|
Field
Sample size (or number of clusters) by treatment arms
|
Before
At least 50 subjects per treatment arm in the moral wiggle room game with 3 treatment arms.
At least 100 subjects per treatment arm in the dice rolling game with 6 treatment arms.
Higher N depends on budget constraints
|
After
At least 170 subjects for the two main treatment arms Pre-Belief and Post-Belief conditions in the moral wiggle room game. At least 100 in the Full Information and Self/Self condition.
At least 100 subjects per treatment arm in the dice rolling game with 6 treatment arms.
Higher N depends on budget constraints
|
|
Field
Power calculation: Minimum Detectable Effect Size for Main Outcomes
|
Before
Moral Wiggle Room Game
In line with Dana, Weber, and Kuang 2007, with a conservative assumption of a 20 percentage point treatment effect (e.g. 60% versus 40% ignorance), then a power analysis for a two-sided test with an alpha of 0.05 and a power of 0.80 indicates about 97 participants per group. However, based on a previous study's exploratory findings, the difference may be as much as 30 percentage point, allowing for reliable detection with about 50 participants. A total of 3 treatment arms between experiments approximated to a target of about 100 to 125 participants per arm (300 to 375 total), depending on the power.
Dice Rolling Game
The goal is to test whether the distribution of reported outcomes in each group differs from the uniform distribution, and whether treatment affects that distribution. Based on Fischbacher and Föllmi-Heusi 2013 who recruited 265 subjects, a Chi-square test with a medium effect size between of 0.20 requires a minimum sample size of about 198 participants per treatment arm, rounding up to 200 in case of missing data or incomplete subject responses.
|
After
Moral Wiggle Room Game
In line with Dana, Weber, and Kuang 2007, with a conservative assumption of a 20 percentage point treatment effect (e.g. 60% versus 40% ignorance), then a power analysis for a two-sided test with an alpha of 0.05 and a power of 0.80 indicates about 97 participants per group. However, based on a previous study's exploratory findings, the difference may be as much as 30 percentage point, allowing for reliable detection with about 50 participants. A total of 3 treatment arms between experiments approximated to a target of about 100 to 125 participants per arm (300 to 375 total), depending on the power.
Amendment 8.7.2025: A 15 percentage point treatment effect (e.g. 50% ignorance versus 35% ignorance), then a power analysis for a two-sided test with an alpha of 0.05 and a power of 0.80 indicates about 169 participants per group.
Dice Rolling Game
The goal is to test whether the distribution of reported outcomes in each group differs from the uniform distribution, and whether treatment affects that distribution. Based on Fischbacher and Föllmi-Heusi 2013 who recruited 265 subjects, a Chi-square test with a medium effect size between of 0.20 requires a minimum sample size of about 198 participants per treatment arm, rounding up to 200 in case of missing data or incomplete subject responses.
|