A mixed design combines a between-subjects factor (different groups of participants) with a within-subjects factor (the same participants measured repeatedly).
It is also called a split-plot design.
This design is common in psychology, education, and medicine.
Example: groups of patients (between factor) measured at different time points (within factor).
Structure of the Design
- Between-subjects factor: separate groups of participants (e.g., Drug vs. Placebo).
- Within-subjects factor: repeated measures on each participant (e.g., Week 1, Week 2, Week 3).
- Interaction: tests whether the effect of the within factor depends on the between factor.
Degrees of Freedom
For a design with:
- $$a$$ levels of the between-subjects factor
- $$b$$ levels of the within-subjects factor
- $$n$$ subjects in total
- Between: $$df_{\text{between}} = a - 1$$
- Subjects (within groups): $$df_{\text{subjects}} = N - a$$
- Within: $$df_{\text{within}} = b - 1$$
- Interaction: $$df_{A \times B} = (a-1)(b-1)$$
- Error terms depend on design partitioning.
Example
Two groups of students (Drug, Placebo) are tested across three weeks.
| Group | Week 1 | Week 2 | Week 3 |
|---|---|---|---|
| Drug | 70 | 80 | 90 |
| Placebo | 70 | 72 | 74 |
- Between factor (Group): Drug vs. Placebo
- Within factor (Time): Weeks 1–3
- Interaction: Drug improves over time, Placebo stays flat
Symbolic Formula
$$F = \frac{MS_{\text{effect}}}{MS_{\text{error}}}$$
Where $$\text{effect}$$ may be between, within, or interaction, depending on the hypothesis.
Definition
- Mixed (split-plot) ANOVA: combines a between factor (different groups) and a within factor (repeated measures).
- Use: tests real-world designs where groups are compared across time or conditions.
Visuals
Figure L9.1 — Mixed ANOVA Layout. Two groups (Drug, Placebo) × three repeated measures (Weeks 1–3).
Figure L9.2 — Mixed ANOVA Interaction Plot. Drug group line rises sharply; Placebo line flat.
Figure L9.3 — ANOVA Summary Table for mixed design.
Why This Matters
Mixed designs are realistic and powerful.
They reflect how experiments are often run: groups compared across time.
This design unites the logic of between- and within-subjects testing.
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