Two-alternative forced choice

Two-alternative forced choice (2AFC) is a method for measuring the sensitivity of a person or animal to some particular sensory input, stimulus, through that observer's pattern of choices and response times to two versions of the sensory input.

For example, to determine a person's sensitivity to dim light, the observer would be presented with a series of trials in which a dim light was randomly either in the top or bottom of the display.

Both options can be presented concurrently (as in the above example) or sequentially in two intervals (also known as two-interval forced choice, 2IFC).

For example, to determine sensitivity to a dim light in a two-interval forced choice procedure, an observer could be presented with series of trials comprising two sub-trials (intervals) in which the dim light is presented randomly in the first or the second interval.

The term 2AFC is sometimes used to describe a task in which an observer is presented with a single stimulus and must choose between one of two alternatives.

2AFC is a method of psychophysics developed by Gustav Theodor Fechner.

There are various manipulations in the design of the task, engineered to test specific behavioral dynamics of choice.

[2] In this design there is an arrow that cues which stimulus (location) to attend to.

The person then has to make a response between the two stimuli (locations) when prompted.

[3] A 2AFC task has also been designed to test decision making and the interaction of reward and probability learning in monkeys.

A response can then be made in the form of a saccade to the left or to the right stimulus.

The amount of juice reward is then varied to modulate choice.

In a different application, the 2AFC is designed to test discrimination of motion perception.

It is possible to introduce biases in decision making in the 2AFC task.

[4][7] Introducing biases in the 2AFC task is used to modulate decision making and examine the underlying processes.

The 2AFC task has yielded consistent behavioral results on decision-making, which lead to the development of theoretical and computational models of the dynamics and results of decision-making.

A common model is to assume that the stimuli came from normal distributions

Under this normal model, the optimal decision strategy (of the ideal observer) is to decide which of two bivariate normal distributions is more likely to produce the tuple

[18] The probability of error with this ideal decision strategy is given by the generalized chi-square distribution:

This model can also extend to the cases when each of the two stimuli is itself a multivariate normal vector, and also to the situations when the two categories have different prior probabilities, or the decisions are biased due to different values attached to the possible outcomes.

There are typically three assumptions made by computational models using the 2AFC:i) evidence favoring each alternative is integrated over time; ii) the process is subject to random fluctuations; and iii) the decision is made when sufficient evidence has accumulated favoring one alternative over the other.It is typically assumed that the difference in evidence favoring each alternative is the quantity tracked over time and that which ultimately informs the decision; however, evidence for different alternatives could be tracked separately.

As the sensory input which constitutes the evidence is noisy, the accumulation to the threshold is stochastic rather than deterministic – this gives rise to the directed random-walk-like behavior.

The DDM has been shown to describe accuracy and reaction times in human data for 2AFC tasks.

A is positive if the correct response is represented by the upper threshold, and negative if the lower.

from separate distributions – this provides a better fit to experimental data for both accuracy and reaction times.

[7] The race model is not mathematically reducible to the DDM,[7] and hence cannot be used to implement an optimal decision procedure.

, and increases based on the current values of the other two accumulators, at a rate modulated by

In the parietal lobe, lateral intraparietal cortex (LIP) neuron firing rate in monkeys predicted the choice response of direction of motion suggesting this area is involved in decision making in the 2AFC.

[4][24][26] Neural data recorded from LIP neurons in rhesus monkeys supports the DDM, as firing rates for the direction selective neuronal populations sensitive to the two directions used in the 2AFC task increase firing rates at stimulus onset, and average activity in the neuronal populations is biased in the direction of the correct response.

[24][27][28][29] In addition, it appears that a fixed threshold of neuronal spiking rate is used as the decision boundary for each 2AFC task.

Example of a random dot kinetogram as used in a 2AFC task.
The optimal strategy in a 2AFC task for univariate normal stimuli from categories and is to classify between the two joint bivariate normal distributions and . [ 18 ] The probability of the correct choice is 0.74 here.
Example of six evidence accumulation sequences from an unbiased (100% noise) source. The dotted lines indicate the thresholds for decision making for each of the two alternatives.
Example of ten evidence accumulation sequences for the DDM, where the true result is assigned to the upper threshold. Due to the addition of noise, two sequences have produced an inaccurate decision.