In FAIR-NHH/mmbruteluck: Replication Package for "mmbruteluck" Paper

knitr::opts_chunk$set(
  fig.width = 7,
  fig.height = 4.5,
  collapse = TRUE,
  comment = "#>"
)

Power analysis before the online experiment was based on us seeing if we could replicate the large interaction effect between "left" political preference and the treatment involving "choice". The relevant regression coefficient on inequality was -0.192 with a standard error of 0.074. We wanted more treatment variants in the online experiment, but wanted to test if this replicated in what corresponds to the 3-treatment subset that would be most similar to the lab experiment (base, forced, and nominal choice -- with work). We also wanted sufficient power even for a more moderate effect size of 0.1.

To apply the R t-test command, we scale the coefficient to fit into a t-test framework. What kind of power would 700 participants per treatments give us? Test of a regression coefficient against null is equivalent to a one-sample test in pooled data.

SD <- 0.074 * sqrt(422)   # SE and n from lab experiment
power.t.test(n=700*3, delta=0.1, sd=SD, sig.level=0.05, 
             type="one.sample", alternative="one.sided")

Even if we were to consider a two-sided test of the null, we would have sufficient power:

power.t.test(n=700*3, delta=0.1, sd=SD, sig.level=0.05, 
             type="one.sample", alternative="two.sided")

FAIR-NHH/mmbruteluck documentation built on Oct. 29, 2020, 9 p.m.