# Mixed-design ANOVA

From Wikiversity

The **mixed-model design ANOVA** gets its name because there are two types of variables involved, that is at least one between-subjects variable and at least one within-subjects variable.

## Design[edit]

The **mixed-design ANOVA** model (also known as Split-plot ANOVA (SPANOVA)) tests for mean differences between two or more independent groups whilst 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 amongst the heights of males and females at age 10 and age 20 years?

- Gender (male or female) is the between-subjects variable
- Age (10 or 20 years) is the within-subjects variable
- Of interest are the main effects for Gender and Age, and the Gender-Age interaction effect.
- This could be described as a 2 x (2) mixed-design ANOVA

More mixed-design ANOVA research scenarios.

## Assumption testing[edit]

**Design**:- One or more
**within-subject variables**e.g., time (pre-exercise and post-exercise pulse rates) - 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]

Search for on Wikipedia.Mixed-design ANOVA |

## External links[edit]

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