Mixed ANOVA Learning Objectives

Question 1

Describe the characteristics of a mixed factorial design

Answer 1

A mixed factorial design contains at least one of each type of fixed factor (between-participants and within-participants). For example, in relation to factor 1, different groups take part in each level, however in relation to factor 2, the same people take part in their each level.

Question 2

List the various names used to describe “mixed” designs

Answer 2

Split-plot design

Question 3

Specify the general and specific notations for a mixed factorial design

Answer 3

2x3 mixed design (2-level factor 1, 3 level factor 2)

Question 4

Explain what is meant by the following:
- One factor is nested under another factor
- One factor is crossed with another factor

Answer 4

A factor is nested within levels of the between-participant factor, as each participant only participates in one condition of the BP factor. A factor is crossed with the within-participant factor when each participant participates in every condition of the WP factor.

Question 5

Describe the research questions that can be addressed in two-way mixed ANOVA

Answer 5

Is there a main effect of BP on the DV? If there a main effect of WP on the DV? Is there an interaction?

Question 6

Explain how variance is partitioned in two-way mixed ANOVA
- Explain which sources of variance are considered “between-participants” and sources of variance are considered “within-participants”

Answer 6

Variance is divided into between-participants factor variance (between participants variance), participants variance (error) (between participants variance), within participants factor variance (within participants variance), WPFxBPF interaction variance (within participants variance) and WP factor and participant interaction (error) (within participants variance).

Question 7

Explain what each of the following tell us in two-way mixed ANOVA:
- A significant F test for the main effect of the between-participants factor
- A significant F test for the main effect of the within-participants factor
- A significant F test for the WP x BP interaction

Answer 7

• A significant F test for the main effect of the between-participants factor
  That there is a main effect somewhere within the between participant factor
  • A significant F test for the main effect of the within-participants factor
    That there is a main effect somewhere within the within-participants factor
  • A significant F test for the WP x BP interaction
    That there is a significant interaction somewhere within WP x BP.

Question 8

When the F ratio is calculated for each omnibus test in two-way mixed ANOVA, identify which MS terms are used in the numerator and denominator in each case
- Explain how this differs compared to terms used in a fully between-participants design and fully within-participants design

Answer 8

F = MS BPF / MSparticipants
F = MS WPF / MS WPFxBPFparticipants
F = MS WPFxBPF / MS WPFxparticipants

They use different participant/error variance on the denominator.

Question 9

Explain the advantages of mixed ANOVA relative to fully between-participants designs and fully within-participants designs

Answer 9

New factorial possibilities: allow us to test interactions between WP and BP factors, and better mirror real world scenarios
Greater flexibility in design
Greater statistical power and efficiency
Greater clarity regarding order effects