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
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]
- One or more within-subject variables e.g., day (weekday and weekend)
- One or more between-subject variables e.g., gender
- 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]
[edit | edit source]
- Mixed between-within subjects ANOVA (allnurses.com)