Problem set 12

Complete this task individually.

Submission information: please submit on ZoneCours

• a PDF report
• your code

Elliott et al. (2021) attempt to replicate a study of Flavell et al. (1966) and study unprompted verbalization by children aged 5 to 10 in an experiment. The data containing the counts of the number of verbalization across all labs are given in the FBC66_T1 and MULTI21_D1 datasets.

The data from Table 1 of Flavell et al. (1966) is the number of children who verbalized without prompting overall in the first two experimental conditions (immediate recall and delayed recall subtasks).¹

For the \(\chi^2\) test to be valid, we need the expected number of counts to be at least five in each subcondition (otherwise the large sample approximation breaks down and is unreliable).

The number of students for each grade (kindergarden, second and fifth) is 20. The rows of the table are the ordered number of instances of verbalization.

# Reinstall package
# remotes::install_github("lbelzile/hecedsm")
data(FBC66_T1, package = "hecedsm")
chisq.test(xtabs(count ~ grade + frequency, data = FBC66_T1))

    Pearson's Chi-squared test

data:  xtabs(count ~ grade + frequency, data = FBC66_T1)
X-squared = 28.358, df = 4, p-value = 1.055e-05

1. Looking at the output, what is the conclusion of the test?
2. The authors report a test for second versus fifth grade only. Repeat their analysis by discarding the row for kindergarden students: do the result match those reported in the paper?
3. Usual recommendations for the chi-square test is that the expected counts in each cell be at least 5. Under the null hypothesis of equal frequency per grade, what is the expected number of students in each cell? Hint: calculate the marginal proportion per column.²

4. The replication Elliott et al. (2021) consider children of different ages corresponding roughly to Flavell et al. (1966), but with an additional year. Repeat the test and the pairwise comparisons (Hint: use xtabs to cross-classify counts of factor).
5. Why is the \(p\)-value so small in their replication?

References

Elliott, E. M., Morey, C. C., AuBuchon, A. M., Cowan, N., Jarrold, C., Adams, E. J., Attwood, M., Bayram, B., Beeler-Duden, S., Blakstvedt, T. Y., Büttner, G., Castelain, T., Cave, S., Crepaldi, D., Fredriksen, E., Glass, B. A., Graves, A. J., Guitard, D., Hoehl, S., … Voracek, M. (2021). Multilab direct replication of Flavell, Beach, and Chinsky (1966): Spontaneous verbal rehearsal in a memory task as a function of age. Advances in Methods and Practices in Psychological Science, 4(2), 1–20. https://doi.org/10.1177/25152459211018187

Flavell, J. H., Beach, D. R., & Chinsky, J. M. (1966). Spontaneous verbal rehearsal in a memory task as a function of age. Child Development, 37(2), 283–299. http://proxy2.hec.ca/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=pbh&AN=10398223&lang=fr&site=ehost-live

Footnotes

1. The last task, point-and-name, is not considered because it specifically instructed students to speak out loud.

2. If the expected number is less than 5, the asymptotic \(\chi^2\) approximation is dubious. We could resort to permutation and simulation to assess the accuracy of the \(\chi^2\) benchmark. The row sum for the counts (per grade) is fixed to 20, but the columns are allowed to vary.