12.3 ANOVA (Analysis of Variance)
12.3.1 What is ANOVA?
ANOVA, which stands for Analysis of Variance, is a statistical method used to compare the means of three or more independent (unrelated) groups. It is often used when we want to determine if there are any significant differences between the means of these groups. While the t-test is used to compare two means, ANOVA is a more suitable option when we want to compare more than two means. This is because it allows us to test for differences between several groups at once.
As mentioned earlier, the null hypothesis in an ANOVA test is that all group means are equal. However, the alternative hypothesis is that at least one group mean is different from the others. This means that ANOVA is a powerful tool for detecting differences between groups, which makes it a valuable tool for researchers who are trying to understand the effects of different variables on a particular outcome.
Furthermore, ANOVA allows us to examine the variance within...