2025

Question 1

You run an experiment with three groups of participants: Control, Treatment A, and Treatment B. Each participant provides one score. You want to test whether there is a difference in means across the groups.

What kind of ANOVA is appropriate, and what are the degrees of freedom for the group effect?

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  • Design: One-way between-subjects ANOVA
  • Effect of interest: Group
  • DFn (numerator): \(3 - 1 = 2\)
  • DFd (denominator): \(N - 3\)
  • Error term: Between-subjects residual variance

Question 2

You run a study where each subject completes a memory task under 4 levels of distraction. You collect one score per condition per subject.

What kind of ANOVA is appropriate, and what are the degrees of freedom for the main effect?

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  • Design: One-way repeated-measures ANOVA
  • Effect of interest: Distraction level (within-subjects factor)
  • DFn: \(4 - 1 = 3\)
  • DFd: \((4 - 1)(N - 1) = 3(N - 1)\)
  • Error term: \(A \times \text{Subject}\)
  • Assumption: Sphericity (test with Mauchly’s test)

Question 3

You run an experiment with 2 groups (Control vs Training) and 3 testing sessions per subject. Group is a between-subjects factor, Session is a within-subjects factor.

What kind of ANOVA is appropriate, and what are the degrees of freedom for each effect?

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  • Design: 2 (Group) × 3 (Session) mixed ANOVA
  • Group effect (between):
    • DFn: \(2 - 1 = 1\)
    • DFd: \(N - 2\)
  • Session effect (within):
    • DFn: \(3 - 1 = 2\)
    • DFd: \((3 - 1)(N - 2) = 2(N - 2)\)
  • Group × Session interaction:
    • DFn: \((2 - 1)(3 - 1) = 2\)
    • DFd: same as for Session = \(2(N - 2)\)
  • Error term for within-subjects: Session × Subject (nested in Group)

Question 4

You are comparing two groups using a one-way between-subjects ANOVA. Below is a plot of the population distributions from which data are assumed to be sampled.

Which ANOVA assumption is violated?

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  • The group means are equal, so there’s no mean difference.
  • But the variances are unequal: Group B has a much wider distribution.
  • This violates the homogeneity of variance assumption for between-subjects ANOVA.
  • A Levene’s test would likely detect this violation.

Question 5

A within-subjects factor has 3 levels: A1, A2, A3. Each subject provides one score at each level. The distributions below show the population-level pairwise differences between conditions.

What assumption does this violate?

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  • The sphericity assumption states that the variances of all pairwise differences between levels of a within-subjects factor should be equal.
  • But here, the variance of the A2 - A3 distribution is clearly much larger than the others.
  • This is a violation of sphericity.
  • It would likely be flagged by Mauchly’s test, and you’d need a correction like Greenhouse-Geisser.

Question 6

You are running a one-way repeated-measures ANOVA. Each subject provides a score in each of 3 conditions: A1, A2, A3. The plot below shows sample means with SEM error bars for each condition.

It looks like the spread may differ between conditions. Is any ANOVA assumption violated?

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  • No assumption is violated here.
  • Although the bars have different heights, the error bars reflect variability around the mean, not group-level variance differences.
  • The within-subject variance is equal across conditions (true by design).
  • The sphericity assumption concerns the variances of the pairwise differences between conditions — not the height of the error bars.
  • This is a red herring: everything is fine for a one-way repeated-measures ANOVA.