Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Main Outcome: Obtaining a counteroffer (binary)
I am planning to gather data in 200 cities or for 10,000 observations, whichever is reached first. For the case that I gather fewer than 50 observations per city on average, I additionally report minimum detectable effect sizes for smaller sample sizes.
By gender. The pilot yielded a mean likelihood of receiving a counteroffer for female “employers” of 0.45, with a standard deviation of 0.50. With a sample of 10,000 (8000, 6000) observations, the minimum detectable effect size for the gender difference in obtaining a counteroffer is 0.028 (0.031, 0.036).
By negotiation treatment. The pilot yielded a mean likelihood of receiving a counteroffer for “employers” using the plain negotiation of 0.41, with a standard deviation of 0.49. With a sample of 10,000 (8000, 6000) observations, the minimum detectable effect size for the gender difference in obtaining a counteroffer is 0.028 (0.031, 0.036).
By gender—no negotiation treatment. The pilot yielded a mean likelihood of receiving a counteroffer for female “employers” using the plain negotiation of 0.37, with a standard deviation of 0.49. With a sample of 10,000 (8000, 6000) observations, the minimum detectable effect size for the gender difference in obtaining a counteroffer is 0.028 (0.031, 0.036).
By gender—negotiation treatment. The pilot yielded a mean likelihood of receiving a counteroffer for female “employers” using the negotiation justification of 0.52, with a standard deviation of 0.50. With a sample of 10,000 (8000, 6000) observations, the minimum detectable effect size for the gender difference in obtaining a counteroffer is 0.028 (0.031, 0.036).