One-Way MANOVA vs One-Way ANOVA
Multi-dependent variable analysis of variance
Tests the hypothesis that the mean vectors of two or more groups are equal across multiple dependent variables
Assumes multivariate normality and equal covariance matrices across groups
One-Way ANOVA
Single-dependent variable analysis of variance
Tests the hypothesis that the mean values of two or more groups are equal on a single dependent variable
Assumes normality and equal variances across groups
Key Differences
| Feature | One-Way MANOVA | One-Way ANOVA |
|---|---|---|
| Number of dependent variables | Multiple | Single |
| Hypothesis | Mean vectors are equal across groups | Mean values are equal across groups |
| Assumptions | Multivariate normality, equal covariance matrices | Normality, equal variances |
| Statistical test | Wilk's Lambda or Pillai's Trace test | F-test |
| Output | Test statistic, p-value, effect size (e.g., eta squared) | Test statistic, p-value, effect size (e.g., eta squared) |
When to Use
One-Way MANOVA: When there are multiple dependent variables that are suspected to be related or correlated, and the researcher is interested in testing their joint effect on the independent variable.
One-Way ANOVA: When there is only one dependent variable, and the researcher is interested in testing the effect of the independent variable on its mean value.
One-Way MANOVA
Advantages:
Controls for correlations among dependent variables
Provides a more comprehensive understanding of group differences
Disadvantages:
More complex to interpret than ANOVA
Requires larger sample sizes
One-Way ANOVA
Advantages:
Simpler to interpret
Requires smaller sample sizes
Disadvantages:
Does not account for correlations among dependent variables
May not provide a complete picture of group differences
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