVA)

by | Jan 30, 2020

ANOVA is a hypothesis test to check whether the average differences between groups are significant or only due to random chance. It works when the Y variable is continuous and the X variable is discrete.

Practitioner’s Tip: The name ANOVA (ANalysis Of VAriances) comes from the statistical procedure the tool conducts. However, for the practitioner, it’s important to remember that the tool compares averages, not variances.

Assumptions:

  • Equal variances and normal distribution within the groups under comparison

Step-by-step approach:

  1. Visualize the data: Use a stratified frequency plot, e.g. dot plot
  2. Formulate hypotheses:
    • H0: 𝜇1=𝜇2=𝜇3=𝜇4=𝜇5…
    • HA: At least one m is different
  3. Decide on Alpha risk: Usually 0.05
  4. Select and conduct an appropriate test: Retrieve p-value
  5. Verify test assumptions:
    • Data in the groups are normally distributed.
    • Groups don’t have different variances
  6. Make a decision: If p<α decide for the Alternative Hypothesis (there’s a difference)