ANOVA (Analysis of Variance) is a statistical test used to determine whether there are significant differences between the means of three or more groups. It helps answer: Are the group means statistically different from each other?
1. Null Hypothesis (H₀): All group means are equal.
2. Alternative Hypothesis (H₁): At least one group mean is different.
3. Use Case: When comparing more than two groups. If you only have two groups, a t-test is simpler.
ANOVA compares two types of variation:
1. Between-group variation: Differences between the group means.
2. Within-group variation: Variability of data points within each group.
If the between-group variation is much larger than the within-group variation, it suggests the means are significantly different.
Types of ANOVA:
1. One-way ANOVA: Tests the impact of one factor (e.g., comparing test scores across three teaching methods).
2. Two-way ANOVA: Tests the impact of two factors and their interaction (e.g., comparing test scores by teaching methods and gender).
Example: One-Way ANOVA
Scenario: You test three diets (A, B, C) to see if they lead to different weight loss results.
Data:
Group A: [4, 5, 6]
Group B: [7, 8, 9]
Group C: [3, 4, 5]
Steps:
1. Calculate the mean for each group.
2. Measure the variation between and within groups.
3. Compute the F-ratio (a statistic that compares the variations).
4. Check the F-value against a critical value or p-value:
If p-value < 0.05, reject the null hypothesis (significant difference exists).
ANOVA tells you if there's a difference but not which groups differ. For that, use a post-hoc test (e.g., Tukey's test).
Data should meet these assumptions:
1. Groups are independent.
2. Data is normally distributed.
3. Variances are roughly equal (homogeneity of variance).