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Field
Power calculation: Minimum Detectable Effect Size for Main Outcomes
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Before
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%.
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After
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%.
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