Mixed-design ANOVA

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
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?
 * 1) Gender (male or female) is the between-subjects variable
 * 2) Happiness Day (weekday or weekend) is the within-subjects variable
 * 3) Of interest are the main effects for Gender and Happiness Day, and the Gender-Happiness Day interaction effect.
 * 4) 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:
 * 1) Main effect for the within-subject variable
 * 2) Main effect for the between-subject variable
 * 3) Interaction between the within- and between-subject variable

Assumption testing

 * 1) Design:
 * 2) One or more within-subject variables e.g., day (weekday and weekend)
 * 3) One or more between-subject variables e.g., gender
 * 4) Sample size - ideally, at least 20 cases per cell
 * 5) Normality - Distribution of the DV (e.g., pulse rate) for each cell is normal
 * 6) Independence: Each participants' responses are sampled independently from each other participants' responses (e.g., this can be satisfied by random selection).
 * 7) Homogeneity of variance: Cells have similar variances.
 * 8) 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).
 * 9) 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)
 * 10) See also these lecture slides