One-Way Within-Subjects ANOVA

What is a one-way within-subjects ANOVA?

A statistical test used to compare the means of three or more related groups where the same participants take part in every condition.

What does “one-way” mean in a within-subjects ANOVA?

There is one independent variable.

What does “within-subjects” mean?

The same participants complete all experimental conditions.

What is another term for a within-subjects design?

Repeated-measures design.

Why is a within-subjects design called repeated measures?

Because the same participants are measured multiple times across conditions.

When should a one-way within-subjects ANOVA be used?

When comparing three or more related measurements from the same participants.

Give an example of a within-subjects design.

Measuring the same participants’ reaction times under three different noise conditions.

What type of independent variable is used in a within-subjects ANOVA?

A categorical variable with three or more levels.

What type of dependent variable is required?

A continuous variable.

What is the main advantage of a within-subjects design?

It reduces variability caused by individual differences.

Why do within-subjects designs reduce error variance?

Because each participant acts as their own control.

What is the main disadvantage of within-subjects designs?

Order effects.

What are order effects?

Changes in participant performance caused by the order in which conditions are experienced.

What are practice effects?

Participants improve because they become more familiar with the task.

What are fatigue effects?

Participants perform worse due to tiredness or boredom.

What are carryover effects?

The effect of one condition influences performance in the next condition.

How can researchers reduce order effects?

Counterbalancing the order of conditions.

What is counterbalancing?

Presenting experimental conditions in different orders to different participants.

What is the central question of a within-subjects ANOVA?

Whether the mean scores differ across the different conditions.

What is the null hypothesis in a within-subjects ANOVA?

All condition means are equal.

What is the alternative hypothesis in a within-subjects ANOVA?

At least one condition mean differs from the others.

What statistic is used in ANOVA to test the hypothesis?

The F-statistic.

What does the F-statistic represent?

A ratio comparing explained variance to unexplained variance.

What does a large F-value suggest?

The experimental manipulation explains more variance than random error.

What are the main sources of variance in within-subjects ANOVA?

Variance due to the experimental manipulation, variance due to individual differences, and residual error.

Why must within-subjects ANOVA separate individual differences?

Because the same participants appear in all conditions, their personal characteristics influence scores.

What happens if individual differences are not accounted for?

Error variance increases and statistical power decreases.

What is statistical power?

The probability of correctly detecting a real effect.

Why do within-subjects designs often have higher power than between-subjects designs?

They remove variability caused by individual differences.

What assumption is important in within-subjects ANOVA regarding variance across conditions?

Sphericity.

What is sphericity?

The assumption that the variances of the differences between all pairs of conditions are equal.

Why is the sphericity assumption important?

Violations can inflate the Type I error rate.

What statistical test is used to test the sphericity assumption?

Mauchly’s test of sphericity.

What does a significant Mauchly’s test indicate?

The sphericity assumption has been violated.

What should be done if sphericity is violated?

Apply corrections such as Greenhouse-Geisser or Huynh-Feldt.

What does the Greenhouse-Geisser correction do?

Adjusts the degrees of freedom to reduce Type I error.

Why do sphericity corrections reduce degrees of freedom?

To make the statistical test more conservative.

What does it mean if the ANOVA result is significant?

At least one condition mean differs from another.

Why are post-hoc tests needed after a significant ANOVA?

Because ANOVA only tells us that a difference exists, not where it occurs.

What are post-hoc tests?

Tests used after ANOVA to compare specific pairs of conditions.

Why must multiple comparison corrections be used in post-hoc tests?

To reduce the risk of Type I error.

What is the main difference between within-subjects and between-subjects ANOVA?

Within-subjects uses the same participants in all conditions, while between-subjects uses different participants in each condition.

Why are within-subjects designs more efficient with small samples?

Because each participant contributes data to every condition.

What is the main limitation when interpreting within-subjects ANOVA results?

Potential order and carryover effects.

How should a within-subjects ANOVA result be reported?

F(df condition, df error) = value, p = value, effect size.

What effect size is commonly reported for ANOVA?

Eta squared (η²) or partial eta squared.

What does eta squared represent?

The proportion of variance explained by the independent variable.

Why is effect size important alongside p-values?

It indicates the magnitude of the effect, not just whether it is statistically significant.