# Mixed-design ANOVA

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The **mixed-model design ANOVA** gets its name because there are two types of variables involved, that is at least one:

- between-subjects variable
- within-subjects variable

## Design[edit | edit source]

The **mixed-design ANOVA** model (also known as Split-plot ANOVA (SPANOVA)) tests for mean differences between two or more independent groups while subjecting participants to repeated measures. Thus, there is at least one between-subjects variable and at least one within-subjects variable.

For example, are there differences in males' and females' happiness on weekdays and weekends?

- Gender (male or female) is the between-subjects variable
- Happiness Day (weekday or weekend) is the within-subjects variable
- Of interest are the main effects for Gender and Happiness Day, and the Gender-Happiness Day interaction effect.
- This could be described as a 2 x (2) mixed-design ANOVA

More mixed-design ANOVA research scenarios

The results are interest in a two-variable mixed-design ANOVA are:

- Main effect for the within-subject variable
- Main effect for the between-subject variable
- Interaction between the within- and between-subject variable

## Assumption testing[edit | edit source]

**Design**:- One or more
**within-subject variables**e.g., day (weekday and weekend) - One or more
**between-subject variables**e.g., gender

- One or more
**Sample size**- ideally, at least 20 cases per cell**Normality**- Distribution of the DV (e.g., pulse rate) for each cell is normal**Independence**: Each participants' responses are sampled independently from each other participants' responses (e.g., this can be satisfied by random selection).**Homogeneity of variance**: Cells have similar variances.**Sphericity**: Population variances of the repeated measurements are equal and the population correlations among all pairs of measures are equal. Tested by Mauchly's. Violation increases Type I error rate. If violated, interpret adjusted results (e.g., Greenhouse-Geisser).**Homogeneity of inter-correlations**: Tested by Box's*M*: "The assumption ... is that the vector of the dependent variables follow a multivariate normal distribution, and the variance-covariance matrices are equal across the cells formed by the between-subjects effects." (SPSS 14 Help - Tutorial)- See also these lecture slides

## See also[edit | edit source]

Search for on Wikipedia.Mixed-design ANOVA |

## External links[edit | edit source]

- Mixed between-within subjects ANOVA (allnurses.com)