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Field
Power calculation: Minimum Detectable Effect Size for Main Outcomes
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Before
In a pilot experiment with 200 participants (100 trustees), a logit regression revealed a positive impact of the amount trustees intend to give to trustors on their participation decision (p=0.279, including controls about the beliefs on the behavior of trustees, gender, age, and risk attitude). The probability of the mean amount sent back participating was at 65% and the probability of the mean plus one standard deviation amount sent back participating was at 72%. Assuming this effect prevails, a logit regression power analysis reveals that we need about 220 observations of trustees (one-tailed test, 5% significance level, 80% power).
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After
In a pilot experiment with 200 participants (100 trustees), a logit regression revealed a positive impact of the amount trustees intend to give to trustors on their participation decision (p=0.279, including controls about the beliefs on the behavior of trustees, gender, age, and risk attitude). The probability of the mean amount sent back participating was at 65% and the probability of the mean plus one standard deviation amount sent back participating was at 72%. Assuming this effect prevails, a logit regression power analysis reveals that we need about 220 observations of trustees (one-tailed test, 5% significance level, 80% power).
UPDATE:
Adjustment of sample size: We have collected 220 observations for trustees in each of the two treatments. In line with our pilot, the impact of the returned amount on the participation decision is always positive, both with non-parametric and parametric analyses. However, depending on the combination of control variables, the amount is sometimes significantly positive at the 5%-level and sometimes barely insignificant at the 10% level, so that no robust conclusions can be drawn yet. We therefore decided to increase the statistical power by doubling the number of observations to see whether results prevail.
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