Problem set 6
Complete this task in teams of two or three students.
Submission information: please submit on ZoneCours
- a PDF report
- your code
We consider Experiment 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.
The result we want to reproduce is the following:
There was a significant main effect of image hue, \(F(2,102) = 11.61\), \(p < .001\) […] Follow-up pairwise comparisons (Bonferroni corrected) showed that […] participants were more accurate in the colour and mixed conditions than in the grayscale condition, \(p < .001\) […] and \(p < .004\), respectively […] the mixed and colour conditions did not differ from each other, \(p = .36\) […]
Accuracy was also examined for mismatched trials, using within-subjects ANOVA with three hue levels […] There was a significant main effect of condition, \(F(2,102)=15.32\), \(p<.001\). Pairwise comparisons (Bonferroni corrected) revealed that the accuracy was lower in the “mixed” condition than in colour and grayscale conditions […] Accuracy in grayscale and colour conditions did not differ.
Perform a repeated measure one-way ANOVA with color
as within-factor and either accuracy
or pcorr
as response with the BMH19_E2
data, which can be found in the R package hecedsm
. You can also download the SPSS database via this link.
- Explain in your own words the purpose of randomization and counterbalancing in a repeated measure experiment.
- Is there evidence against the hypothesis of sphericity? Report Mauchly’s statistic and the conclusion of the hypothesis test.
- Are there differences overall between color match (monochrome, mixed or colored)? Report the \(F\)-statistic, the degrees of freedom and the \(p\)-value. 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 \(\widehat{\epsilon}\).1
- Compute pairwise differences applying Tukey’s honest significance difference or Bonferroni multiplicity correction. Report the pairwise differences in terms of percentage of correct values (differences in
pcorr
andaccuracy
), the \(t\)-test statistics and the associated \(p\)-values.2
References
Footnotes
Use
anova(..., correction = "none")
forafex
output in R to get the ANOVA table without correction, as the authors reported.↩︎Note 2: only the \(p\)-values are reported, and the estimated marginal means in Table 2 of the paper. The \(d\) values quoted in the article (with confidence intervals) are Cohen’s \(d\), which we will cover later.↩︎