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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
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Decision-variable correlation.

Stephen Sebastian1, Wilson S Geisler1

  • 1Center for Perceptual Systems and Department of Psychology, University of Texas at Austin, Austin, TX, USA.

Journal of Vision
|April 4, 2018
PubMed
Summary

This study extends signal-detection theory for identification tasks, introducing decision-variable correlations (DVCs) to compare subjects and models. Findings reveal DVCs relate to ideal observer efficiency and vary with target contrast and presence.

Area of Science:

  • Cognitive Science
  • Psychophysics
  • Computational Neuroscience

Background:

  • Signal-detection theory (SDT) is a foundational framework for understanding perception and decision-making.
  • Existing SDT models often lack methods to directly compare subject performance with theoretical models or characterize inter-subject variability.
  • Two-alternative identification tasks are common in research but require robust analytical tools for detailed performance assessment.

Purpose of the Study:

  • To extend the signal-detection theory framework to accommodate joint performance analysis between subjects and models.
  • To introduce and define decision-variable correlations (DVCs) as fundamental quantities for characterizing joint performance.
  • To provide a versatile framework for testing computational models and assessing individual differences in perceptual and cognitive studies.

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Main Methods:

  • Developed an extended SDT framework incorporating decision-variable correlations (DVCs).
  • Applied the framework to a two-alternative identification task involving the detection of a Gaussian target in white noise.
  • Analyzed joint performance by quantifying discriminability (d'), decision criteria, and DVCs for different stimulus categories.

Main Results:

  • Subjects' DVCs were found to approximate the square root of their efficiency relative to an ideal observer, aligning with predictions from certain models.
  • Between-subjects and within-subject DVCs demonstrated an increase with target contrast.
  • DVCs were consistently higher for target-present trials compared to target-absent trials, challenging numerous existing models.

Conclusions:

  • The extended SDT framework with DVCs offers a powerful tool for model testing and understanding individual differences in perception.
  • The observed relationship between DVCs and ideal observer efficiency provides valuable insights into the mechanisms of human visual search.
  • Findings regarding the modulation of DVCs by target contrast and presence necessitate refinement of current computational models of perceptual decision-making.