“Thus, when we calculate the net degree of expressive responding by subtracting the acceptance effect from the rejection effect—essentially differencing off the baseline effect of the incentive from the reduction in rumor acceptance with payment—we find that the net expressive effect is negative 0.5%—the opposite sign of what we would expect if there was expressive responding. However, the substantive size of the estimate of the expressive effect is trivial.

https://journals.uchicago.edu/doi/abs/10.1086/694258Moreover, the standard error on this estimate is 10.6, meaning the estimate of expressive responding is essentially zero.”

(**Note**: This is not a full review of all the claims in the paper. There is more data in the paper than in the quote above. I am merely using the quote to clarify a couple of statistical points.)

There are two main points:

- The fact that estimate is close to zero and the s.e. is super fat are technically unrelated. The last line of the quote, however, seems to draw a relationship between the two.
- The estimated effect sizes of expressive responding in the literature are much smaller than the s.e. Bullock et al. (Table 2) estimate the effect of expressive responding at about 4% and Prior et al. (Figure 1) at about ~ 5.5% (“Figure 1(a) shows, the model recovers the raw means from Table 1, indicating a drop in bias from 11.8 to 6.3.”). Thus, one reasonable inference is that the study is underpowered to reasonably detect expected effect sizes.