# Problem set 9

**Submission information**: please submit on ZoneCours

- a PDF report
- your code

Look at the effect size and power; this should be helpful in completing the problem set.

## Task 1

The following text is a quote from Investigating variation in replicability: A “Many Labs” Replication Project by Richard A. Klein, Kate A. Ratliff, and Brian A. Nosek (pp. 13-14) about a replication of Oppenheimer & Monin (2009) work on the retrospective gambler fallacy.

The differences between groups was reliable, omnibus \(F(2, 77) = 4.8\), […] Cohen’s \(f = 0.18\). Pairwise comparisons showed that all differences between conditions were reliable as well, \(t(47, 48, 57) = 1.94, 2.32, 2.65\); \(p < .05\), Cohen’s \(d\) = \((.56, .67, .69)\).

- Using the information from the quote, compute the effect size for Cohen’s \(f\) and \(\widehat{\omega}^2\).
^{1}Note that you won’t necessarily get the same value of Cohen’s \(f\) that is reported. - Compute the overall sample size necessary to replicate this study with a power of at least \(0.99:\) compute the power for both the overall effect and the three pairwise \(t\)-tests based on the reported values of Cohen’s \(d\) and pick the maximum sample size needed for balanced design (i.e., gathering the same number of participants in each subgroup).
- Read the results of the replication in ManyLabs1; these are illustrated in Figure 1 and summary statistics about standardized mean differences (Cohen’s \(d\)) are reported in Table 2 (Klein et al., 2014) under retrospective gambler fallacy. Comment about the success of the replication.
- Based on observation of Figure 1 of Klein et al. (2014), why might one object to using estimated effect size reported in peer-reviewed papers?
^{2}

## Task 2

Read the Section “Going Beyond Null Hypothesis Significance Testing” of the Academy of Management Journal 2024 editorial (Bliese et al., 2024) in preparation for a in-class discussion.

## References

*Academy of Management Journal*,

*67*(4), 893–902. https://doi.org/10.5465/amj.2024.4004

*Social Psychology*,

*45*, 142–152. https://doi.org/10.1027/1864-9335/a000178

*Judgment and Decision Making*,

*4*, 326–334.