How do I interpret the results of an ANOVA test?

Interpreting the results of an ANOVA test involves examining the statistical significance of the test, as well as the effect size and the confidence intervals around the mean differences between groups. Here are the key steps to interpreting the results of an ANOVA test:

1. Check for statistical significance: Look at the p-value, which indicates the probability of obtaining the observed result by chance. If the p-value is less than the alpha level (usually set at 0.05), then the result is considered statistically significant, which means that there is strong evidence to support the conclusion that there is a difference between the groups being compared.
2. Evaluate effect size: Even if the result is statistically significant, it is important to evaluate the effect size, which measures the strength of the relationship between the independent variable(s) and the dependent variable. A common measure of effect size in ANOVA is eta-squared (η²), which ranges from 0 to 1, with higher values indicating a stronger effect.
3. Examine mean differences: If the result is statistically significant, look at the mean differences between groups to see which group(s) are significantly different from one another. This is typically done using post-hoc tests, such as Tukey’s Honestly Significant Difference (HSD) or the Bonferroni correction.
4. Evaluate confidence intervals: Finally, evaluate the confidence intervals around the mean differences to determine the range of plausible values. If the confidence intervals do not overlap between groups, this indicates that the difference between the means is statistically significant.

Overall, interpreting the results of an ANOVA test involves considering both statistical significance and practical significance (effect size), as well as evaluating the mean differences and confidence intervals to determine the significance and direction of differences between groups.