ANOVA

Compare means across groups

ANOVA

ANOVA (Analysis of Variance) compares means across three or more groups to determine if there are significant differences.

When to Use

  • Multiple groups: Compare means across 3+ groups
  • Categorical predictor: One categorical variable defining groups
  • Continuous outcome: Numeric variable to compare

Example: Compare test scores across students in different schools.

Data Requirements

  • Outcome Variable: Continuous numeric variable
  • Group Variable: Categorical variable with 3+ groups
  • Sample Size: At least 2 observations per group
  • Independence: Observations are independent

How to Run

  1. Select “ANOVA” from the test dropdown
  2. Choose your CSV file
  3. Select your outcome variable
  4. Select your group variable
  5. Click “Run Test”

Interpreting Results

Key Statistics

  • F-statistic: Ratio of between-group to within-group variance
  • p-value: Probability of observing these differences by chance
  • Degrees of Freedom: Between and within groups
  • Group Means: Average values for each group

Statistical Significance

  • p < 0.05: At least one group differs significantly
  • p < 0.01: Strong evidence of differences
  • p < 0.001: Very strong evidence of differences

Effect Size

  • Eta-squared: Proportion of variance explained by groups
  • Large effect: η² > 0.14
  • Medium effect: η² = 0.06 - 0.14
  • Small effect: η² < 0.06

Assumptions

  • Normality: Data approximately follows normal distribution
  • Independence: Observations are independent
  • Equal Variance: Groups have similar variability
  • Random Sampling: Data collected randomly

Export Options

  • LaTeX: Copy-paste ready tables
  • CSV: Structured data files

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