Assessing sensitivity in a multidimensional space: some problems and a definition of a general d'

Area of Science:

• Psychology
• Cognitive Science
• Signal Detection Theory

Background:

• Multivariate signal detection theory (SDT) is used to assess perceptual representations.
• Previous methods, like the diagonal d' test, infer perceptual separability from response probabilities.
• Existing models attempt to link perceptual independence with dimensional orthogonality.

Purpose of the Study:

• To formally define a new sensitivity measure, d'g, for multivariate stimuli.
• To analyze the shortcomings of the diagonal d' test.
• To evaluate the assumptions linking perceptual independence and dimensional orthogonality.

Main Methods:

• Formal definition of the d'g sensitivity measure.
• Analysis of existing tests based on multidimensional SDT.
• Comparison of d'g with Mahalanobis distance.

Main Results:

• The proposed d'g measure reveals shortcomings in the diagonal d' test.
• Assumptions equating perceptual independence to dimensional orthogonality are shown to be too weak.
• d'g can be related to Mahalanobis distance under specific conditions (equal covariance matrices).

Conclusions:

• The d'g measure offers a more robust approach to assessing multivariate stimulus perception.
• Existing methods for inferring perceptual separability require re-evaluation.
• The relationship between perceptual independence and dimensional orthogonality is more complex than previously assumed.