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M09.02.14 Analysis of Variance (ANOVA)
ANOVA, or Analysis of Variance, is a statistical method used to compare the means of three or more groups. It calculates an F-statistic, which helps determine if there are significant differences between group means. A significant p-value in an ANOVA result indicates that at least two group means differ from each other.
Types of ANOVA
- One-Way ANOVA
- Purpose: Compares the means of two or more groups based on a single nominal variable and an interval variable.
- Interpretation: A significant p-value suggests that there is a difference between at least two of the groups.
- Use Case: Used when examining a single factor across multiple groups.
- Two-Way ANOVA
- Purpose: Compares the means of groups generated by two nominal variables using an interval variable.
- Interpretation: Tests for the main effects of each variable and interaction effects between the variables.
- Use Case: Useful when examining the impact of two independent factors on a dependent variable.
- Repeated Measures ANOVA
- Purpose: Analyze data from multiple measurements taken from the same individuals over time.
- Interpretation: Assesses whether there are changes over time and if individual measurements differ.
- Use Case: Commonly used in longitudinal studies or experiments with repeated observations on the same subjects.
ANOVA Output Table
| ANOVA Type | Nominal Variables | Interval Variable | Purpose | Significance Interpretation |
|---|---|---|---|---|
| One-Way ANOVA | 1 | 1 | Tests if there are differences in means among groups | Significant p-value: at least two groups differ |
| Two-Way ANOVA | 2 | 1 | Tests main and interaction effects of two variables | Significant p-value: main and/or interaction effects |
| Repeated Measures ANOVA | 1 | 1 | Examines changes over time in the same individuals | Significant p-value: indicates variation over time |
Key Points to Remember
- F-Statistic: Used to evaluate if variances between groups are significantly different.
- P-Value: Determines the significance of the observed differences.
- Assumptions: Normal distribution, homogeneity of variance, and independence of observations.
- Applications: Useful in experimental design and comparative studies.
Bibliography
- Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2021). Statistics for Business and Economics. Cengage Learning.
- McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.