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Field
Power calculation: Minimum Detectable Effect Size for Main Outcomes
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Before
Power analysis for the main hypothesis: Subjects are more likely to choose to Pay when they are in a group in which most people chose to Not Pay in Decision 1 than when they are in a group in which most people chose to Pay in Decision 1. This hypothesis is tested between-subject (second stage) and within-subject (third stage).
I performed the power analyses through simulations (the STATA code is available upon request). I assume that 60% of the subjects choose to Pay in Decision 1. I only analyze the decisions of those subjects when they are in groups of 2 and 3 AP.
I assume that 55% (70%) of the subjects choose to Pay in the pool in which most AP chose to (Not) Pay in Decision 1. Therefore, I study an effect size of 15 percentage points. The test I perform is a Wilcoxon ranksum test.
Power to find a significant effect at the 5% level for the between-subject test: 85.3%.
Power to find a significant effect at the 5% level for the within-subject test: 99%.
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After
Power analysis for the main between-subject hypothesis: the weak bystander effect (defined as the difference between the percentage of bystanders helping when alone and when in a group) increases as the percentage of bystanders who chose to Pay in Decision 1 increases. If, for example, subjects help with the same frequency when they are alone regardless of the pool composition, then this hypothesis means that subjects are more likely to choose to Pay when they are in a group in which most people chose to Not Pay in Decision 1 than when they are in a group in which most people chose to Pay in Decision 1. This hypothesis is tested between-subject (second stage) and within-subject (third stage).
I performed the power analyses through simulations (the STATA code is available upon request). I assume that 60% of the subjects choose to Pay in Decision 1. I only analyze the decisions of those subjects when they are in groups of 2 and 3 AP.
I assume that 55% (70%) of the subjects choose to Pay in the pool in which most AP chose to (Not) Pay in Decision 1. Therefore, I study an effect size of 15 percentage points. The test I perform is a Wilcoxon ranksum test.
Power to find a significant effect at the 5% level for the between-subject test: 85.3%.
Power to find a significant effect at the 5% level for the within-subject test: 99%.
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