One-Way MANOVA vs One-Way ANOVA

 One-Way MANOVA








 












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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