What is linear on the fly testing?

Linear on the fly testing (LOFT) is an approach to delivering assessments to examinees.  In general, there are two families of test delivery.  Static approaches deliver the same test form or forms to everyone; this is the ubiquitous and traditional “linear” method of testing.  Algorithmic approaches deliver the test to each examinee based on a computer algorithm; this includes LOFT, computerized adaptive testing (CAT), and multistage testing (MST).

What is linear on the fly testing?

The purpose of linear on the fly testing is to give every an examinee a linear form that is uniquely created for them – but each one is create to be psychometrically equivalent to all others to ensure fairness.  For example, we might have a pool of 200 items, and every person only gets 100, but that 100 is balanced for each person.  This can be done be ensuring content and/or statistical equivalency, as well ancillary metadata such as item types or cognitive level.

Content Equivalence

This portion is relatively straightforward.  If your test blueprint calls for 20 items in each of 5 domains, for a total of 100 items, then each form administered to examinees should follow this blueprint.  Sometimes the content blueprint might go 2 or even 3 levels deep.

Statistical Equivalence

There are, of course, two predominant psychometric paradigms: classical test theory and item response theory.  With CTT, forms can easily be built to have an equivalent P value, and therefore expected mean score.  If point-biserial statistics are available for each item, you can also design the algorithm to design forms that have the same standard deviation and reliability.  With item response theory, the typical approach is to design forms to have the same test information function, or inversely, conditional standard error of measurement function.  To learn more about how these are implemented, download our IRT Scoring Spreadsheet or Classical Form Assembly Tool.

Implementing LOFT

LOFT is typically implemented by publishing a pool of items with an algorithm to select subsets that meet the requirements.  Therefore, you need a psychometrically sophisticated testing engine that stores the necessary statistics and item metadata, lets you define a pool of items, specify the relevant options such as target statistics and blueprints, and deliver the test in a secure manner.  Very few testing platforms can implement a quality LOFT assessment.

Why all this?

It certainly is not easy to build a strong item bank, design LOFT pools, and develop a complex algorithm that meets content and statistical balancing needs.  So why would an organization use linear on the fly testing?  Well, it is much more secure than having a few linear forms.  Since everyone receives a unique form, it is impossible for word to get out about what the first questions on the test are.  And of course, we could simply perform a random selection of 100 items from a pool of 200, but that would be potentially unfair.  Using LOFT will ensure the test remains fair and defensible.

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Nathan Thompson, PhD

Chief Product Officer at ASC
I am a psychometrician, software developer, author, and researcher, currently serving as Chief Product Officer for Assessment Systems Corporation (ASC). My mission is to elevate the profession of psychometrics by using software to automate the menial stuff like job analysis and Angoff studies, so we can focus on more innovative work. My core goal is to improve assessment throughout the world. I was originally trained as a psychometrician, doing an undergrad at Luther College in Math/Psych/Latin and then a PhD in Psychometrics at the University of Minnesota. I then worked multiple roles in the testing industry, including item writer, test development manager, essay test marker, consulting psychometrician, software developer, project manager, and business leader. Research and innovation are incredibly important to me. In addition to my own research, I am cofounder and Membership Director at the International Association for Computerized Adaptive Testing, You can often find me at other important conferences like ATP, ICE, CLEAR, and NCME. I've published many papers and presentations, and my favorite remains http://pareonline.net/getvn.asp?v=16&n=1.
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