Is your task really 2AFC?

Probably not.

You probably know that 2AFC stands for “two-alternative forced choice.” However, you may not know that this means 2AFC tasks involve the presentation of two stimuli on each trial!

Let’s say that you want your participants to distinguish between faces and houses. On each trial, you present an image and ask participants to decide if it’s a face or a house. This is a fantastic design, just not a 2AFC task. Rather, it’s a discrimination task though some psychophysicists would also call it a detection task. Likewise if your subjects are judging the direction of motion in a random dot kinematogram, or if they are deciding whether an item is old or new, or whenever they are judging a single stimulus per trial.

Example of tasks that are and aren't 2AFC.
Example of tasks that are and aren’t 2AFC.

So, what are 2AFC tasks? There are two variants: spatial 2AFC and temporal 2AFC (also called two-interval forced choice, or 2IFC). In the spatial 2AFC, on each trial you’d present a face and a house in different locations (usually left and right of fixation). In 2IFC tasks, on each trial you’d present first the face and then the house (or vice versa) in the same spatial location. In both cases, participants’ task is to determine which of the two stimuli was the face.

Despite my best efforts, I haven’t been able to find out how the confusion around what a 2AFC task is emerged. According to this Wikipedia page, Fechner developed 2AFC back in the 19th century. Confusing 1-stimulus discrimination tasks with 2AFC seems to have already been the rule by the middle of the 20th century (and perhaps much earlier). It appears to be the rule now, at least outside of the vision science world.

What is so special about 2AFC tasks? They are supposed to be ‘unbiased.’ In other words, subjects are often assumed not to have much of a bias between left/right or first/second interval decisions. Such lack of bias is great for measuring performance and generally makes distributional assumptions (like assuming Gaussians in SDT) unnecessary. The problem is this assumption has been shown to be empirically false (Yeshurun, Carrasco, & Maloney, 2008). Yeshurun and colleagues even recommend against using 2IFC tasks altogether.

A note on comparing 1-stimulus discrimination and 2AFC tasks: because 2AFC tasks present two stimuli on each trial, participants have more information to work with and thus are expected to perform better. In fact, their signal-to-noise ratio (d’) should be exactly √2 higher in 2AFC tasks. Empirically, however, it has been found to be both substantially higher or substantially lower. Math is prettier than actual human performance!

In the end, perhaps it’s not a bad thing if you’ve used a simple discrimination task in your experiment. Just don’t call it 2AFC.

Confidence leak

What determines if you are confident in your decisions? In the perceptual domain, the standard answer to this question is usually “signal strength.” The idea is that we are more confident for larger, brighter, less noisy stimuli. Beyond that, however, our previous decisions also have an impact: after making a decision with high confidence, we are more likely to be very confident again. This is an example of the ubiquitous sequential effect that turns up everywhere in perception.

But what if your previous decision was for a different task altogether? Does your confidence on a completely different task still influence you when you are deciding on your current task?

In a paper that just came out in Psychological Science (data and code here), we show that sequential effects of confidence appear even between different tasks. We called this effect confidence leak.

The task used in 2 of the 5 experiments.

Our design was simple: present 40 letters (Xs and Os) in different colors (red or blue), and then ask participants to judge whether there are more Xs or Os, and whether there are more blue or red letters. Even though the processing of letter form and color tend to be separated in the visual system, we find that, on a trial-by-trial basis, confidence on one task predicts the confidence on the other.

A number of analyses and control experiments confirmed that the effect is not due to trivial reasons such as motor priming, attentional fluctuations, or confidence drifts. What really convinced us, though, was our causal manipulation. We increased the difficulty of one of the tasks, so that confidence decreased. Lo and behold, we found a corresponding decrease in the confidence in the other task. In other words, the lowered confidence in the first task leaked into the second task.

Why does confidence leak happen? We think that people believe that the environment is consistent (autocorrelated) and thus an easy trial ought to be followed by another easy trial, even if the tasks are different. We constructed a Bayesian model that demonstrates how this assumption would naturally produce the observed confidence leak.

Who are the people that show more of this (suboptimal) confidence leak? In a separate experiment, we found that people with lower gray matter volume in the anterior prefrontal cortex (aPFC) exhibited higher confidence leak and so did people with lower metacognitive sensitivity.

It is interesting to consider the limits of the phenomenon. Would confidence leak appear for tasks that involve different modalities (e.g., vision and audition)? Would it happen for memory or general knowledge tasks? If our model is correct, as long as people are willing to assume that the difficulty of different tasks is correlated in the natural environment, confidence leak would invariably follow.