FrACT is based on an mAFC paradigm. So, what is “mAFC”?
“mAFC” stands for m-alternative forced-choice, where:
- m could be 2 (e.g., Vernier or oblique gratings), 4 (Tumbling E), 8 (Landolt Ring) or 10 (Letters)
- “alternative” refers to “alternative with equal standing”, where “equal” means e.g., “left/right/up/down” (largely equivalent), and not “seen/not seen”.
To decide whether I have “seen” something depends on my “psychophysical criterion”: Am I cautious, wanting to avoid errors, and only report “seen” when very certain (criterion more to the right)? Or am I bold (criterion more to the left), happily pressing “Seen”?
Equivalent alternatives can be reported whether easily seen (above threshold) or not seen (ending in “forced” pure guessing, which is accounted for in the analysis).
Background
In psychophysics, the m-alternative forced-choice (mAFC) paradigm is widely considered the gold standard for obtaining “criterion-free” measures of sensitivity. Unlike Yes/No (=Seen/Not seen) tasks, where a participant’s internal “criterion” or “bias” (see above) can shift the results, mAFC forces a choice between equivalent alternatives, effectively neutralizing the decision-making strategy. The criterion is an individual “character” trait, varies between individuals and over time, and is affected by learning, motivation or the “exaggeration effect”.
Sources
- Green & Swets (1966) Signal Detection Theory and Psychophysics. New York: Wiley (ISBN 13: 978-0932146236)
This is the “bible” of signal detection theory and goes back a long way. Decades ago, I only read short parts of it. They prove that in an mAFC task, the observer’s goal is simply to choose the alternative with the highest sensory evidence. Since the signal is equally likely to appear as any of the m alternatives, there is no “optimal” bias toward one alternative over another. They derive the relationship between the proportion of correct responses P(C) and the sensitivity index d’. - Kingdom & Prins (2016) Psychophysics: A Practical Introduction. Academic Press (ISBN-13: 978-0124071568)
A less ancient source. They explain that because the stimulus level corresponding to a specific performance level (like 75% correct for a 4-AFC) is tied to the d’ value, the resulting threshold is a pure measure of sensory capacity and NOT influenced by expectation/motivation like it would be in a yes/no (or seen/not seen) design.
Simplified Summary: Why an mAFC task is “criterion-free”
| Feature | Yes/No Task | mAFC Task |
|---|---|---|
| Decision Rule | Is evidence > C? | Which alternative has maximal evidence? |
| Bias Type | From liberal/bold to conservative/cautious | Positional in space or time (left/right, first/last) |
| Threshold | Influenced by expectation, motivation, and more | Reflects sensory limit |
| Calculated Metric | d’ (d-prime) and C (Criterion) | d’ (criterion is typically assumed to be 0) |
Misunderstandings re “forced choice”
Recently, the “forced choice” term has been muddied by misunderstandings. This was caused by referring to an mAFC too briefly as a “forced choice” paradigm, without qualifying it with “of equivalent alternatives” (guilty of this myself). Anyone unaware of the old literature might understand the term “forced choice” literally, and might easily refer to a “yes/no” or “seen/not seen” paradigm as “forced choice”, because participants have to press either a “seen” or “not seen” button. For the latter, however, the so-called “psychometric criterion” confounds the threshold unless a d’ analysis is performed.
An example is the full‑field stimulus test (FST): While it might be designed as “press button YES if seen, NO if not seen”, this would not be a 2AFC. But it can be converted into one, for instance like so: Set up two time intervals, indicated by tones, and then ask if the stimulus appeared in the first or second interval (everything, of course, block-randomised).
Note: LLMs aided in researching and composing this text. Still: all errors are mine.