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Updated: Oct 31, 2025

Measuring Statistical Learning Across Modalities and Domains in School-Aged Children Via an Online Platform and Neuroimaging Techniques

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Extrapolation accuracy underestimates rule learning: Evidence from the function-learning paradigm.

Nadia Said¹, Helen Fischer²

¹Department of Psychology, University of Tübingen, Schleichstr. 4, 72076 Tübingen, Germany; Institute of Psychology, Heidelberg University, Hauptstr. 47-51, 69117 Heidelberg, Germany; InterdisciplinaryCenter for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.

Acta Psychologica

|June 28, 2021

Summary

This summary is machine-generated.

Accurate extrapolation requires rule learning, but inaccurate extrapolation doesn't rule out understanding the underlying function. This study reveals that assessing rule learning solely by extrapolation accuracy underestimates true understanding in function-learning experiments.

Keywords:

Function-learning Non-linear processes Rule-based vs exemplar-based learners Understanding

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Area of Science:

Cognitive psychology
Decision science
Behavioral economics

Background:

Understanding non-linear processes like economic or population growth is crucial for informed decision-making.
The function-learning paradigm often uses extrapolation accuracy to measure understanding of underlying rules.
However, extrapolation accuracy may not fully capture an individual's grasp of the function rule.

Purpose of the Study:

To investigate whether inaccurate extrapolation in function learning necessarily implies a lack of rule understanding.
To determine if rule application is equivalent to rule learning.
To assess if current methods of measuring rule learning via extrapolation accuracy underestimate the proportion of individuals who have learned the rule.

Main Methods:

Experiment 1: Employed a rule-selection paradigm to assess participants' understanding of function rules, contrasting with their extrapolation accuracy.
Experiment 2: Investigated potential biases in the rule-selection paradigm, such as a priori guessing probabilities and access to function values.
Compared rule learning and rule application within the function-learning paradigm.

Main Results:

Over one-third of participants classified as "exemplar-based learners" based on extrapolation accuracy demonstrated accurate rule understanding in a rule-selection task.
The higher proportion of rule learning observed in the rule-selection paradigm compared to rule application is not attributable to guessing probabilities or limited access to function values.
Rule application was found to be distinct from rule learning.

Conclusions:

Rule application is not synonymous with rule learning.
Assessing rule learning solely through extrapolation accuracy in function-learning experiments leads to an underestimation of the actual proportion of rule learners.
Cognitive models of function learning should differentiate between rule learning and rule application for more accurate assessments.