5 = Extremely confident, i.e., 90% confidence interval spans +/- 4 points or less)
For 0-100 ratings, code the LB as \(max(R - 4,0)\) and the UB as \(min(R + 4,100)\), where R is the stated (middle) rating. This ‘scales’ the CI, as interpreted, to be proportional to the rating, with a maximum ‘interval’ of about 8, with the rating is about 96.
4 = Very*confident: 90% confidence interval +/- 8 points or less
For 0-100 ratings, code the LB as \(max(R - 8,0)\) and the UB as \(min(R + 8,100)\), where R is the stated (middle) rating.
3 = Somewhat** confident: 90% confidence interval +/- 15 points or less
2 = Not very** confident: 90% confidence interval, +/- 25 points or less
Comparable scaling for the 2-3 ratings as for the 4 and 5 rating.
1 = Not** confident: (90% confidence interval +/- more than 25 points)
Code LB as \(max(R - 37.5,0)\) and the UB as \(min(R + 37.5,100)\).
This is just a first-pass. There might be a more information-theoretic way of doing this. On the other hand, we might be switching the evaluations to use a different tool soon, perhaps getting rid of the 1-5 confidence ratings altogether.