### 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.

#### Post-Hoc Tests:

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