Cue validity is the conditional probability

Conditional probability

In probability theory, the "conditional probability of A given B" is the probability of A if B is known to occur. It is commonly notated P, and sometimes P_B. P can be visualised as the probability of event A when the sample space is restricted to event B...

 that an object falls in a particular category given a particular feature or cue. The term was popularized by , and especially by Eleanor Rosch

Eleanor Rosch

Eleanor Rosch is a professor of psychology at the University of California, Berkeley, specializing in cognitive psychology and primarily known for her work on categorization, in particular her prototype theory, which has profoundly influenced the field of cognitive psychology...

 in her investigations of the acquisition of so-called basic categories .

Definition of cue validity

Formally, the cue validity of a feature with respect to category has been defined in the following ways:

• As the conditional probability ; see , , .
• As the deviation of the conditional probability from the category base rate, ; see , .
• As a function of the linear correlation; see , , , .
• Other definitions; see , .

For the definitions based on probability, a high cue validity for a given feature means that the feature or attribute is more diagnostic of the class membership than a feature with low cue validity. Thus, a high-cue validity feature is one which conveys more information about the category or class variable, and may thus be considered as more useful for identifying objects as belonging to that category. Thus, high cue validity expresses high feature informativeness. For the definitions based on linear correlation, the expression of "informativeness" captured by the cue validity measure is not the full expression of the feature's informativeness (as in mutual information

Mutual information

In probability theory and information theory, the mutual information of two random variables is a quantity that measures the mutual dependence of the two random variables...

, for example), but only that portion of its informativeness that is expressed in a linear relationship. For some purposes, a bilateral measure such as the mutual information

Mutual information

In probability theory and information theory, the mutual information of two random variables is a quantity that measures the mutual dependence of the two random variables...

 or category utility

Category utility

Category utility is a measure of "category goodness" defined in and . It was intended to supersede more limited measures of category goodness such as "cue validity" and "collocation index"...

 is more appropriate than the cue validity.

Examples

As an example, let us consider the domain of "numbers" and allow that every number has an attribute (i.e., a cue) named "is_positive_integer", which we call , and which adopts the value 1 if the number is actually a positive integer

Integer

The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

. Then we can inquire what the validity of this cue is with regard to the following classes: {rational number, irrational number, even integer}:

• If we know that a number is a positive integer we know that it is a rational number
  Rational number
  In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...
  
  . Thus, , the cue validity for is_positive_integer as a cue for the category rational number is 1.
• If we know that a number is a positive integer then we know that it is not an irrational number
  Irrational number
  In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number....
  
  . Thus, , the cue validity for is_positive_integer as a cue for the category irrational number is 0.
• If we know only that a number is a positive integer, then its chances of being even or odd are 50-50 (there being the same number of even and odd integers). Thus, , the cue validity for is_positive_integer as a cue for the category even integer is 0.5, meaning that the attribute is_positive_integer is entirely uninformative about the number's membership in the class even integer.

In perception

Perception

Perception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...

, "cue validity" is often short for ecological validity

Ecological validity (perception)

The ecological validity of a sensory cue in perception is the correlation between the cue and a property of the world . For example, the color of a banana is a cue that indicates whether the banana is ripe...

of a perceptual cue, and is defined as a correlation rather than a probability (see above). In this definition, an uninformative perceptual cue has an ecological validity of 0 rather than 0.5.

Use of the cue validity

In much of the work on modeling human category learning, there has been the assumption made (and sometimes validated) that attentional weighting tracks the cue validity, or tracks some related measure of feature informativeness. This would imply that attributes are differently weighted by the perceptual system; informative or high-cue validity attributes being weighted more heavily, while uninformative or low-cue validity attributes are weighted more lightly or ignored altogether (see, e.g., Navarro 1998).