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


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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

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

See also

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Search for Mixed-design ANOVA on Wikipedia.
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