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Comment by bitshiftfaced

The authors did "X - Y vs X," but that's not even the biggest problem. The authors subtracted two measures that had been transformed and bounded from 0 to 1 (think percentiles). What happens at the extremes of those bounds? How much can your top performers overestimate their performance? They're almost at 1 already, so not much. If they were to overestimate and underestimate at the same rate and by the same magnitude in terms of raw values, the ceiling effect on the transformed values means that the graph will make it look like they underestimate more often. The opposite problem happens for the worst performers.

See "Random Number Simulations Reveal How Random Noise Affects the Measurements and Graphical Portrayals of Self-Assessed Competency." Numeracy 9, Iss. 1 (2016), particularly figures 7, 8, and 9.

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