What is the Difference Between ANOVA and MANOVA?

The main difference between ANOVA (Analysis of Variance) and MANOVA (Multivariate Analysis of Variance) is the number of dependent variables they analyze. ANOVA is used to assess differences in means on a single continuous dependent variable, while MANOVA evaluates mean differences on two or more dependent variables simultaneously.

To summarize:

• ANOVA:
• Evaluates mean differences on a single dependent criterion variable.
• Mainly checks the differences between the means of two samples/populations.
• Helps in mean comparison simultaneously.
• MANOVA:
• Evaluates mean differences on two or more dependent criterion variables simultaneously.
• Assesses differences in means on multiple continuous dependent variables.
• Minimizes the Type 1 error rates and thoroughly analyzes.

Researchers typically use MANOVA when they want to investigate the relationships among variables instead of looking at each variable individually. Both ANOVA and MANOVA tests are used to analyze variance by measuring the differences in means between groups. However, MANOVA is often used when the dependent variables are highly negatively or positively correlated, whereas ANOVA is used for a single continuous variable.

Comparative Table: ANOVA vs MANOVA

Here is a table comparing ANOVA and MANOVA:

Both ANOVA and MANOVA are statistical tools used to measure the means of independent groups having dependent variables. The main difference between them is the number of dependent variables involved. ANOVA deals with a single dependent variable, while MANOVA handles multiple dependent variables.