ANOVA (Analysis of Variance)
ANOVA is a statistical method used to compare the means of three or more groups. It determines if there are any statistically significant differences between the means of multiple groups.
Assumptions of ANOVA:
- Independence: Each group’s observations are independent of the other groups. Typically, this is achieved by random sampling.
- Normality: The dependent variable should be approximately normally distributed for each group. This assumption can be checked using histograms, Q-Q plots, or statistical tests like the Shapiro-Wilk test.
- Homogeneity of Variance: The variances of the different groups should be roughly equal. Levene’s test is often used to check this assumption.
- Random Sampling: Each group’s observations should be randomly sampled from the population.
- Measurement Level: The dependent variable should be measured on an interval or ratio scale (i.e., continuous), while the independent variable should be categorical.
- Absence of Outliers: Outliers can influence the results of the ANOVA test. It’s essential to check for and appropriately handle outliers in each group.
Why use ANOVA for more than three groups?
When comparing the means of more than two groups, you might think of conducting multiple t-tests between each pair of groups. However, doing so increases the probability of committing a Type I error (falsely rejecting the null hypothesis). ANOVA is designed to compare multiple groups simultaneously, while controlling the Type I error rate.
If the ANOVA test is significant, it only tells you that there’s a difference in means somewhere among the groups, but it doesn’t specify where the difference lies. To pinpoint which groups differ from one another, post-hoc tests (like Tukey’s HSD or Bonferroni) are conducted