Problem set 9

Complete this task in teams of two or three students.

Submission information: please submit on ZoneCours

We consider Study 2 of Bobak et al. (2019), who collected responses for 52 participants and computed the average of the correctly identified figures as response out of 96 trials (32 per condition). Bobak et al. (2019) report that

Participants saw all 96 trials in a random order and the colour condition was counterbalanced for each set.

Perform a repeated measure one-way ANOVA with color as within-factor and pcorr as response with the BMH19_S2 data, which can be found in the R package hecedsm. You can also download the SPSS database via this link.

  1. Explain in your own words the purpose of randomization and counterbalancing in a repeated measure experiment.
  2. Is there evidence against the hypothesis of sphericity? Report Mauchly’s statistic and the conclusion of the hypothesis test.
  3. Are there differences overall between color match (monochrome, mixed or colored)? Report the \(F\)-statistic, the degrees of freedom and the \(p\)-value and a measure of effect size (e.g., \(\widehat{R}^2_p\)). If the sphericity assumption isn’t met, use the Greenhouse–Geisser adjustment for the degrees of freedom of the tests and report the estimated correction factor \(\widehat{\epsilon}\).
  4. Compute pairwise differences applying Tukey’s honest significance difference multiplicity correction. Report the pairwise differences in terms of percentage of correct values (differences in pcorr), the \(t\)-test statistics and the associated \(p\)-values.
  5. An alternative procedure would be to fit the model as a one-way MANOVA: do this and report the value of Pillai’s trace with the approximate \(F\) statistic, degrees of freedom and \(p\)-values. Does your conclusions change?1


Bobak, A. K., Mileva, V. R., & Hancock, P. J. B. (2019). A grey area: How does image hue affect unfamiliar face matching? Cognitive Research: Principles and Implications, 4(1), 27.


  1. If you fit the model with afex package functions aov_ez, the output contains a slot $Anova with the value of this test.↩︎