# Glossary

## Terminology

accuracy

An overall measure of performance defined as the proportion of all responses that are correct responses as opposed to error responses.

base rate (prevalence)

The proportion of all events that are of a specified type. For a signal detection task, the proportion of all trials for which the signal is present.

bias (response bias)

The tendency to make one response (either ‘present’ or ‘absent’) more than the other in a signal detection task.

block

A sequence of trials in a psychology experiment. A typical design of such an experiment is to have one or more experimental sessions, each of which consist of one or more blocks, each of which consist of many trials. Some factors may be varied within each block, while others may be varied across blocks.

c

A measure of response bias in signal detection theory. It is defined as the distance of the decision threshold from the neutral point exactly half way between the noise distribution and the signal-plus-noise distribution. It may take on any value between negative infinity and infinity, with negative values indicating a threshold below the neutral point, and positive values indicating a threshold above the neutral point.

coherent motion

Motion in the same direction by multiple objects in a display. In a random dot kinematogram, it refers to dots moving in the same direction in a stimulus.

conservative bias

A tendency to respond that a signal is ‘absent’ more often than that it is ‘present’. In our formulation of signal detection theory, this would be represented by a positive value for the parameter c.

correct

The outcome that occurs when the response that is made is the one that should have been made given the definition of the task. In a signal detection task, this occurs when the signal is present and the participant responds ‘present’ or the signal is absent and they respond ‘absent’.

correct rejection (true negative)

The outcome that occurs in a signal detection task when the signal is absent, and the participant correctly responds ‘absent’.

d′

A measure of sensitivity in signal detection theory. It is defined as the distance between the mean of the noise distribution and the signal-plus-noise distribution. It may take on any value between negative infinity and infinity, with negative values indicating the signal-plus-noise distribution is below the noise distribution, and positive values indicating the signal-plus-noise distribution is above the noise distribution.

d′etectable

The explorable explanation of signal detection theory that this glossary is a part of. The word is a portmanteau of ‘detection’ and ‘explorable’. The stylization of the ‘d’ as d′ and the ‘c’ as c is a nod to the two key parameters of signal detection theory. The author takes great joy in this sort of thing.

decision

The selection of an action (or lack thereof) in a particular circumstance. Or even more broadly, “a commitment to a course of action that is intended to yield results that are satisfying for specified individuals” (Yates & Tschirhart, 2006). In a signal detection task, it is the process that leads on each trial from the stimulus, which might have a signal present or absent, to a response, which might be ‘present’ or ‘absent’, or to no response.

difficulty

How hard it is to do something. In a signal detection task, it refers to how hard it is to distinguish whether a signal is present or absent. The higher the difficulty, the lower the sensitivity, and vice versa.

error

The outcome that occurs when the response that is made is not the one that should have been made given the definition of the task. In a signal detection task, this occurs when the signal is present and the participant responds ‘absent’ or the signal is absent and they respond ‘present’.

evidence

In the context of signal detection theory, it is the value obtained by measuring whether or not a signal is present. This quantity is sampled from a probability distribution and is then compared to a threshold in order to determine the response.

false alarm (false positive or type I error)

The outcome that occurs in a signal detection task when the signal is absent, and the participant erroneously responds ‘present’.

false alarm rate (FAR or false positive rate)

A summary measure of performance defined as the proportion of trials where the signal was absent where the participant incorrectly responded ‘present’ as opposed to ‘absent’.

false omission rate (FOR)

A summary measure of performance defined as the proportion of trials where the participant responded ‘absent’ on which the signal was actually present as opposed to absent.

fixation

A symbol presented to a participant on a display to act as a target for their attention before a substantive cue or stimulus is presented. Often used before the start of a trial to help prepare the participant.

histogram

A bar chart where the height of each bar represents the count of instances that fall in a certain range along the x-axis. It can function as a rough approximation of the distribution from which the instances have been drawn.

hit (true positive)

The outcome that occurs in a signal detection task when the signal is present, and the participant correctly responds ‘present’.

hit rate (HR or true positive rate)

A summary measure of performance defined as the proportion of trials where the signal was present where the participant correctly responded ‘present’ as opposed to ‘absent’.

inter-trial interval (ITI)

The time between the end of one trial and the start of the next trial in a block of trials in a psychology experiment.

incentive

A reward or punishment that occurs due to the outcome of an action.

iso-bias curve

A curve in ROC space that represents a set of points that all have the same value of bias.

iso-sensitivity curve

A curve in ROC space that represents a set of points that all have the same value of sensitivity.

liberal bias

A bias towards responding ‘present’ over ‘absent’. In our formulation of signal detection theory, it means that c is negative.

marginal measure (marginal)

In a table of outcomes, a measure that depends on the values of an entire row or column, and is typically displayed along the edge (i.e. margin) of that table.

measurement

The process of acquiring evidence. In a signal detection theory task, it is the process of acquiring evidence about the presence or absence of a signal.

miss (false negative or type II error)

