# Multidimensional Models of Perception and Cognition

By F. Gregory Ashby | Go to book overview

appear the weakest of the four operational tasks discussed. The assumptions of the Restricted Classification Task are not easily tested, and, even if satisfied, the task is too susceptible to extraneous effects (e.g., stimulus, task, and observer). The Redundancy Task is also susceptible to extraneous variables, such as the subject's level of experience with the task. In addition, the ideal observer frequently violates decisional separability in the redundancy condition, thereby invalidating the Redundancy Task as a test of perceptual separability. The assumptions of Direct Dissimilarity Scaling are more easily tested, but have weak empirical validity (e.g., Tversky, 1977). Despite this fact, consistency, a relation that can be tested on dissimilarity data, is related to perceptual separability and decisional separability (see Proposition 7.2). Of the four operational tests reviewed in this chapter, the Filtering Task provides the best test of perceptual separability, because the ideal observer frequently utilizes decisional separability in the filtering condition.

Data from an identification task provide the most rigorous tests of perceptual separability because converging evidence from several quantitative tests (e.g., marginal response invariance or transmitted information) can be obtained. In addition, the parameters of each perceptual distribution can be estimated, and fits between general and more constrained models can be compared.

APPENDIX A

Proof of Proposition 7.1: The first several steps of the proof are identical to those of Ashby and Perrin ( 1988, Theorem 1) and will not be repeated. Begin with their equation stating

s(A, B) =Φ{-1/2[μA - μB)′∑-1(μA - μB)]1/2}, (A1)

where Φ represents the standard normal cumulative distribution function. Now, since = σr2I, s(A, B) = Φ(-dAB/2), where dAB is the Euclidean distance between means.

Denote the monotonically decreasing function that relates dissimilarity and similarity by g. Then

(A2)

As dAB increases, Φ(-dAB/2) decreases, so g[Φ(-dAB/2)] is increasing, which proves the theorem.

Proof of Proposition 7.2: For simplicity, I derive only Equation 8. The proof for Equation 9 follows analogously. If components A and B are perceptually separable, then

-179-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

#### Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.
Citations (0)
Some of your citations are legacy items.
Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
• Saved book/article
• Highlights
• Quotes/citations
• Notes
• Bookmarks
Notes

#### Cited page

Style
Citations are available only to our active members.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited page

Multidimensional Models of Perception and Cognition

Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
/ 526

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.