ANOVA: Analysis of Variance

ANOVA (Analysis of Variance)

is a statistical method used to determine whether there are significant differences between the means of three or more independent groups. It helps test if at least one group differs from the others.

F-Statistic (F-Ratio):

• A measure used to compare group means.

• Lower F-ratios suggest that group means are closer to each other.

All group means are equal (no significant difference).

ANOVA Null Hypothesis (H₀):

At least one group mean is different.

ANOVA Alternative Hypothesis (H₁):

One-Way ANOVA

• TYPES OF ANOVA

• Used when there is one independent variable with three or more levels (groups).

One-Way ANOVA

• Example: Comparing weight loss across three diet types.

• Dependent Variable: Weight loss (continuous).

• Independent Variable: Diet type (three levels)

Two-Way ANOVA

• Used when there are two independent variables.

• It allows you to analyze the main effects and interactions between the two variables.

• TYPES OF ANOVA

Two-Way ANOVA

• Example: Comparing exam performance across teaching methods (factor 1) and gender (factor 2).

does not specify which groups differ.

LIMITATION OF ONE-WAY ANOVA

One-way ANOVA identifies that there is a difference between groups but

1. Continuous (interval or ratio scale).

2. Observations are independent (random sampling)

3. The dependent variable within each group is normally distributed (Shapiro-Wilk Test).

4. Variance among groups is approximately equal (Levene's Test).

ASSUMPTIONS FOR ONE-WAY ANOVA

1. Dependent Variable:

2. Independence: .

3. Normality:

4. Homogeneity of Variance: