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From a Measure of Confidence to a Measure of the Level of Knowledge Cover

From a Measure of Confidence to a Measure of the Level of Knowledge

By: Daniel Defays  
Open Access
|May 2025

Figures & Tables

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Figure 1

Representation of Under and Overestimations.

Note. Top left panel: all the items of a domain known correctly (red dots) or incorrectly (black dots) by a person, distributed according to their level of knowledge. Top right panel: all the items sampled (green subset) through a questionnaire. Bottom left panel: the sample of items with their given confidence and their level of knowledge. Bottom right panel: the sample of items with, in yellow, those that are underestimated (confidence lower than level of knowledge) and, in blue, those that are overestimated (confidence higher the level of knowledge).

Table 1

Number of Correct and Incorrect Responses by Level of Confidence for a Respondent on a 60 2AFC Questionnaire.

50%60%70%80%90%100%
Correct42441023
Incorrect223132
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Figure 2

Two Different Representations of Observed and Estimated Data.

Note. The number of correct/incorrect responses as a function of confidence represented in 2 different ways. Bottom panels: the distribution of the LOK, superposed with the confidences given by the respondent on the left, and with the highlighting of under and overestimations on the right.

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Figure 3

Percentages of Correct Responses as a Function of the Degree of Confidence with Standard Deviations.

Note. The red line shows what the percentage should be if the students were perfectly realistic.

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Figure 4

Distribution of the Realism of the 41 Students.

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Figure 5

Distribution of the Mean Amplitude of the Confidence Error in Absolute Value among the 41 Students.

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Figure 6

Distribution (in Mean Number of Items per Student) of Confidence at the Second Trial for the Items with Confidence Degrees 50%, 60%, 70%, 80%, 90% and 100% at the First Trial.

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Figure 7

Distribution (in Mean Number of Items per Student) of Confidence Given at the First Trial for the Items with Confidence Degree 50%, 60%, 70%, 80% at the Second Trial.

Table 2

Identification of the Best Model with the AIC.

MODEL SMODEL HMODEL OMODEL A
Number of students161249
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Figure 8

Conditional Distribution of Confidences at One Trial Given Confidence Levels of 50%, 60%, 70%, and 80% at the Other Trial.

Note. Left panel: distribution (in mean number of items per student) of confidence at the second trial for the items with confidence degrees 50%, 60%, 70%, 80% at the first trial, for students significantly attracted by the confidence level 100% according to model A. Right panel: the same distributions when the two trials are permuted.

DOI: https://doi.org/10.5334/pb.1332 | Journal eISSN: 0033-2879
Language: English
Submitted on: Jun 20, 2024
|
Accepted on: Apr 18, 2025
|
Published on: May 22, 2025
Published by: Ubiquity Press
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2025 Daniel Defays, published by Ubiquity Press
This work is licensed under the Creative Commons Attribution 4.0 License.