The outcome that occurs in a signal detection task when the signal is present, and the participant erroneously responds ‘absent’.

model

In this context, a quantitative specification, based on a particular theory, of how stimulus and response are linked via an intervening set of cognitive processes. Whereas a theory tends to be a more general explanation of a cognitive process, a model is a specific application to a particular situation or task. Signal detection theory can be applied to model a wide variety of different signal detection tasks. It is specified as a mathematical model, as opposed to a symbolic or computational model. Note that the distinctions between theories and models, and between mathematical and computational models, are fuzzy, contested, and philosophically charged.

neutral point

In signal detection theory, it refers to the level of evidence at which we can place the threshold so that we are equally likely to respond ‘absent’ or ‘present’. In the case of equal variance, this is where the noise distribution and the signal-plus-noise distribution intersect.

noise

Stimuli other than the stimulus of interest (i.e. the signal). This can refer to random, unstructured stimulation, but it can also mean any stimulation that is not the stimulus of interest, even if it is structured and/or meaningful. It can also refer to sources of variance within the system itself that limit the ability to distinguish cases where the signal is present from those where it is absent.

noise distribution

The probability distribution from which a measurement of evidence is drawn on trials when the signal is absent.

normal (Gaussian)

An oft-used probability distribution with a bell-shaped curve, that tends to arise from natural processes that are composed of many sub-processes.

outcome

The result of taking a particular action in a particular situation. In the context of signal detection theory, it typically refers to the four possible combinations of stimulus (present or absent) and response (‘present’ or ‘absent’): hits, misses, correct rejections, and false alarms.

positive predictive value (PPV or precision)

A summary measure of performance defined as the proportion of trials where the participant responded ‘present’ on which the signal was actually present as opposed to absent.

probability distribution

A function specifying the probabilities of occurrence of a set or range of possible events. In signal detection theory, a distribution is used to describe the evidence measured by observing the stimulus on each trial.

random motion

Motion in different, unrelated directions by multiple objects in a display. In a random dot kinematogram, it refers to dots for which the direction of motion of each dot was independently selected from a uniform distribution across all possible directions.

random-dot kinematogram (RDK)

A stimulus consisting of lots of small identically shaped and colored dots moving on a display. The starting locations of the dots is selected randomly, so there is no intended structure or features in the dots when they are still.

receiver/relative operating characteristic space (ROC space)

A two-dimensional graph with false alarm rate plotted on the x-axis, and hit rate plotted on the y-axis. It is a standard way to represent performance in signal detection tasks.

response

An action taken as a result of the presentation of a stimulus. In a signal detection task, it is typically either ‘present’ or ‘absent’ to indicate whether the participant thinks the signal was present or absent.

σ

A measure of unequal variance in signal detection theory. It is defined as the relative variance of the signal-plus-noise distribution compared to the noise distribution. It may take on any value between zero and infinity, with values smaller than one indicating the signal-plus-noise distribution has a smaller variance than the noise distribution, a value of one indicating the distributions have equal variance and values greater than one indicating the signal-plus-noise distribution has a greater variance than the noise distribution.

sensitivity

The ability to distinguish whether a signal is present or absent.

signal

The stimulus of interest that a participant is trying to detect.

signal-plus-noise distribution

The probability distribution from which a measurement of evidence is drawn on trials when the signal is present. Note that it’s name emphasizes that there is always noise, even when the signal is present.

signal detection theory (SDT)

A theory, explained throughout this explorable explanation, of how individuals decide whether to respond ‘present’ or ‘absent’ in signal detection tasks where a signal is either present or absent.

stimulus

In general, anything that causes a sensory and/or perceptual response. In the context of a signal detection experiment, the combination of signal and/or noise presented to the participant on each trial.

What a participant does in a typical cognitive psychology experiment. It typically consists of one or more sessions, each consisting of one or more blocks, each consisting of many trials. On each trial, there is typically a sequence of events, including one or more stimuli, and one or more responses.

theory

In this context, a proposed explanation for how one or more cognitive processes work. Theories can be more or less precise in their specification, which can make them hard to evaluate. One approach to address this is to implement quantitative models based on the theory. (See the entry for model for more discussion.)

threshold

In signal detection theory, a particular level of evidence used as a cutoff. If a measurement of evidence is greater than this level, then a ‘present’ response is made, and if the evidence is less than this level, then an ‘absent’ response is made.

trial

A single unit in an experimental task. In a signal detection task, this typically consists of a stimulus with a signal present or absent, followed by a response of either ‘present’ or ‘absent’, possibly followed by feedback such as the outcome and/or incentive. Within a block, the next trial then starts after an inter-trial interval.

variance

The width of the noise distribution and signal-plus-noise distribution. We can assume that these two variances are equal, as in equal variance SDT, or we can allow for the possibility that they are unequal, as in unequal variance SDT.

z-transformation

The result of applying the inverse cumulative distribution function of the normal distribution.

zROC space

A graph of ROC space that plots the x- and y-axes using z-transformed false alarm rate and hit rate.