PSYC3010 – Within-Participants ANOVA & Related Concepts

Flashcards cover key terminology, formulas, assumptions, variance components, statistical tests, advantages, disadvantages, and practical examples related to one-way and two-way within-participants ANOVA as presented in the lecture.

What is a within-participants (repeated-measures) design?

A design in which the same participants provide data in every condition/level of the independent variable.

In a fully within-participants factorial design, what kinds of factors are included?

Only within-participants factors; every participant completes every combination of factor levels.

What are the three main sources of variance partitioned in a one-way WP ANOVA?

Participant variance, Treatment (IV) variance, and Error (treatment × participant interaction) variance.

Which variance component is removed from the error term in a WP ANOVA to increase power?

Participant (individual-difference) variance.

Write the structural model equation for a score in a one-way WP design.

Xᵢⱼ = μ· + πᵢ + τⱼ + eᵢⱼ

In the one-way WP ANOVA, what does τⱼ represent?

The treatment effect for condition j (systematic mean difference due to the IV).

How is the F-ratio calculated in a one-way WP ANOVA?

F = MStreatment / MSerror

Give the degrees-of-freedom formula for df_error in a one-way WP ANOVA.

df_error = (n − 1)(a − 1)

Why is the error term different in WP versus BP ANOVA?

In WP designs error is the treatment × participant interaction, whereas in BP designs error is within-groups variance including unexplained individual differences.

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

Greater power because individual-difference variance is estimated and removed, producing a smaller error term.

Name two major disadvantages of within-participants designs.

Susceptibility to demand characteristics and order/sequence effects.

What methodological technique is essential for controlling order effects in WP studies?

Counterbalancing the order of conditions across participants.

List three common types of order effects.

Practice effects, fatigue effects, sensitisation/desensitisation, and carry-over (contrast) effects.

What assumption unique to WP ANOVA concerns the equality of variances of difference scores?

Sphericity.

Which statistical test is used to check sphericity?

Mauchly’s Test of Sphericity.

If Mauchly’s test is significant, what does that indicate?

The sphericity assumption is violated.

Name the three epsilon (ε) adjustments for sphericity violations.

Greenhouse-Geisser, Huynh-Feldt, and Lower-Bound corrections.

Which ε correction is most conservative?

Lower-Bound (ε = 1/(k − 1)).

Which ε correction is generally recommended as a default?

Greenhouse-Geisser.

How does an ε adjustment affect an F-test?

It multiplies the numerator and denominator df, changing the critical F value (more conservative when ε < 1).

In a two-way WP ANOVA, which three omnibus effects are tested?

Main effect of Factor A, Main effect of Factor B, and the A × B interaction.

For the main effect of Factor A in a two-way WP ANOVA, what is the appropriate error term?

MS_A×P (Factor A × Participant interaction).

Provide the F-ratio formula for the main effect of Factor B in a two-way WP ANOVA.

F = MSB / MSB×P

What is the error term for the A × B interaction in a two-way WP ANOVA?

MS_A×B×P

Why does each omnibus effect in a two-way WP ANOVA have its own error term?

Because each reflects inconsistencies of that specific effect across participants (different interaction components).

How are follow-up pairwise comparisons conducted after a significant WP main effect with >2 levels?

Using within-participants t-tests with a freshly calculated MS_error for each comparison.

What is the difference between within-participants and between-participants t-tests in follow-ups?

WP t-tests use a unique error term per comparison; BP t-tests reuse the pooled ANOVA MS_error for all comparisons.

State the degrees-of-freedom for the participant effect in a one-way WP ANOVA.

df_participants = n − 1

What is the formula for SS_total in a WP ANOVA?

SStotal = Σi Σj (Xij − X··)^2

How is SS_treatment computed in a one-way WP ANOVA?

SStreatment = n × Σj (X_j· − X··)^2

Which sum of squares captures individual differences across participants?

SSparticipants = a × Σi (X_i· − X··)^2

Give two alternative names for within-participants designs.

Repeated-measures designs and within-groups designs.

When is sphericity not an issue in WP ANOVA?

For factors with only two levels (variance of one difference score only).

Explain 'carry-over effect'.

An effect where experience in one condition influences responses in later conditions beyond general practice or fatigue.

What are fixed and random factors in WP ANOVA?

Fixed factors are the IVs whose specific levels are of interest; the participant factor is treated as random to control individual differences.

What practical advantage do WP designs offer regarding sample size?

Fewer participants are required to achieve the same statistical power as a BP design.

In the stress-ball example, what IV and DV were used?

IV: Video type (no video, news video, non-news video); DV: Number of stress-ball squeezes.

What was the main finding of the stress-ball WP ANOVA example?

Stress was significantly higher in the news-video condition compared to both no-video and non-news video; no difference between no-video and non-news.

Describe the participant × treatment interaction in a WP design.

Variation showing that the magnitude of the treatment effect differs across individual participants (forms the WP error term).

What is the purpose of counterbalancing?

To distribute order effects evenly across conditions, preventing them from confounding treatment effects.

Why can’t counterbalancing always be used (give one example)?

In pre-post intervention studies the temporal order is fixed (pre must precede post).

What does a significant Time (pre vs post) main effect indicate in the phobia intervention example?

Anxiety scores changed from pre- to post-intervention, averaged across animal stimuli.

In WP ANOVA, how is total variance conceptually split?

Into between-participants (participant) variance and within-participants variance (treatment plus error).