To be determined after the pilot session based on power analyses. If indicated at a later stage that the power is too low, we will follow a data augmentation strategy with p-value correction following Sagarin, Ambler, and Lee's (2014, Perspectives on Psychological Science, 9, 293-304) procedure.
Approximately 168 observations for HardEasy and EasyHard treatments
(6 laboratory sessions with approximately 30 subjects each, 6x2 Observers are not part of the treatment conditions)
Sample size (or number of clusters) by treatment arms
We aim at a balanced design in which about 50% of overall observations are assigned to treatment EasyHard and about 50% to treatment HardEasy.
We aim at a balanced design in which about 50% of observations are assigned to treatment EasyHard and about 50% to treatment HardEasy, i.e. about 80 observations per treatment.
Power calculation: Minimum Detectable Effect Size for Main Outcomes
We define the key variable DiceDiff = DiceSubject – DiceSample, where
- DiceSubject is a reported dice roll for oneself (on a scale of 1 to 6),
- DiceSample is a reported dice roll for the reference group (on a scale of 1 to 6), and
- DiceDiff is a reported dice roll difference (on a scale -5 to 5, larger differences are more favorable for a subject).
We then compare DiceDiff for treatments HardEasy and EasyHard: DiceDiffDiff = DiceDiffHardEasy – DiceDiffEasyHard (on a scale -10 to 10, the smaller DiceDiffDiff, the more favorable for oneself were subjects’ reported dice rolls in the treatment EasyHard in comparison to the HardEasy).
According to power analyses based on the data of our pilot session (conducted on 31.10.2018, N=25), we will be able to detect an effect size of -1.077 (DiceDiffDiff) using a two-sample means Satterthwaite's t-test assuming unequal variances, with 80 observations per treatment with a power of 95%.