Extended Data Fig. 1: Interpreting σθ.
From: A rational model of the Dunning–Kruger effect supports insensitivity to evidence in low performers
Model predictions in a toy example where participants solve 10 problems (a) when the standard deviation on ability (σθ) is adjusted (σθ = 1 or 2) and (b) when both this and the parameter ϵ are adjusted (σθ= 1, ϵ = 0.35 or ϵ = 0, σθ= 0.5) to reveal comparable results. In the main paper, we consider a single value for the standard deviation of the prior on ability (σθ). As shown in Fig. 1a, increasing the standard deviation of the prior implies more accurate estimation of scores, although some under and over estimation is still present. The pattern of Fig. 1a is similar to the pattern of predictions when changing ϵ. As shown in Fig. 1b, adjustments to either of these parameters can lead to very similar predictions for the relationship between true scores and estimated scores. This is not surprising given that both of these parameters represent uncertainty. Choosing to focus on fitting participants' values of ϵ allows us to capture variation in estimates of correctness on each question. On the other hand, if we were to focus on fitting participants' σθ values, we would be assuming variation in prior beliefs about ability. Given the framing of the Dunning–Kruger effect in terms of sensitivity to errors, we fixed σθ and focused on ϵ in our modeling approach. We have expressed our conclusions in terms consistent with variation in either ϵ or σθ, which affect the degree of updating of prior beliefs in light of evidence.
