PSYC3010 – Mixed ANOVA & Within-Participants Designs

Question-and-Answer flashcards covering key concepts, formulas, advantages, disadvantages, and practical examples related to within-participants designs and two-way mixed ANOVA from the PSYC3010 lecture.

What is the key statistical advantage of a within-participants (WP) design?

It allows variance due to individual differences to be estimated and removed, yielding a smaller error term and more statistical power.

Why do within-participants ANOVAs typically require fewer participants than between-participants (BP) ANOVAs?

Because each participant provides data in all conditions, reducing the number of unique participants needed to detect the same effect size.

Name two common order effects that threaten WP designs.

Learning/practice effects and fatigue effects (others include sensitisation, habituation, contrast, etc.).

How can researchers minimise order effects in WP designs when feasible?

By counterbalancing the order of conditions across participants using randomised sequences.

Why is counterbalancing often impossible in a pre–post intervention study?

Because the temporal ordering (pre-test then post-test) is inherent to the research question and cannot be rearranged.

What combination of factors defines a mixed factorial design?

It contains at least one fixed between-participants factor and at least one fixed within-participants factor.

In a two-way mixed design, how many omnibus tests are conducted?

Three: BP main effect, WP main effect, and the BP × WP interaction.

Which error term is used for the BP main effect F-test in a mixed ANOVA?

Participants-within-groups variance (MSparticipants).

Which error term is used for both the WP main effect and the BP × WP interaction in a mixed ANOVA?

The WP factor × Participant interaction variance (MSWP×P).

Complete the research question: ‘Does the effect of the WP factor on the DV change …?’

… at each level of the BP factor (i.e., is there a BP × WP interaction?).

What does a significant BP × WP interaction indicate?

That the simple effect of one factor differs across levels of the other factor.

After finding a significant WP main effect with three levels, what follow-up analyses are needed?

Pairwise comparisons (e.g., paired t-tests) with separate error terms calculated for each comparison (Time × Participant interaction).

When following up a significant BP main effect with more than two levels, what error term is retained?

The original Participants-within-groups error term from the omnibus BP test.

In the social-anxiety example, what were the two factors and their levels?

WP factor = Time (Pre-test, 1-week post-test, 6-month post-test); BP factor = Condition (Control, Intervention).

Why is adding a BP control group useful in a WP pre–post design when counterbalancing is impossible?

It helps detect natural changes over time, allowing researchers to attribute WP effects specifically to the intervention.

Define ‘participants’ as a factor in a mixed ANOVA.

A random factor nested within BP levels and crossed with WP levels, capturing individual differences.

State the formula for the F-ratio for the WP main effect in a mixed ANOVA.

F = MSWP / MSWP×Participants.

What does MSBP×WP represent in the ANOVA table?

The mean square for the BP × WP interaction, reflecting systematic variance not explained by the two main effects.

List two advantages of mixed designs relative to fully BP designs.

1) Reduced error variance through WP factors; 2) Fewer participants needed because each person contributes multiple scores.

List two advantages of mixed designs relative to fully WP designs.

1) Ability to include a BP control group to check order effects; 2) Avoids impossible counterbalancing by assigning certain factors between subjects.

Give an example of a factor better tested between participants and explain why.

Intervention condition, because exposure to multiple interventions would contaminate effects and is often impossible or unethical.

Give an example of a factor better tested within participants.

Time (e.g., pre-, post-test), because each participant naturally experiences all time points.

What is the main disadvantage of WP designs that mixed designs help to offset?

Susceptibility to order/sequencing effects.

Why is statistical power typically higher in WP designs compared with BP designs?

Because the error variance is reduced by accounting for individual differences, increasing the F-value for true effects.

What degrees-of-freedom formula is used for the BP factor in a 2×3 mixed design?

dfBP = b – 1, where b = number of BP levels (e.g., 2 – 1 = 1).

In variance partitioning, what is SSparticipants?

Sum of squares representing variability among participants within each BP group (individual differences).

What does the term ‘nested’ mean regarding participants in mixed ANOVA?

Each participant is contained within (belongs to) only one level of the BP factor.

Which graphical display is most helpful for interpreting a significant interaction in mixed ANOVA?

A line or bar graph of the cell means plotting one factor on the x-axis and separate lines/bars for the other factor.

Describe the pattern of results that would confirm the social-anxiety intervention was effective.

Social anxiety decreases from pre-test to both post-tests in the intervention group but remains unchanged in the control group (significant Time × Condition interaction).

How is the simple effect of time tested within each BP group?

By running separate one-way WP ANOVAs (or paired t-tests) on the time points for each BP condition and using their own Time × Participant error terms.

When are separate error terms recalculated for follow-up tests in mixed ANOVA?

For any WP follow-up comparisons (main effects or simple effects) because the error term must match the subset of data being analysed.

What consequence arises if researchers interpret only a significant main effect while ignoring an interaction?

They may draw misleading conclusions because the main effect could mask different patterns across the other factor’s levels.

Why are WP designs more susceptible to hypothesis guessing by participants?

Participants experience every condition and can detect study aims, potentially altering their behaviour to help or hinder the experimenter.

What distinct advantage do mixed designs offer for real-world modelling?

They reflect natural scenarios where individuals belong to distinct groups (BP) yet experience repeated conditions or times (WP).

State the generic definition of an F-test in ANOVA.

An F-test is the ratio of variance associated with an effect to the error variance appropriate for that effect (F = MSeffect / MSerror).