Half-length Force Concept Inventory (HFCI)

Developed by Jing Han, Lei Bao, Li Chen, Tianfang Cai, Yuan Pi, Shaona Zhou, Yan Tu, and Kathleen Koenig

Purpose Assess the topics on the FCI in less time, with two equivalent parallel half-length versions (HFCI1 and HFCI2).
Format Pre/post, Multiple-choice
Duration 15 min
Focus Mechanics Content knowledge (forces, kinematics)
Level Intro college, High school
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Sample question from the HFCI:

HFCI Implementation and Troubleshooting Guide

Everything you need to know about implementing the HFCI in your class.

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J. Han, L. Bao, L. Chen, T. Cai, Y. Pi, S. Zhou, Y. Tu, and K. Koenig, Dividing the Force Concept Inventory into two equivalent half-length tests, Phys. Rev. ST Phys. Educ. Res. 11 (1), 010112 (2015).
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Silver Validation
This is the second highest level of research validation, corresponding to at least 5 of the validation categories below.

Research Validation Summary

Based on Research Into:

  • Student thinking

Studied Using:

  • Student interviews
  • Expert review
  • Appropriate statistical analysis

Research Conducted:

  • At multiple institutions
  • By multiple research groups
  • Peer-reviewed publication

The multiple-choice questions on the HFCI1 and HFCI2 were taken from the original FCI (v95). To create these two half-length tests, physics education researchers first hand picked questions for each shorter test. They tested the shorter tests (HFCI1 and HFCI2) using a large scale FCI data set and a computational regression process to sort through the possible combinations of the two short tests to identify the optimal construction that minimizes the total errors among the mean scores of the different tests. They also used Item Response Theory (IRT) to to estimate and compare the assessment features (difficulty, discrimination, and students' guessing parameters) of the two short tests and the FCI test. They developers found that the descriptive statistics, the total scores, score changes, and normalized gains of the two short tests provide equivalent measures of student performances and learning gains. They also found that the tests had similar assessment features. The FCI scores are slightly but consistently higher than those of the short tests. To allow direct comparisons between the half-length and full-length FCI scores, linear models have been created that relate the scores from these tests. The developers analyzed data from over 4000 university and high school students at three institutions. Results are published in two peer-reviewed publications. 


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Typical Results

Data from Han et. al 2015 containing unmatched pre- and post-test scores for 3139 students on the pretest and 2526 students on the post-test. The results show that the total scores of the two half- length tests are virtually identical; the difference is 0.09% on pretest and 0.32% on post-test. Because of the removal of several high-scoring FCI questions, the scores of the half-length tests are typically 5% lower than that of the FCI. 

The latest version of the HFCI, released in 2015, is version 1.