Grouping-based anti-collusion scheme (GAS): grouping students by competence, optimizing inter-group question overlap, and augmenting the question pool to control collusion gain below any desired level

Design · All designs
Evidence · 2 claims (2 for) · 1 study (1 design), q1 · 0 of 1 report an effect size · 2 claims rest on one study

Description

The GAS is the article's core anti-collusion design for distanced online testing. It consists of three elements the article enumerates: "Grouping: Students with similar competences are grouped together to receive the same sequence of questions in an exam"; Optimization, which aggressively reduces the number of questions that can be copied between groups, even to zero; and Augmentation, enlarging the pool beyond M1 questions. It works because cyclic sequences can reduce maximum question leakage to zero when M2 - M1 + 1 >= C, grouping reduces the equivalent number of students, and similar-competence students gain little from intra-group collusion. Competences can be estimated from GPA, earlier quizzes, or a first portion of the exam via dynamic programming.

Design Implications

Context

Requirements

• Prior knowledge of students' competences, estimated from GPA, earlier quizzes, or a first portion of the exam

Constraints

• The analysis is a first-order approximation of an idealized DOT scenario; intra-group collusion is facilitated because group members share the same sequence

Target Learners

• undergraduate students in math or fact-based courses

Learning Goals

• valid measurement of learning outcomes in remote online exams

Claims

• Theorem1 Collusion Gain Upper Bound [+M]
• Dot Final Exam Collusion Gain Three Orders Reduction [+M]

Related Designs

Examples

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Key Sources

• Mengzhou Li, Lei Luo, Sujoy Sikdar, Navid Ibtehaj Nizam, Shan Gao, Hongming Shan, Melanie Kruger, Uwe Kruger, Hisham Mohamed, Lirong Xia and Ge Wang. (2021). Optimized collusion prevention for online exams during social distancing. npj Science of Learning 6:5. https://doi.org/10.1038/s41539-020-00083-3

Page metadata

Field	Value
type	design
id	gas-grouping-anti-collusion-scheme
title	Grouping-based anti-collusion scheme (GAS): grouping students by competence, optimizing inter-group question overlap, and augmenting the question pool to control collusion gain below any desired level
description	The GAS is the article's core anti-collusion design for distanced online testing.
status	review
generated	by process:settle-candidates on 2026-10-26
trust	unverified — no one has confirmed this page's content
sources	1 — mengzhou-li-2021

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