Field
Power calculation: Minimum Detectable Effect Size for Main Outcomes

Before
We collapse across the treatments e.g., so that we have n=200 in "no min info" condition vs. n=200 in "min info". Similarly, we have n=200 in "no info" condition vs. n=200 in "info" condition.
In detecting the main effects, the minimum detectable effect size is 0.10. This is based on alpha = 0.05, power = 0.8, and n=200 in each group, and assuming the proportion paying the minimum or less to be 10% in the control group (from previous studies).
The minimum detectable effect size is 0.17 with the expected interaction effects. This is based on oneway anova with alpha = 0.05, power=0.8, n=100 with 4 equal groups.

After
We updated the power calculations based on the pilot data we collected. With the following inputs
Effect size ρ = 0.2
α err prob = 0.05
Power (1β err prob) = 0.9
We plan to collect 125 in each cell, giving us 250 in each cell in our 2x2 design experiment.
