L* statistic

Research Method · All research methods
Evidence · 1 claim (1 for) · 1 study (1 theoretical), q2 · 0 of 1 report an effect size · 1 claim rests on one study

Description

L* is a modified version of D'Mello's L statistic intended for use when self-transitions are excluded. It restricts computation to transitions in T_A, the set where the next state is not A, and normalizes the base rates so that, per Theorem 1, "the value of L∗ at chance is equal to zero" when conditional independence holds. The article proves this result and compares L's properties to L. L is equivalent to the λ statistic of Bosch and Paquette (2020) when base rates are computed per sequence, but distinct when averaged over a sample.

Accounts

• L*: a modified L statistic that restores a zero chance value when self-transitions are excluded**: L is a modified version of D'Mello's L statistic intended for use when self-transitions are excluded. It restricts computation to transitions in T_A, the set where the next state is not A, and normalizes the base rates so that, per Theorem 1, "the value of L∗ at chance is equal to zero" when conditional independence holds. The article proves this result and compares L's properties to L. L* is equivalent to the λ statistic of Bosch and Paquette (2020) when base rates are computed per sequence, but distinct when averaged over a sample. (Jeffrey Matayoshi et al. (2020))

Claims

• Theoretical ranges differ sharply: L with self-transitions removed is bounded below by −1 (individual base rates) or −2 (averaged), while L* is bounded by −k+1 (individual) or has no finite lower bound (averaged) [+W]

Related Research Methods

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Key Sources

• Jeffrey Matayoshi and Shamya Karumbaiah. (2020). Adjusting the L Statistic when Self-Transitions are Excluded in Affect Dynamics. Journal of Educational Data Mining, Volume 12, No 4. https://jedm.educationaldatamining.org/index.php/JEDM/article/view/478

Page metadata

Field	Value
type	research-method
id	l-statistic
title	L* statistic
description	L* is a modified version of D'Mello's L statistic intended for use when self-transitions are excluded.
status	review
moved_from	theory/l-star-modified-transition-metric
generated	by process:sweep-kinds on 2026-10-10
trust	unverified — no one has confirmed this page's content
sources	1 — jeffrey-matayoshi-and-shamya-karumbaiah-2020

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